Daily Papers

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods, such as direct logit attribution (DLA) and sparse autoencoders (SAEs), provide restricted insight due to limitations such as the model's output vocabulary or unclear feature names. This work introduces Hyperdimensional Probe, a novel paradigm for decoding information from the LLM vector space. It combines ideas from symbolic representations and neural probing to project the model's residual stream into interpretable concepts via Vector Symbolic Architectures (VSAs). This probe combines the strengths of SAEs and conventional probes while overcoming their key limitations. We validate our decoding paradigm with controlled input-completion tasks, probing the model's final state before next-token prediction on inputs spanning syntactic pattern recognition, key-value associations, and abstract inference. We further assess it in a question-answering setting, examining the state of the model both before and after text generation. Our experiments show that our probe reliably extracts meaningful concepts across varied LLMs, embedding sizes, and input domains, also helping identify LLM failures. Our work advances information decoding in LLM vector space, enabling extracting more informative, interpretable, and structured features from neural representations.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

We present HyperSeg, a hyperdimensional computing (HDC) approach to unsupervised dialogue topic segmentation. HDC is a class of vector symbolic architectures that leverages the probabilistic orthogonality of randomly drawn vectors at extremely high dimensions (typically over 10,000). HDC generates rich token representations through its low-cost initialization of many unrelated vectors. This is especially beneficial in topic segmentation, which often operates as a resource-constrained pre-processing step for downstream transcript understanding tasks. HyperSeg outperforms the current state-of-the-art in 4 out of 5 segmentation benchmarks -- even when baselines are given partial access to the ground truth -- and is 10 times faster on average. We show that HyperSeg also improves downstream summarization accuracy. With HyperSeg, we demonstrate the viability of HDC in a major language task. We open-source HyperSeg to provide a strong baseline for unsupervised topic segmentation.

We present the COGnitive Neural GENerative system (CogNGen), a cognitive architecture that combines two neurobiologically-plausible, computational models: predictive processing and hyperdimensional/vector-symbolic models. We draw inspiration from architectures such as ACT-R and Spaun/Nengo. CogNGen is in broad agreement with these, providing a level of detail between ACT-R's high-level symbolic description of human cognition and Spaun's low-level neurobiological description, furthermore creating the groundwork for designing agents that learn continually from diverse tasks and model human performance at larger scales than what is possible with current systems. We test CogNGen on four maze-learning tasks, including those that test memory and planning, and find that CogNGen matches performance of deep reinforcement learning models and exceeds on a task designed to test memory.

Existing work in language grounding typically study single environments. How do we build unified models that apply across multiple environments? We propose the multi-environment Symbolic Interactive Language Grounding benchmark (SILG), which unifies a collection of diverse grounded language learning environments under a common interface. SILG consists of grid-world environments that require generalization to new dynamics, entities, and partially observed worlds (RTFM, Messenger, NetHack), as well as symbolic counterparts of visual worlds that require interpreting rich natural language with respect to complex scenes (ALFWorld, Touchdown). Together, these environments provide diverse grounding challenges in richness of observation space, action space, language specification, and plan complexity. In addition, we propose the first shared model architecture for RL on these environments, and evaluate recent advances such as egocentric local convolution, recurrent state-tracking, entity-centric attention, and pretrained LM using SILG. Our shared architecture achieves comparable performance to environment-specific architectures. Moreover, we find that many recent modelling advances do not result in significant gains on environments other than the one they were designed for. This highlights the need for a multi-environment benchmark. Finally, the best models significantly underperform humans on SILG, which suggests ample room for future work. We hope SILG enables the community to quickly identify new methodologies for language grounding that generalize to a diverse set of environments and their associated challenges.

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

Scalable Vector Graphics (SVGs) are central to modern design workflows, offering scaling without distortion and precise editability. However, for single object SVGs, generating multi-view consistent SVGs from a single-view input remains underexplored. We present a three stage framework that produces multi-view SVGs with geometric and color consistency from a single SVG input. First, the rasterized input is lifted to a 3D representation and rendered under target camera poses, producing multi-view images of the object. Next, we extend the temporal memory mechanism of Segment Anything 2 (SAM2) to the spatial domain, constructing a spatial memory bank that establishes part level correspondences across neighboring views, yielding cleaner and more consistent vector paths and color assignments without retraining. Finally, during the raster to vector conversion, we perform path consolidation and structural optimization to reduce redundancy while preserving boundaries and semantics. The resulting SVGs exhibit strong geometric and color consistency across views, significantly reduce redundant paths, and retain fine structural details. This work bridges generative modeling and structured vector representation, providing a scalable route to single input, object level multi-view SVG generation and supporting applications such as asset creation and semantic vector editing.

In recent years, rapid advances in computer vision have significantly improved the processing and generation of raster images. However, vector graphics, which is essential in digital design, due to its scalability and ease of editing, have been relatively understudied. Traditional vectorization techniques, which are often used in vector generation, suffer from long processing times and excessive output complexity, limiting their usability in practical applications. The advent of large language models (LLMs) has opened new possibilities for the generation, editing, and analysis of vector graphics, particularly in the SVG format, which is inherently text-based and well-suited for integration with LLMs. This paper provides a systematic review of existing LLM-based approaches for SVG processing, categorizing them into three main tasks: generation, editing, and understanding. We observe notable models such as IconShop, StrokeNUWA, and StarVector, highlighting their strengths and limitations. Furthermore, we analyze benchmark datasets designed for assessing SVG-related tasks, including SVGEditBench, VGBench, and SGP-Bench, and conduct a series of experiments to evaluate various LLMs in these domains. Our results demonstrate that for vector graphics reasoning-enhanced models outperform standard LLMs, particularly in generation and understanding tasks. Furthermore, our findings underscore the need to develop more diverse and richly annotated datasets to further improve LLM capabilities in vector graphics tasks.

Large language models (LLMs) excel at program synthesis, yet their ability to produce symbolic graphics programs (SGPs) that render into precise visual content remains underexplored. We study symbolic graphics programming, where the goal is to generate an SGP from a natural-language description. This task also serves as a lens into how LLMs understand the visual world by prompting them to generate images rendered from SGPs. Among various SGPs, our paper sticks to scalable vector graphics (SVGs). We begin by examining the extent to which LLMs can generate SGPs. To this end, we introduce SGP-GenBench, a comprehensive benchmark covering object fidelity, scene fidelity, and compositionality (attribute binding, spatial relations, numeracy). On SGP-GenBench, we discover that frontier proprietary models substantially outperform open-source models, and performance correlates well with general coding capabilities. Motivated by this gap, we aim to improve LLMs' ability to generate SGPs. We propose a reinforcement learning (RL) with verifiable rewards approach, where a format-validity gate ensures renderable SVG, and a cross-modal reward aligns text and the rendered image via strong vision encoders (e.g., SigLIP for text-image and DINO for image-image). Applied to Qwen-2.5-7B, our method substantially improves SVG generation quality and semantics, achieving performance on par with frontier systems. We further analyze training dynamics, showing that RL induces (i) finer decomposition of objects into controllable primitives and (ii) contextual details that improve scene coherence. Our results demonstrate that symbolic graphics programming offers a precise and interpretable lens on cross-modal grounding.

Vector databases manage large collections of embedding vectors. As AI applications are growing rapidly, so are the number of embeddings that need to be stored and indexed. The Faiss library is dedicated to vector similarity search, a core functionality of vector databases. Faiss is a toolkit of indexing methods and related primitives used to search, cluster, compress and transform vectors. This paper first describes the tradeoff space of vector search, then the design principles of Faiss in terms of structure, approach to optimization and interfacing. We benchmark key features of the library and discuss a few selected applications to highlight its broad applicability.

Recently, text-guided scalable vector graphics (SVG) synthesis has demonstrated significant potential in domains such as iconography and sketching. However, SVGs generated from existing Text-to-SVG methods often lack editability and exhibit deficiencies in visual quality and diversity. In this paper, we propose a novel text-guided vector graphics synthesis method to address these limitations. To enhance the editability of output SVGs, we introduce a Hierarchical Image VEctorization (HIVE) framework that operates at the semantic object level and supervises the optimization of components within the vector object. This approach facilitates the decoupling of vector graphics into distinct objects and component levels. Our proposed HIVE algorithm, informed by image segmentation priors, not only ensures a more precise representation of vector graphics but also enables fine-grained editing capabilities within vector objects. To improve the diversity of output SVGs, we present a Vectorized Particle-based Score Distillation (VPSD) approach. VPSD addresses over-saturation issues in existing methods and enhances sample diversity. A pre-trained reward model is incorporated to re-weight vector particles, improving aesthetic appeal and enabling faster convergence. Additionally, we design a novel adaptive vector primitives control strategy, which allows for the dynamic adjustment of the number of primitives, thereby enhancing the presentation of graphic details. Extensive experiments validate the effectiveness of the proposed method, demonstrating its superiority over baseline methods in terms of editability, visual quality, and diversity. We also show that our new method supports up to six distinct vector styles, capable of generating high-quality vector assets suitable for stylized vector design and poster design. Code and demo will be released at: http://ximinng.github.io/SVGDreamerV2Project/

Machine learning is a prevalent approach to tame the complexity of design space exploration for domain-specific architectures. Using ML for design space exploration poses challenges. First, it's not straightforward to identify the suitable algorithm from an increasing pool of ML methods. Second, assessing the trade-offs between performance and sample efficiency across these methods is inconclusive. Finally, lack of a holistic framework for fair, reproducible, and objective comparison across these methods hinders progress of adopting ML-aided architecture design space exploration and impedes creating repeatable artifacts. To mitigate these challenges, we introduce ArchGym, an open-source gym and easy-to-extend framework that connects diverse search algorithms to architecture simulators. To demonstrate utility, we evaluate ArchGym across multiple vanilla and domain-specific search algorithms in designing custom memory controller, deep neural network accelerators, and custom SoC for AR/VR workloads, encompassing over 21K experiments. Results suggest that with unlimited samples, ML algorithms are equally favorable to meet user-defined target specification if hyperparameters are tuned; no solution is necessarily better than another (e.g., reinforcement learning vs. Bayesian methods). We coin the term hyperparameter lottery to describe the chance for a search algorithm to find an optimal design provided meticulously selected hyperparameters. The ease of data collection and aggregation in ArchGym facilitates research in ML-aided architecture design space exploration. As a case study, we show this advantage by developing a proxy cost model with an RMSE of 0.61% that offers a 2,000-fold reduction in simulation time. Code and data for ArchGym is available at https://bit.ly/ArchGym.

Vector graphics are widely used in digital art and valued by designers for their scalability and layer-wise topological properties. However, the creation and editing of vector graphics necessitate creativity and design expertise, leading to a time-consuming process. In this paper, we propose a novel pipeline that generates high-quality customized vector graphics based on textual prompts while preserving the properties and layer-wise information of a given exemplar SVG. Our method harnesses the capabilities of large pre-trained text-to-image models. By fine-tuning the cross-attention layers of the model, we generate customized raster images guided by textual prompts. To initialize the SVG, we introduce a semantic-based path alignment method that preserves and transforms crucial paths from the exemplar SVG. Additionally, we optimize path parameters using both image-level and vector-level losses, ensuring smooth shape deformation while aligning with the customized raster image. We extensively evaluate our method using multiple metrics from vector-level, image-level, and text-level perspectives. The evaluation results demonstrate the effectiveness of our pipeline in generating diverse customizations of vector graphics with exceptional quality. The project page is https://intchous.github.io/SVGCustomization.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

Scalable Vector Graphics (SVG) is a popular vector image format that offers good support for interactivity and animation. Despite its appealing characteristics, creating custom SVG content can be challenging for users due to the steep learning curve required to understand SVG grammars or get familiar with professional editing software. Recent advancements in text-to-image generation have inspired researchers to explore vector graphics synthesis using either image-based methods (i.e., text -> raster image -> vector graphics) combining text-to-image generation models with image vectorization, or language-based methods (i.e., text -> vector graphics script) through pretrained large language models. However, these methods still suffer from limitations in terms of generation quality, diversity, and flexibility. In this paper, we introduce IconShop, a text-guided vector icon synthesis method using autoregressive transformers. The key to success of our approach is to sequentialize and tokenize SVG paths (and textual descriptions as guidance) into a uniquely decodable token sequence. With that, we are able to fully exploit the sequence learning power of autoregressive transformers, while enabling both unconditional and text-conditioned icon synthesis. Through standard training to predict the next token on a large-scale vector icon dataset accompanied by textural descriptions, the proposed IconShop consistently exhibits better icon synthesis capability than existing image-based and language-based methods both quantitatively and qualitatively. Meanwhile, we observe a dramatic improvement in generation diversity, which is validated by the objective Uniqueness and Novelty measures. More importantly, we demonstrate the flexibility of IconShop with multiple novel icon synthesis tasks, including icon editing, icon interpolation, icon semantic combination, and icon design auto-suggestion.

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Scalable Vector Graphics (SVG) offer a powerful format for representing visual designs as interpretable code. Recent advances in vision-language models (VLMs) have enabled high-quality SVG generation by framing the problem as a code generation task and leveraging large-scale pretraining. VLMs are particularly suitable for this task as they capture both global semantics and fine-grained visual patterns, while transferring knowledge across vision, natural language, and code domains. However, existing VLM approaches often struggle to produce faithful and efficient SVGs because they never observe the rendered images during training. Although differentiable rendering for autoregressive SVG code generation remains unavailable, rendered outputs can still be compared to original inputs, enabling evaluative feedback suitable for reinforcement learning (RL). We introduce RLRF(Reinforcement Learning from Rendering Feedback), an RL method that enhances SVG generation in autoregressive VLMs by leveraging feedback from rendered SVG outputs. Given an input image, the model generates SVG roll-outs that are rendered and compared to the original image to compute a reward. This visual fidelity feedback guides the model toward producing more accurate, efficient, and semantically coherent SVGs. RLRF significantly outperforms supervised fine-tuning, addressing common failure modes and enabling precise, high-quality SVG generation with strong structural understanding and generalization.

We present VecFusion, a new neural architecture that can generate vector fonts with varying topological structures and precise control point positions. Our approach is a cascaded diffusion model which consists of a raster diffusion model followed by a vector diffusion model. The raster model generates low-resolution, rasterized fonts with auxiliary control point information, capturing the global style and shape of the font, while the vector model synthesizes vector fonts conditioned on the low-resolution raster fonts from the first stage. To synthesize long and complex curves, our vector diffusion model uses a transformer architecture and a novel vector representation that enables the modeling of diverse vector geometry and the precise prediction of control points. Our experiments show that, in contrast to previous generative models for vector graphics, our new cascaded vector diffusion model generates higher quality vector fonts, with complex structures and diverse styles.

Vector search has emerged as the foundation for large-scale information retrieval and machine learning systems, with search engines like Google and Bing processing tens of thousands of queries per second on petabyte-scale document datasets by evaluating vector similarities between encoded query texts and web documents. As performance demands for vector search systems surge, accelerated hardware offers a promising solution in the post-Moore's Law era. We introduce FANNS, an end-to-end and scalable vector search framework on FPGAs. Given a user-provided recall requirement on a dataset and a hardware resource budget, FANNS automatically co-designs hardware and algorithm, subsequently generating the corresponding accelerator. The framework also supports scale-out by incorporating a hardware TCP/IP stack in the accelerator. FANNS attains up to 23.0times and 37.2times speedup compared to FPGA and CPU baselines, respectively, and demonstrates superior scalability to GPUs, achieving 5.5times and 7.6times speedup in median and 95th percentile (P95) latency within an eight-accelerator configuration. The remarkable performance of FANNS lays a robust groundwork for future FPGA integration in data centers and AI supercomputers.

Vector graphics are widely used in digital art and highly favored by designers due to their scalability and layer-wise properties. However, the process of creating and editing vector graphics requires creativity and design expertise, making it a time-consuming task. Recent advancements in text-to-vector (T2V) generation have aimed to make this process more accessible. However, existing T2V methods directly optimize control points of vector graphics paths, often resulting in intersecting or jagged paths due to the lack of geometry constraints. To overcome these limitations, we propose a novel neural path representation by designing a dual-branch Variational Autoencoder (VAE) that learns the path latent space from both sequence and image modalities. By optimizing the combination of neural paths, we can incorporate geometric constraints while preserving expressivity in generated SVGs. Furthermore, we introduce a two-stage path optimization method to improve the visual and topological quality of generated SVGs. In the first stage, a pre-trained text-to-image diffusion model guides the initial generation of complex vector graphics through the Variational Score Distillation (VSD) process. In the second stage, we refine the graphics using a layer-wise image vectorization strategy to achieve clearer elements and structure. We demonstrate the effectiveness of our method through extensive experiments and showcase various applications. The project page is https://intchous.github.io/T2V-NPR.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

In the field of computer graphics, the use of vector graphics, particularly Scalable Vector Graphics (SVG), represents a notable development from traditional pixel-based imagery. SVGs, with their XML-based format, are distinct in their ability to directly and explicitly represent visual elements such as shape, color, and path. This direct representation facilitates a more accurate and logical depiction of graphical elements, enhancing reasoning and interpretability. Recognizing the potential of SVGs, the machine learning community has introduced multiple methods for image vectorization. However, transforming images into SVG format while retaining the relational properties and context of the original scene remains a key challenge. Most vectorization methods often yield SVGs that are overly complex and not easily interpretable. In response to this challenge, we introduce our method, Simple-SVG-Generation (S2VG2). Our method focuses on producing SVGs that are both accurate and simple, aligning with human readability and understanding. With simple images, we evaluate our method with reasoning tasks together with advanced language models, the results show a clear improvement over previous SVG generation methods. We also conducted surveys for human evaluation on the readability of our generated SVGs, the results also favor our methods.

Recently, text-guided scalable vector graphics (SVGs) synthesis has shown promise in domains such as iconography and sketch. However, existing text-to-SVG generation methods lack editability and struggle with visual quality and result diversity. To address these limitations, we propose a novel text-guided vector graphics synthesis method called SVGDreamer. SVGDreamer incorporates a semantic-driven image vectorization (SIVE) process that enables the decomposition of synthesis into foreground objects and background, thereby enhancing editability. Specifically, the SIVE process introduce attention-based primitive control and an attention-mask loss function for effective control and manipulation of individual elements. Additionally, we propose a Vectorized Particle-based Score Distillation (VPSD) approach to tackle the challenges of color over-saturation, vector primitives over-smoothing, and limited result diversity in existing text-to-SVG generation methods. Furthermore, on the basis of VPSD, we introduce Reward Feedback Learning (ReFL) to accelerate VPSD convergence and improve aesthetic appeal. Extensive experiments have been conducted to validate the effectiveness of SVGDreamer, demonstrating its superiority over baseline methods in terms of editability, visual quality, and diversity.

Vector format has been popular for representing icons and sketches. It has also been famous for design purposes. Regarding image editing, research on vector graphics editing rarely exists in contrast with the raster counterpart. We considered the reason to be the lack of datasets and benchmarks. Thus, we propose SVGEditBench V2, a benchmark dataset for instruction-based SVG editing. SVGEditBench V2 comprises triplets of an original image, a ground truth image, and the editing prompt. We built the dataset by first extracting image pairs from various SVG emoji datasets. Then, we had GPT-4o to create the prompt. We found that triplets gained by this simple pipeline contain varying sorts of editing tasks. Additionally, we performed the editing tasks with existing LLMs and investigated how those current methods can perform SVG editing. Although there were some successful cases, we found that there is a massive room for improvement.

Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.

Diffusion models have shown impressive results in text-to-image synthesis. Using massive datasets of captioned images, diffusion models learn to generate raster images of highly diverse objects and scenes. However, designers frequently use vector representations of images like Scalable Vector Graphics (SVGs) for digital icons or art. Vector graphics can be scaled to any size, and are compact. We show that a text-conditioned diffusion model trained on pixel representations of images can be used to generate SVG-exportable vector graphics. We do so without access to large datasets of captioned SVGs. By optimizing a differentiable vector graphics rasterizer, our method, VectorFusion, distills abstract semantic knowledge out of a pretrained diffusion model. Inspired by recent text-to-3D work, we learn an SVG consistent with a caption using Score Distillation Sampling. To accelerate generation and improve fidelity, VectorFusion also initializes from an image sample. Experiments show greater quality than prior work, and demonstrate a range of styles including pixel art and sketches. See our project webpage at https://ajayj.com/vectorfusion .

The development of an open and free RISC-V architecture is of great interest for a wide range of areas, including high-performance computing and numerical simulation in mathematics, physics, chemistry and other problem domains. In this paper, we discuss the possibilities of accelerating computations on available RISC-V processors by improving the vectorization of several computer vision and machine learning algorithms in the widely used OpenCV library. It is shown that improved vectorization speeds up computations on existing prototypes of RISC-V devices by tens of percent.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Scalable Vector Graphics (SVG) is an important image format widely adopted in graphic design because of their resolution independence and editability. The study of generating high-quality SVG has continuously drawn attention from both designers and researchers in the AIGC community. However, existing methods either produces unstructured outputs with huge computational cost or is limited to generating monochrome icons of over-simplified structures. To produce high-quality and complex SVG, we propose OmniSVG, a unified framework that leverages pre-trained Vision-Language Models (VLMs) for end-to-end multimodal SVG generation. By parameterizing SVG commands and coordinates into discrete tokens, OmniSVG decouples structural logic from low-level geometry for efficient training while maintaining the expressiveness of complex SVG structure. To further advance the development of SVG synthesis, we introduce MMSVG-2M, a multimodal dataset with two million richly annotated SVG assets, along with a standardized evaluation protocol for conditional SVG generation tasks. Extensive experiments show that OmniSVG outperforms existing methods and demonstrates its potential for integration into professional SVG design workflows.

Vector graphics are essential in design, providing artists with a versatile medium for creating resolution-independent and highly editable visual content. Recent advancements in vision-language and diffusion models have fueled interest in text-to-vector graphics generation. However, existing approaches often suffer from over-parameterized outputs or treat the layered structure - a core feature of vector graphics - as a secondary goal, diminishing their practical use. Recognizing the importance of layered SVG representations, we propose NeuralSVG, an implicit neural representation for generating vector graphics from text prompts. Inspired by Neural Radiance Fields (NeRFs), NeuralSVG encodes the entire scene into the weights of a small MLP network, optimized using Score Distillation Sampling (SDS). To encourage a layered structure in the generated SVG, we introduce a dropout-based regularization technique that strengthens the standalone meaning of each shape. We additionally demonstrate that utilizing a neural representation provides an added benefit of inference-time control, enabling users to dynamically adapt the generated SVG based on user-provided inputs, all with a single learned representation. Through extensive qualitative and quantitative evaluations, we demonstrate that NeuralSVG outperforms existing methods in generating structured and flexible SVG.

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied, optimizations of the vectors in favour of clustering performance are not carefully considered, especially via the reduction of vector dimensionality. This paper reports our recent progress on the combination of dimensionality compression and vector quantization, proposing a Low-Rank Representation Vector Quantization (LR^2VQ) method that outperforms previous VQ algorithms in various tasks and architectures. LR^2VQ joins low-rank representation with subvector clustering to construct a new kind of building block that is directly optimized through end-to-end training over the task loss. Our proposed design pattern introduces three hyper-parameters, the number of clusters k, the size of subvectors m and the clustering dimensionality d. In our method, the compression ratio could be directly controlled by m, and the final accuracy is solely determined by d. We recognize d as a trade-off between low-rank approximation error and clustering error and carry out both theoretical analysis and experimental observations that empower the estimation of the proper d before fine-tunning. With a proper d, we evaluate LR^2VQ with ResNet-18/ResNet-50 on ImageNet classification datasets, achieving 2.8\%/1.0\% top-1 accuracy improvements over the current state-of-the-art VQ-based compression algorithms with 43times/31times compression factor.

Vector graphic documents present visual elements in a resolution free, compact format and are often seen in creative applications. In this work, we attempt to learn a generative model of vector graphic documents. We define vector graphic documents by a multi-modal set of attributes associated to a canvas and a sequence of visual elements such as shapes, images, or texts, and train variational auto-encoders to learn the representation of the documents. We collect a new dataset of design templates from an online service that features complete document structure including occluded elements. In experiments, we show that our model, named CanvasVAE, constitutes a strong baseline for generative modeling of vector graphic documents.

Engineering design operates through hierarchical abstraction from system specifications to component implementations, requiring visual understanding coupled with mathematical reasoning at each level. While Multi-modal Large Language Models (MLLMs) excel at natural image tasks, their ability to extract mathematical models from technical diagrams remains unexplored. We present CircuitSense, a comprehensive benchmark evaluating circuit understanding across this hierarchy through 8,006+ problems spanning component-level schematics to system-level block diagrams. Our benchmark uniquely examines the complete engineering workflow: Perception, Analysis, and Design, with a particular emphasis on the critical but underexplored capability of deriving symbolic equations from visual inputs. We introduce a hierarchical synthetic generation pipeline consisting of a grid-based schematic generator and a block diagram generator with auto-derived symbolic equation labels. Comprehensive evaluation of six state-of-the-art MLLMs, including both closed-source and open-source models, reveals fundamental limitations in visual-to-mathematical reasoning. Closed-source models achieve over 85\% accuracy on perception tasks involving component recognition and topology identification, yet their performance on symbolic derivation and analytical reasoning falls below 19\%, exposing a critical gap between visual parsing and symbolic reasoning. Models with stronger symbolic reasoning capabilities consistently achieve higher design task accuracy, confirming the fundamental role of mathematical understanding in circuit synthesis and establishing symbolic reasoning as the key metric for engineering competence.

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index.

A vector database is used to store high-dimensional data that cannot be characterized by traditional DBMS. Although there are not many articles describing existing or introducing new vector database architectures, the approximate nearest neighbor search problem behind vector databases has been studied for a long time, and considerable related algorithmic articles can be found in the literature. This article attempts to comprehensively review relevant algorithms to provide a general understanding of this booming research area. The basis of our framework categorises these studies by the approach of solving ANNS problem, respectively hash-based, tree-based, graph-based and quantization-based approaches. Then we present an overview of existing challenges for vector databases. Lastly, we sketch how vector databases can be combined with large language models and provide new possibilities.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

Neural architecture search (NAS) finds high performing networks for a given task. Yet the results of NAS are fairly prosaic; they did not e.g. create a shift from convolutional structures to transformers. This is not least because the search spaces in NAS often aren't diverse enough to include such transformations a priori. Instead, for NAS to provide greater potential for fundamental design shifts, we need a novel expressive search space design which is built from more fundamental operations. To this end, we introduce einspace, a search space based on a parameterised probabilistic context-free grammar. Our space is versatile, supporting architectures of various sizes and complexities, while also containing diverse network operations which allow it to model convolutions, attention components and more. It contains many existing competitive architectures, and provides flexibility for discovering new ones. Using this search space, we perform experiments to find novel architectures as well as improvements on existing ones on the diverse Unseen NAS datasets. We show that competitive architectures can be obtained by searching from scratch, and we consistently find large improvements when initialising the search with strong baselines. We believe that this work is an important advancement towards a transformative NAS paradigm where search space expressivity and strategic search initialisation play key roles.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

Unlike bitmap images, scalable vector graphics (SVG) maintain quality when scaled, frequently employed in computer vision and artistic design in the representation of SVG code. In this era of proliferating AI-powered systems, enabling AI to understand and generate SVG has become increasingly urgent. However, AI-driven SVG understanding and generation (U&G) remain significant challenges. SVG code, equivalent to a set of curves and lines controlled by floating-point parameters, demands high precision in SVG U&G. Besides, SVG generation operates under diverse conditional constraints, including textual prompts and visual references, which requires powerful multi-modal processing for condition-to-SVG transformation. Recently, the rapid growth of Multi-modal Large Language Models (MLLMs) have demonstrated capabilities to process multi-modal inputs and generate complex vector controlling parameters, suggesting the potential to address SVG U&G tasks within a unified model. To unlock MLLM's capabilities in the SVG area, we propose an SVG-centric dataset called UniSVG, comprising 525k data items, tailored for MLLM training and evaluation. To our best knowledge, it is the first comprehensive dataset designed for unified SVG generation (from textual prompts and images) and SVG understanding (color, category, usage, etc.). As expected, learning on the proposed dataset boosts open-source MLLMs' performance on various SVG U&G tasks, surpassing SOTA close-source MLLMs like GPT-4V. We release dataset, benchmark, weights, codes and experiment details on https://ryanlijinke.github.io/.

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available.

The unprecedented advancements in Large Language Models (LLMs) have profoundly impacted natural language processing but have yet to fully embrace the realm of scalable vector graphics (SVG) generation. While LLMs encode partial knowledge of SVG data from web pages during training, recent findings suggest that semantically ambiguous and tokenized representations within LLMs may result in hallucinations in vector primitive predictions. Additionally, LLM training typically lacks modeling and understanding of the rendering sequence of vector paths, which can lead to occlusion between output vector primitives. In this paper, we present LLM4SVG, an initial yet substantial step toward bridging this gap by enabling LLMs to better understand and generate vector graphics. LLM4SVG facilitates a deeper understanding of SVG components through learnable semantic tokens, which precisely encode these tokens and their corresponding properties to generate semantically aligned SVG outputs. Using a series of learnable semantic tokens, a structured dataset for instruction following is developed to support comprehension and generation across two primary tasks. Our method introduces a modular architecture to existing large language models, integrating semantic tags, vector instruction encoders, fine-tuned commands, and powerful LLMs to tightly combine geometric, appearance, and language information. To overcome the scarcity of SVG-text instruction data, we developed an automated data generation pipeline that collected our SVGX-SFT Dataset, consisting of high-quality human-designed SVGs and 580k SVG instruction following data specifically crafted for LLM training, which facilitated the adoption of the supervised fine-tuning strategy popular in LLM development.

Large Language Models (LLMs) have demonstrated remarkable capabilities in Register Transfer Level (RTL) design, enabling high-quality code generation from natural language descriptions. However, LLMs alone face significant limitations in real-world hardware design workflows, including the inability to execute code, lack of debugging capabilities, and absence of long-term memory. To address these challenges, we present ASIC-Agent, an autonomous system designed specifically for digital ASIC design tasks. ASIC-Agent enhances base LLMs with a multi-agent architecture incorporating specialized sub-agents for RTL generation, verification, OpenLane hardening, and Caravel chip integration, all operating within a comprehensive sandbox environment with access to essential hardware design tools. The system leverages a vector database containing documentation, API references, error knowledge, and curated insights from the open-source silicon community. To evaluate ASIC-Agent's performance, we introduce ASIC-Agent-Bench, the first benchmark specifically designed to assess agentic systems in hardware design tasks. We evaluate ASIC-Agent with various base LLMs, providing quantitative comparisons and qualitative insights into agent behavior across different design scenarios. Our results demonstrate that ASIC-Agent, when powered by Claude 4 Sonnet, successfully automates a broad range of ASIC design tasks spanning varying levels of complexity, showing the potential of significantly accelerating the ASIC design workflow.

In this work, we present a new network design paradigm. Our goal is to help advance the understanding of network design and discover design principles that generalize across settings. Instead of focusing on designing individual network instances, we design network design spaces that parametrize populations of networks. The overall process is analogous to classic manual design of networks, but elevated to the design space level. Using our methodology we explore the structure aspect of network design and arrive at a low-dimensional design space consisting of simple, regular networks that we call RegNet. The core insight of the RegNet parametrization is surprisingly simple: widths and depths of good networks can be explained by a quantized linear function. We analyze the RegNet design space and arrive at interesting findings that do not match the current practice of network design. The RegNet design space provides simple and fast networks that work well across a wide range of flop regimes. Under comparable training settings and flops, the RegNet models outperform the popular EfficientNet models while being up to 5x faster on GPUs.

Computer-Aided Design (CAD) generative modeling is driving significant innovations across industrial applications. Recent works have shown remarkable progress in creating solid models from various inputs such as point clouds, meshes, and text descriptions. However, these methods fundamentally diverge from traditional industrial workflows that begin with 2D engineering drawings. The automatic generation of parametric CAD models from these 2D vector drawings remains underexplored despite being a critical step in engineering design. To address this gap, our key insight is to reframe CAD generation as a sequence-to-sequence learning problem where vector drawing primitives directly inform the generation of parametric CAD operations, preserving geometric precision and design intent throughout the transformation process. We propose Drawing2CAD, a framework with three key technical components: a network-friendly vector primitive representation that preserves precise geometric information, a dual-decoder transformer architecture that decouples command type and parameter generation while maintaining precise correspondence, and a soft target distribution loss function accommodating inherent flexibility in CAD parameters. To train and evaluate Drawing2CAD, we create CAD-VGDrawing, a dataset of paired engineering drawings and parametric CAD models, and conduct thorough experiments to demonstrate the effectiveness of our method. Code and dataset are available at https://github.com/lllssc/Drawing2CAD.

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we study the internal mechanisms that support abstract reasoning in LLMs. We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

While AI systems demonstrate exponentially improving capabilities, the pace of AI research itself remains linearly bounded by human cognitive capacity, creating an increasingly severe development bottleneck. We present ASI-Arch, the first demonstration of Artificial Superintelligence for AI research (ASI4AI) in the critical domain of neural architecture discovery--a fully autonomous system that shatters this fundamental constraint by enabling AI to conduct its own architectural innovation. Moving beyond traditional Neural Architecture Search (NAS), which is fundamentally limited to exploring human-defined spaces, we introduce a paradigm shift from automated optimization to automated innovation. ASI-Arch can conduct end-to-end scientific research in the domain of architecture discovery, autonomously hypothesizing novel architectural concepts, implementing them as executable code, training and empirically validating their performance through rigorous experimentation and past experience. ASI-Arch conducted 1,773 autonomous experiments over 20,000 GPU hours, culminating in the discovery of 106 innovative, state-of-the-art (SOTA) linear attention architectures. Like AlphaGo's Move 37 that revealed unexpected strategic insights invisible to human players, our AI-discovered architectures demonstrate emergent design principles that systematically surpass human-designed baselines and illuminate previously unknown pathways for architectural innovation. Crucially, we establish the first empirical scaling law for scientific discovery itself--demonstrating that architectural breakthroughs can be scaled computationally, transforming research progress from a human-limited to a computation-scalable process. We provide comprehensive analysis of the emergent design patterns and autonomous research capabilities that enabled these breakthroughs, establishing a blueprint for self-accelerating AI systems.

Large language models (LLMs) are rapidly approaching the level of proficiency in university-level symbolic mathematics required for applications in advanced science and technology. However, existing benchmarks fall short in assessing the core skills of LLMs in symbolic mathematics-such as integration, differential equations, and algebraic simplification. To address this gap, we introduce ASyMOB, a novel assessment framework focused exclusively on symbolic manipulation, featuring 17,092 unique math challenges, organized by similarity and complexity. ASyMOB enables analysis of LLM generalization capabilities by comparing performance in problems that differ by simple numerical or symbolic `perturbations'. Evaluated LLMs exhibit substantial degradation in performance for all perturbation types (up to -70.3%), suggesting reliance on memorized patterns rather than deeper understanding of symbolic math, even among models achieving high baseline accuracy. Comparing LLM performance to computer algebra systems, we identify examples where they fail while LLMs succeed, as well as problems solved only by combining both approaches. Models capable of integrated code execution yielded higher accuracy compared to their performance without code, particularly stabilizing weaker models (up to +33.1% for certain perturbation types). Notably, the most advanced models (o4-mini, Gemini 2.5 Flash) demonstrate not only high symbolic math proficiency (scoring 96.8% and 97.6% on the unperturbed set), but also remarkable robustness against perturbations, (-21.7% and -21.2% vs. average -50.4% for the other models). This may indicate a recent "phase transition" in the generalization capabilities of frontier LLMs. It remains to be seen whether the path forward lies in deeper integration with sophisticated external tools, or in developing models so capable that symbolic math systems like CAS become unnecessary.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Neuro-symbolic artificial intelligence (NSAI) represents a transformative approach in artificial intelligence (AI) by combining deep learning's ability to handle large-scale and unstructured data with the structured reasoning of symbolic methods. By leveraging their complementary strengths, NSAI enhances generalization, reasoning, and scalability while addressing key challenges such as transparency and data efficiency. This paper systematically studies diverse NSAI architectures, highlighting their unique approaches to integrating neural and symbolic components. It examines the alignment of contemporary AI techniques such as retrieval-augmented generation, graph neural networks, reinforcement learning, and multi-agent systems with NSAI paradigms. This study then evaluates these architectures against comprehensive set of criteria, including generalization, reasoning capabilities, transferability, and interpretability, therefore providing a comparative analysis of their respective strengths and limitations. Notably, the Neuro > Symbolic < Neuro model consistently outperforms its counterparts across all evaluation metrics. This result aligns with state-of-the-art research that highlight the efficacy of such architectures in harnessing advanced technologies like multi-agent systems.

Neural Architecture Search (NAS) has garnered significant research interest due to its capability to discover architectures superior to manually designed ones. Learning text representation is crucial for text classification and other language-related tasks. The NAS model used in text classification does not have a Hybrid hierarchical structure, and there is no restriction on the architecture structure, due to which the search space becomes very large and mostly redundant, so the existing RL models are not able to navigate the search space effectively. Also, doing a flat architecture search leads to an unorganised search space, which is difficult to traverse. For this purpose, we propose HHNAS-AM (Hierarchical Hybrid Neural Architecture Search with Adaptive Mutation Policies), a novel approach that efficiently explores diverse architectural configurations. We introduce a few architectural templates to search on which organise the search spaces, where search spaces are designed on the basis of domain-specific cues. Our method employs mutation strategies that dynamically adapt based on performance feedback from previous iterations using Q-learning, enabling a more effective and accelerated traversal of the search space. The proposed model is fully probabilistic, enabling effective exploration of the search space. We evaluate our approach on the database id (db_id) prediction task, where it consistently discovers high-performing architectures across multiple experiments. On the Spider dataset, our method achieves an 8% improvement in test accuracy over existing baselines.

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic unified understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training, which employs joint contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the pre-trained embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in few-shot learning scenarios where available data is limited.

Contemporary intelligent systems incorporate software components, including machine learning components. As they grow in complexity and data volume such machine learning systems face unique quality challenges like scalability and performance. To overcome them, engineers may often use specific architectural patterns, however their impact on ML systems is difficult to quantify. The effect of software architecture on traditional systems is well studied, however more work is needed in the area of machine learning systems. This study proposes a framework for quantitative assessment of architectural patterns in ML systems, focusing on scalability and performance metrics for cost-effective CPU-based inference. We integrate these metrics into a systematic evaluation process for selection of architectural patterns and demonstrate its application through a case study. The approach shown in the paper should enable software architects to objectively analyze and select optimal patterns, addressing key challenges in ML system design.

In the realm of vision models, the primary mode of representation is using pixels to rasterize the visual world. Yet this is not always the best or unique way to represent visual content, especially for designers and artists who depict the world using geometry primitives such as polygons. Vector graphics (VG), on the other hand, offer a textual representation of visual content, which can be more concise and powerful for content like cartoons or sketches. Recent studies have shown promising results on processing vector graphics with capable Large Language Models (LLMs). However, such works focus solely on qualitative results, understanding, or a specific type of vector graphics. We propose VGBench, a comprehensive benchmark for LLMs on handling vector graphics through diverse aspects, including (a) both visual understanding and generation, (b) evaluation of various vector graphics formats, (c) diverse question types, (d) wide range of prompting techniques, (e) under multiple LLMs. Evaluating on our collected 4279 understanding and 5845 generation samples, we find that LLMs show strong capability on both aspects while exhibiting less desirable performance on low-level formats (SVG). Both data and evaluation pipeline will be open-sourced at https://vgbench.github.io.

Training Large Language Models (LLMs) requires immense computational power and vast amounts of data. As a result, protecting the intellectual property of these models through fingerprinting is essential for ownership authentication. While adding fingerprints to LLMs through fine-tuning has been attempted, it remains costly and unscalable. In this paper, we introduce FP-VEC, a pilot study on using fingerprint vectors as an efficient fingerprinting method for LLMs. Our approach generates a fingerprint vector that represents a confidential signature embedded in the model, allowing the same fingerprint to be seamlessly incorporated into an unlimited number of LLMs via vector addition. Results on several LLMs show that FP-VEC is lightweight by running on CPU-only devices for fingerprinting, scalable with a single training and unlimited fingerprinting process, and preserves the model's normal behavior. The project page is available at https://fingerprintvector.github.io .

We build upon vec2vec, a procedure designed to align text embedding spaces without parallel data. vec2vec finds a near-perfect alignment, but it is expensive and unstable. We present mini-vec2vec, a simple and efficient alternative that requires substantially lower computational cost and is highly robust. Moreover, the learned mapping is a linear transformation. Our method consists of three main stages: a tentative matching of pseudo-parallel embedding vectors, transformation fitting, and iterative refinement. Our linear alternative exceeds the original instantiation of vec2vec by orders of magnitude in efficiency, while matching or exceeding their results. The method's stability and interpretable algorithmic steps facilitate scaling and unlock new opportunities for adoption in new domains and fields.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

Scalable Vector Graphics (SVG) is widely used in front-end development and UI/UX design due to its scalability, editability, and rendering efficiency. However, turning creative ideas into precise vector graphics remains a time-consuming challenge. To address this, we introduce SVG-1M, a large-scale dataset of high-quality SVGs paired with natural language descriptions. Through advanced data augmentation and annotation, we create well-aligned Text to SVG training pairs, including a subset with Chain of Thought annotations for enhanced semantic guidance. Based on this dataset, we propose SVGen, an end-to-end model that generates SVG code from natural language inputs. Our approach ensures semantic accuracy and structural completeness, supported by curriculum learning and reinforcement learning optimization. Experiments show that SVGen outperforms general large models and traditional rendering methods in both effectiveness and efficiency. Code, model, and dataset are available on GitHub.

Code has emerged as a precise and executable medium for reasoning and action in the agent era. Yet, progress has largely focused on language-centric tasks such as program synthesis and debugging, leaving visual-centric coding underexplored. Inspired by how humans reason over sketches, we advocate SVG code as a compact, interpretable, and executable visual representation. We introduce VCode, a benchmark that reframes multimodal understanding as code generation: given an image, a model must produce SVG that preserves symbolic meaning for downstream reasoning. VCode covers three domains - general commonsense (MM-Vet), professional disciplines (MMMU), and visual-centric perception (CV-Bench). To assess symbolic fidelity, we propose CodeVQA, a novel evaluation protocol in which a policy model answers questions over rendered SVGs; correct answers indicate faithful symbolic preservation. Empirically, frontier VLMs struggle to generate faithful SVGs, revealing a persistent gap between language-centric and visual-centric coding. To close this gap, we introduce VCoder, an agentic framework that augments VLMs along two axes: (i) Thinking with Revision, which iteratively analyzes discrepancies and refines SVG code; and (ii) Acting with Visual Tools, where detectors and parsers supply structured cues such as objects, shapes, and text beyond the model's intrinsic capacity. Across benchmarks, frontier VLMs with strong reasoning capabilities score well overall yet remain limited in professional knowledge and 3D reasoning. VCoder delivers a 12.3-point overall gain over the top-performing Claude-4-Opus. Human studies show that both humans and VLMs perform worse on rendered SVGs, their consistency reveals the promise of symbolic visual representation. The benchmark and code are available at https://github.com/CSU-JPG/VCode.

Scalable Vector Graphics (SVGs) have become integral in modern image rendering applications due to their infinite scalability in resolution, versatile usability, and editing capabilities. SVGs are particularly popular in the fields of web development and graphic design. Existing approaches for SVG modeling using deep learning often struggle with generating complex SVGs and are restricted to simpler ones that require extensive processing and simplification. This paper introduces StarVector, a multimodal SVG generation model that effectively integrates Code Generation Large Language Models (CodeLLMs) and vision models. Our approach utilizes a CLIP image encoder to extract visual representations from pixel-based images, which are then transformed into visual tokens via an adapter module. These visual tokens are pre-pended to the SVG token embeddings, and the sequence is modeled by the StarCoder model using next-token prediction, effectively learning to align the visual and code tokens. This enables StarVector to generate unrestricted SVGs that accurately represent pixel images. To evaluate StarVector's performance, we present SVG-Bench, a comprehensive benchmark for evaluating SVG methods across multiple datasets and relevant metrics. Within this benchmark, we introduce novel datasets including SVG-Stack, a large-scale dataset of real-world SVG examples, and use it to pre-train StarVector as a large foundation model for SVGs. Our results demonstrate significant enhancements in visual quality and complexity handling over current methods, marking a notable advancement in SVG generation technology. Code and models: https://github.com/joanrod/star-vector

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

The recent exponential growth of Large Language Models (LLMs) has relied on GPU-based systems. However, CPUs are emerging as a flexible and lower-cost alternative, especially when targeting inference and reasoning workloads. RISC-V is rapidly gaining traction in this area, given its open and vendor-neutral ISA. However, the RISC-V hardware for LLM workloads and the corresponding software ecosystem are not fully mature and streamlined, given the requirement of domain-specific tuning. This paper aims at filling this gap, focusing on optimizing LLM inference on the Sophon SG2042, the first commercially available many-core RISC-V CPU with vector processing capabilities. On two recent state-of-the-art LLMs optimized for reasoning, DeepSeek R1 Distill Llama 8B and DeepSeek R1 Distill QWEN 14B, we achieve 4.32/2.29 token/s for token generation and 6.54/3.68 token/s for prompt processing, with a speed up of up 2.9x/3.0x compared to our baseline.

Assessing the capabilities of large language models (LLMs) is often challenging, in part, because it is hard to find tasks to which they have not been exposed during training. We take one step to address this challenge by turning to a new task: focusing on symbolic graphics programs, which are a popular representation for graphics content that procedurally generates visual data. LLMs have shown exciting promise towards program synthesis, but do they understand symbolic graphics programs? Unlike conventional programs, symbolic graphics programs can be translated to graphics content. Here, we characterize an LLM's understanding of symbolic programs in terms of their ability to answer questions related to the graphics content. This task is challenging as the questions are difficult to answer from the symbolic programs alone -- yet, they would be easy to answer from the corresponding graphics content as we verify through a human experiment. To understand symbolic programs, LLMs may need to possess the ability to imagine how the corresponding graphics content would look without directly accessing the rendered visual content. We use this task to evaluate LLMs by creating a large benchmark for the semantic understanding of symbolic graphics programs. This benchmark is built via program-graphics correspondence, hence requiring minimal human efforts. We evaluate current LLMs on our benchmark to elucidate a preliminary assessment of their ability to reason about visual scenes from programs. We find that this task distinguishes existing LLMs and models considered good at reasoning perform better. Lastly, we introduce Symbolic Instruction Tuning (SIT) to improve this ability. Specifically, we query GPT4-o with questions and images generated by symbolic programs. Such data are then used to finetune an LLM. We also find that SIT data can improve the general instruction following ability of LLMs.

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications. Graph-based indices are currently the best performing techniques for billion-scale similarity search. However, their random-access memory pattern presents challenges to realize their full potential. In this work, we present new techniques and systems for creating faster and smaller graph-based indices. To this end, we introduce a novel vector compression method, Locally-adaptive Vector Quantization (LVQ), that uses per-vector scaling and scalar quantization to improve search performance with fast similarity computations and a reduced effective bandwidth, while decreasing memory footprint and barely impacting accuracy. LVQ, when combined with a new high-performance computing system for graph-based similarity search, establishes the new state of the art in terms of performance and memory footprint. For billions of vectors, LVQ outcompetes the second-best alternatives: (1) in the low-memory regime, by up to 20.7x in throughput with up to a 3x memory footprint reduction, and (2) in the high-throughput regime by 5.8x with 1.4x less memory.

This paper explores the integration of two AI subdisciplines employed in the development of artificial agents that exhibit intelligent behavior: Large Language Models (LLMs) and Cognitive Architectures (CAs). We present three integration approaches, each grounded in theoretical models and supported by preliminary empirical evidence. The modular approach, which introduces four models with varying degrees of integration, makes use of chain-of-thought prompting, and draws inspiration from augmented LLMs, the Common Model of Cognition, and the simulation theory of cognition. The agency approach, motivated by the Society of Mind theory and the LIDA cognitive architecture, proposes the formation of agent collections that interact at micro and macro cognitive levels, driven by either LLMs or symbolic components. The neuro-symbolic approach, which takes inspiration from the CLARION cognitive architecture, proposes a model where bottom-up learning extracts symbolic representations from an LLM layer and top-down guidance utilizes symbolic representations to direct prompt engineering in the LLM layer. These approaches aim to harness the strengths of both LLMs and CAs, while mitigating their weaknesses, thereby advancing the development of more robust AI systems. We discuss the tradeoffs and challenges associated with each approach.

The generation of Scalable Vector Graphics (SVG) assets from textual data remains a significant challenge, largely due to the scarcity of high-quality vector datasets and the limitations in scalable vector representations required for modeling intricate graphic distributions. This work introduces SVGFusion, a Text-to-SVG model capable of scaling to real-world SVG data without reliance on a text-based discrete language model or prolonged SDS optimization. The essence of SVGFusion is to learn a continuous latent space for vector graphics with a popular Text-to-Image framework. Specifically, SVGFusion consists of two modules: a Vector-Pixel Fusion Variational Autoencoder (VP-VAE) and a Vector Space Diffusion Transformer (VS-DiT). VP-VAE takes both the SVGs and corresponding rasterizations as inputs and learns a continuous latent space, whereas VS-DiT learns to generate a latent code within this space based on the text prompt. Based on VP-VAE, a novel rendering sequence modeling strategy is proposed to enable the latent space to embed the knowledge of construction logics in SVGs. This empowers the model to achieve human-like design capabilities in vector graphics, while systematically preventing occlusion in complex graphic compositions. Moreover, our SVGFusion's ability can be continuously improved by leveraging the scalability of the VS-DiT by adding more VS-DiT blocks. A large-scale SVG dataset is collected to evaluate the effectiveness of our proposed method. Extensive experimentation has confirmed the superiority of our SVGFusion over existing SVG generation methods, achieving enhanced quality and generalizability, thereby establishing a novel framework for SVG content creation. Code, model, and data will be released at: https://ximinng.github.io/SVGFusionProject/{https://ximinng.github.io/SVGFusionProject/}

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. SymbolicAI enables the seamless integration of generative models with a diverse range of solvers by treating large language models (LLMs) as semantic parsers that execute tasks based on both natural and formal language instructions, thus bridging the gap between symbolic reasoning and generative AI. We leverage probabilistic programming principles to tackle complex tasks, and utilize differentiable and classical programming paradigms with their respective strengths. The framework introduces a set of polymorphic, compositional, and self-referential operations for data stream manipulation, aligning LLM outputs with user objectives. As a result, we can transition between the capabilities of various foundation models endowed with zero- and few-shot learning capabilities and specialized, fine-tuned models or solvers proficient in addressing specific problems. In turn, the framework facilitates the creation and evaluation of explainable computational graphs. We conclude by introducing a quality measure and its empirical score for evaluating these computational graphs, and propose a benchmark that compares various state-of-the-art LLMs across a set of complex workflows. We refer to the empirical score as the "Vector Embedding for Relational Trajectory Evaluation through Cross-similarity", or VERTEX score for short. The framework codebase and benchmark are linked below.

Learning in weight spaces, where neural networks process the weights of other deep neural networks, has emerged as a promising research direction with applications in various fields, from analyzing and editing neural fields and implicit neural representations, to network pruning and quantization. Recent works designed architectures for effective learning in that space, which takes into account its unique, permutation-equivariant, structure. Unfortunately, so far these architectures suffer from severe overfitting and were shown to benefit from large datasets. This poses a significant challenge because generating data for this learning setup is laborious and time-consuming since each data sample is a full set of network weights that has to be trained. In this paper, we address this difficulty by investigating data augmentations for weight spaces, a set of techniques that enable generating new data examples on the fly without having to train additional input weight space elements. We first review several recently proposed data augmentation schemes %that were proposed recently and divide them into categories. We then introduce a novel augmentation scheme based on the Mixup method. We evaluate the performance of these techniques on existing benchmarks as well as new benchmarks we generate, which can be valuable for future studies.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

Innovations like protein diffusion have enabled significant progress in de novo protein design, which is a vital topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where atoms do not exist. Most prior encoders rely on atom-wise features, such as angles and distances between atoms, which are not available in this context. Thus far, only several simple encoders, such as IPA, have been proposed for this scenario, exposing the frame modeling as a bottleneck. In this work, we proffer the Vector Field Network (VFN), which enables network layers to perform learnable vector computations between coordinates of frame-anchored virtual atoms, thus achieving a higher capability for modeling frames. The vector computation operates in a manner similar to a linear layer, with each input channel receiving 3D virtual atom coordinates instead of scalar values. The multiple feature vectors output by the vector computation are then used to update the residue representations and virtual atom coordinates via attention aggregation. Remarkably, VFN also excels in modeling both frames and atoms, as the real atoms can be treated as the virtual atoms for modeling, positioning VFN as a potential universal encoder. In protein diffusion (frame modeling), VFN exhibits an impressive performance advantage over IPA, excelling in terms of both designability (67.04% vs. 53.58%) and diversity (66.54% vs. 51.98%). In inverse folding (frame and atom modeling), VFN outperforms the previous SoTA model, PiFold (54.7% vs. 51.66%), on sequence recovery rate. We also propose a method of equipping VFN with the ESM model, which significantly surpasses the previous ESM-based SoTA (62.67% vs. 55.65%), LM-Design, by a substantial margin.

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with gradients remains a challenge. In this paper, we propose a segmentation-guided vectorization framework to convert raster images into concise vector graphics with radial gradient fills. With the guidance of an embedded gradient-aware segmentation subroutine, our approach progressively appends gradient-filled B\'ezier paths to the output, where primitive parameters are initiated with our newly designed initialization technique and are optimized to minimize our novel loss function. We build our method on a differentiable renderer with traditional segmentation algorithms to develop it as a model-free tool for raster-to-vector conversion. It is tested on various inputs to demonstrate its feasibility, independent of datasets, to synthesize vector graphics with improved visual quality and layer-wise topology compared to prior work.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

In this work we present successor heads: attention heads that increment tokens with a natural ordering, such as numbers, months, and days. For example, successor heads increment 'Monday' into 'Tuesday'. We explain the successor head behavior with an approach rooted in mechanistic interpretability, the field that aims to explain how models complete tasks in human-understandable terms. Existing research in this area has found interpretable language model components in small toy models. However, results in toy models have not yet led to insights that explain the internals of frontier models and little is currently understood about the internal operations of large language models. In this paper, we analyze the behavior of successor heads in large language models (LLMs) and find that they implement abstract representations that are common to different architectures. They form in LLMs with as few as 31 million parameters, and at least as many as 12 billion parameters, such as GPT-2, Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how successor heads increment in LLMs across different architectures and sizes. We perform vector arithmetic with these features to edit head behavior and provide insights into numeric representations within LLMs. Additionally, we study the behavior of successor heads on natural language data, identifying interpretable polysemanticity in a Pythia successor head.

Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely unexplored. Our study attempts to reveal the star operation's ability to map inputs into high-dimensional, non-linear feature spaces -- akin to kernel tricks -- without widening the network. We further introduce StarNet, a simple yet powerful prototype, demonstrating impressive performance and low latency under compact network structure and efficient budget. Like stars in the sky, the star operation appears unremarkable but holds a vast universe of potential. Our work encourages further exploration across tasks, with codes available at https://github.com/ma-xu/Rewrite-the-Stars.

In nature, the behaviors of many complex systems can be described by parsimonious math equations. Automatically distilling these equations from limited data is cast as a symbolic regression process which hitherto remains a grand challenge. Keen efforts in recent years have been placed on tackling this issue and demonstrated success in symbolic regression. However, there still exist bottlenecks that current methods struggle to break when the discrete search space tends toward infinity and especially when the underlying math formula is intricate. To this end, we propose a novel Reinforcement Symbolic Regression Machine (RSRM) that masters the capability of uncovering complex math equations from only scarce data. The RSRM model is composed of three key modules: (1) a Monte Carlo tree search (MCTS) agent that explores optimal math expression trees consisting of pre-defined math operators and variables, (2) a Double Q-learning block that helps reduce the feasible search space of MCTS via properly understanding the distribution of reward, and (3) a modulated sub-tree discovery block that heuristically learns and defines new math operators to improve representation ability of math expression trees. Biding of these modules yields the state-of-the-art performance of RSRM in symbolic regression as demonstrated by multiple sets of benchmark examples. The RSRM model shows clear superiority over several representative baseline models.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

This paper presents a novel generative model for Computer Aided Design (CAD) that 1) represents high-level design concepts of a CAD model as a three-level hierarchical tree of neural codes, from global part arrangement down to local curve geometry; and 2) controls the generation or completion of CAD models by specifying the target design using a code tree. Concretely, a novel variant of a vector quantized VAE with "masked skip connection" extracts design variations as neural codebooks at three levels. Two-stage cascaded auto-regressive transformers learn to generate code trees from incomplete CAD models and then complete CAD models following the intended design. Extensive experiments demonstrate superior performance on conventional tasks such as random generation while enabling novel interaction capabilities on conditional generation tasks. The code is available at https://github.com/samxuxiang/hnc-cad.

Despite high benchmark scores, Large Language Models (LLMs) often fail simple problem, raising a critical question: Do LLMs learn mathematical principles or merely memorize patterns? Rather than designing increasingly complex benchmarks like recent works, we investigate this using elementary two-integer addition (0 to 2^{64}), probing two core properties: commutativity (A+B=B+A) and compositional generalization (via isomorphic symbolic mappings, e.g., 7 rightarrow y). While state-of-the-art LLMs achieve 73.8-99.8\% accuracy on numerical addition, performance collapses to leq7.5\% under symbolic mapping, indicating failure to generalize learned rules. Non-monotonic performance scaling with digit count and frequent commutativity violations (over 1,700 cases of A+B neq B+A) further support this. Explicitly providing addition rules degrades performance by 81.2\% on average, while self-explanation maintains baseline accuracy, suggesting LLM arithmetic processing is misaligned with human-defined principles. Our findings indicate current LLMs rely on memory pattern over genuine rule learning, highlighting architectural limitations and the need for new approaches to achieve true mathematical reasoning.

Architecture design and optimization are challenging problems in the field of artificial neural networks. Working in this context, we here present SPARCS (SPectral ARchiteCture Search), a novel architecture search protocol which exploits the spectral attributes of the inter-layer transfer matrices. SPARCS allows one to explore the space of possible architectures by spanning continuous and differentiable manifolds, thus enabling for gradient-based optimization algorithms to be eventually employed. With reference to simple benchmark models, we show that the newly proposed method yields a self-emerging architecture with a minimal degree of expressivity to handle the task under investigation and with a reduced parameter count as compared to other viable alternatives.

Neural Architecture Search (NAS) has been increasingly appealing to the society of object Re-Identification (ReID), for that task-specific architectures significantly improve the retrieval performance. Previous works explore new optimizing targets and search spaces for NAS ReID, yet they neglect the difference of training schemes between image classification and ReID. In this work, we propose a novel Twins Contrastive Mechanism (TCM) to provide more appropriate supervision for ReID architecture search. TCM reduces the category overlaps between the training and validation data, and assists NAS in simulating real-world ReID training schemes. We then design a Multi-Scale Interaction (MSI) search space to search for rational interaction operations between multi-scale features. In addition, we introduce a Spatial Alignment Module (SAM) to further enhance the attention consistency confronted with images from different sources. Under the proposed NAS scheme, a specific architecture is automatically searched, named as MSINet. Extensive experiments demonstrate that our method surpasses state-of-the-art ReID methods on both in-domain and cross-domain scenarios. Source code available in https://github.com/vimar-gu/MSINet.

Neural Architecture Search is a costly practice. The fact that a search space can span a vast number of design choices with each architecture evaluation taking nontrivial overhead makes it hard for an algorithm to sufficiently explore candidate networks. In this paper, we propose AutoBuild, a scheme which learns to align the latent embeddings of operations and architecture modules with the ground-truth performance of the architectures they appear in. By doing so, AutoBuild is capable of assigning interpretable importance scores to architecture modules, such as individual operation features and larger macro operation sequences such that high-performance neural networks can be constructed without any need for search. Through experiments performed on state-of-the-art image classification, segmentation, and Stable Diffusion models, we show that by mining a relatively small set of evaluated architectures, AutoBuild can learn to build high-quality architectures directly or help to reduce search space to focus on relevant areas, finding better architectures that outperform both the original labeled ones and ones found by search baselines. Code available at https://github.com/Ascend-Research/AutoBuild

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Recent advancements in Large Language Models (LLMs) have revolutionized artificial intelligence, yet developing an effective foundational LLM that balances high performance with computational efficiency remains challenging, especially for emerging research groups. To address this gap, we introduce Motif-2.6B, a 2.6-billion-parameter foundation model designed to democratize advanced LLM capabilities. Motif-2.6B incorporates several innovative architectural enhancements, including Differential Attention and PolyNorm activation functions, which improve long-context comprehension, reduce hallucination, and enhance in-context learning capabilities. We rigorously tested multiple novel architectural components through extensive experimentation to determine the optimal architecture for Motif-2.6B. Comprehensive evaluations demonstrate that Motif-2.6B consistently meets or exceeds the performance of similarly sized state-of-the-art models across diverse benchmarks, showcasing its effectiveness, scalability, and real-world applicability. Through detailed experiments and tailored techniques, Motif-2.6B significantly advances the landscape of efficient, scalable, and powerful foundational LLMs, offering valuable insights and a robust foundation for future research and deployment.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

Equation discovery from data is a core challenge in machine learning for science, requiring the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent approaches with large language models (LLMs) show promise in symbolic regression, but their success often hinges on memorized formulas or overly simplified functional forms. Existing benchmarks exacerbate this limitation: they focus on scalar functions, ignore domain grounding, and rely on brittle string-matching based metrics that fail to capture scientific equivalence. We introduce SurfaceBench, first comprehensive benchmark for symbolic surface discovery. SurfaceBench comprises 183 tasks across 15 categories of symbolic complexity, spanning explicit, implicit, and parametric equation representation forms. Each task includes ground-truth equations, variable semantics, and synthetically sampled three dimensional data. Unlike prior SR datasets, our tasks reflect surface-level structure, resist LLM memorization through novel symbolic compositions, and are grounded in scientific domains such as fluid dynamics, robotics, electromagnetics, and geometry. To evaluate equation discovery quality, we pair symbolic checks with geometry-aware metrics such as Chamfer and Hausdorff distances, capturing both algebraic fidelity and spatial reconstruction accuracy. Our experiments reveal that state-of-the-art frameworks, while occasionally successful on specific families, struggle to generalize across representation types and surface complexities. SurfaceBench thus establishes a challenging and diagnostic testbed that bridges symbolic reasoning with geometric reconstruction, enabling principled benchmarking of progress in compositional generalization, data-driven scientific induction, and geometry-aware reasoning with LLMs. We release the code here: https://github.com/Sanchit-404/surfacebench

Scalable Vector Graphics (SVGs) are highly favored by designers due to their resolution independence and well-organized layer structure. Although existing text-to-vector (T2V) generation methods can create SVGs from text prompts, they often overlook an important need in practical applications: style customization, which is vital for producing a collection of vector graphics with consistent visual appearance and coherent aesthetics. Extending existing T2V methods for style customization poses certain challenges. Optimization-based T2V models can utilize the priors of text-to-image (T2I) models for customization, but struggle with maintaining structural regularity. On the other hand, feed-forward T2V models can ensure structural regularity, yet they encounter difficulties in disentangling content and style due to limited SVG training data. To address these challenges, we propose a novel two-stage style customization pipeline for SVG generation, making use of the advantages of both feed-forward T2V models and T2I image priors. In the first stage, we train a T2V diffusion model with a path-level representation to ensure the structural regularity of SVGs while preserving diverse expressive capabilities. In the second stage, we customize the T2V diffusion model to different styles by distilling customized T2I models. By integrating these techniques, our pipeline can generate high-quality and diverse SVGs in custom styles based on text prompts in an efficient feed-forward manner. The effectiveness of our method has been validated through extensive experiments. The project page is https://customsvg.github.io.

We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We also outline the basic principles of the vector formulation of stoichiometry, interpreting reactions as integer vectors in composition space, this geometric view supports compact visualizations of reagent-product interactions and helps surface distinct reaction families. The method enumerates valid balances for arbitrary user-specified species lists without special-case balancing rules or symbolic tricks, and it provides a clean foundation for developing new algorithmic variants (e.g., alternative objectives or constraints). On representative examples (neutralization, double displacement, decomposition, classical redox, small multicomponent sets) and a negative control, the method produced correct integer balances. When multiple balances exist, we report a canonical one - minimizing the total coefficient sum with a simple tie-breaker - without claiming global optimality beyond the solutions the search enumerates. The procedure applies per reaction and extends to reaction networks via consistent per-reaction application. We do not report runtimes, broader benchmarking and code/data release are planned.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

Learning manipulable representations of the world and its dynamics is central to AI. Joint-Embedding Predictive Architectures (JEPAs) offer a promising blueprint, but lack of practical guidance and theory has led to ad-hoc R&D. We present a comprehensive theory of JEPAs and instantiate it in {\bf LeJEPA}, a lean, scalable, and theoretically grounded training objective. First, we identify the isotropic Gaussian as the optimal distribution that JEPAs' embeddings should follow to minimize downstream prediction risk. Second, we introduce a novel objective--{\bf Sketched Isotropic Gaussian Regularization} (SIGReg)--to constrain embeddings to reach that ideal distribution. Combining the JEPA predictive loss with SIGReg yields LeJEPA with numerous theoretical and practical benefits: (i) single trade-off hyperparameter, (ii) linear time and memory complexity, (iii) stability across hyper-parameters, architectures (ResNets, ViTs, ConvNets) and domains, (iv) heuristics-free, e.g., no stop-gradient, no teacher-student, no hyper-parameter schedulers, and (v) distributed training-friendly implementation requiring only approx50 lines of code. Our empirical validation covers 10+ datasets, 60+ architectures, all with varying scales and domains. As an example, using imagenet-1k for pretraining and linear evaluation with frozen backbone, LeJEPA reaches 79\% with a ViT-H/14. We hope that the simplicity and theory-friendly ecosystem offered by LeJEPA will reestablish self-supervised pre-training as a core pillar of AI research (https://github.com/rbalestr-lab/lejepa{GitHub repo}).

The mechanisms by which reasoning training reshapes LLMs' internal computations remain unclear. We study lightweight steering vectors inserted into the base model's residual stream and trained with a reinforcement-learning objective. These vectors match full fine-tuning performance while preserving the interpretability of small, additive interventions. Using logit-lens readouts and path-patching analyses on two models, we find that (i) the last-layer steering vector acts like a token-substitution bias concentrated on the first generated token, consistently boosting tokens such as "To" and "Step"; (ii) the penultimate-layer vector leaves attention patterns largely intact and instead operates through the MLP and unembedding, preferentially up-weighting process words and structure symbols; and (iii) middle layers de-emphasize non-English tokens. Next, we show that a SAE isolates features associated with correct generations. We also show that steering vectors (i) transfer to other models, (ii) combine across layers when trained in isolation, and (iii) concentrate magnitude on meaningful prompt segments under adaptive token-wise scaling. Taken together, these results deepen understanding of how trained steering vectors shape computation and should inform future work in activation engineering and the study of reasoning models.

Differentiable architecture search (DARTS) is an effective method for data-driven neural network design based on solving a bilevel optimization problem. Despite its success in many architecture search tasks, there are still some concerns about the accuracy of first-order DARTS and the efficiency of the second-order DARTS. In this paper, we formulate a single level alternative and a relaxed architecture search (RARTS) method that utilizes the whole dataset in architecture learning via both data and network splitting, without involving mixed second derivatives of the corresponding loss functions like DARTS. In our formulation of network splitting, two networks with different but related weights cooperate in search of a shared architecture. The advantage of RARTS over DARTS is justified by a convergence theorem and an analytically solvable model. Moreover, RARTS outperforms DARTS and its variants in accuracy and search efficiency, as shown in adequate experimental results. For the task of searching topological architecture, i.e., the edges and the operations, RARTS obtains a higher accuracy and 60\% reduction of computational cost than second-order DARTS on CIFAR-10. RARTS continues to out-perform DARTS upon transfer to ImageNet and is on par with recent variants of DARTS even though our innovation is purely on the training algorithm without modifying search space. For the task of searching width, i.e., the number of channels in convolutional layers, RARTS also outperforms the traditional network pruning benchmarks. Further experiments on the public architecture search benchmark like NATS-Bench also support the preeminence of RARTS.

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

The paper presents a novel approach for vector-floorplan generation via a diffusion model, which denoises 2D coordinates of room/door corners with two inference objectives: 1) a single-step noise as the continuous quantity to precisely invert the continuous forward process; and 2) the final 2D coordinate as the discrete quantity to establish geometric incident relationships such as parallelism, orthogonality, and corner-sharing. Our task is graph-conditioned floorplan generation, a common workflow in floorplan design. We represent a floorplan as 1D polygonal loops, each of which corresponds to a room or a door. Our diffusion model employs a Transformer architecture at the core, which controls the attention masks based on the input graph-constraint and directly generates vector-graphics floorplans via a discrete and continuous denoising process. We have evaluated our approach on RPLAN dataset. The proposed approach makes significant improvements in all the metrics against the state-of-the-art with significant margins, while being capable of generating non-Manhattan structures and controlling the exact number of corners per room. A project website with supplementary video and document is here https://aminshabani.github.io/housediffusion.

This paper revisits Ramon Llull's Ars combinatoria - a medieval framework for generating knowledge through symbolic recombination - as a conceptual foundation for building a modern Llull's thinking machine for research ideation. Our approach defines three compositional axes: Theme (e.g., efficiency, adaptivity), Domain (e.g., question answering, machine translation), and Method (e.g., adversarial training, linear attention). These elements represent high-level abstractions common in scientific work - motivations, problem settings, and technical approaches - and serve as building blocks for LLM-driven exploration. We mine elements from human experts or conference papers and show that prompting LLMs with curated combinations produces research ideas that are diverse, relevant, and grounded in current literature. This modern thinking machine offers a lightweight, interpretable tool for augmenting scientific creativity and suggests a path toward collaborative ideation between humans and AI.

Scalable Vector Graphics (SVG) is a code-based representation for 2D visuals. Leveraging recent advances in large language models (LLMs), we study text-to-SVG generation and address two persistent gaps: weak generalization and poor adherence to input instructions. We present SVGThinker, a reasoning-driven framework that aligns the production of SVG code with the visualization process and supports the full set of SVG primitives. Our pipeline first renders each primitive in sequence and uses a multimodal model to annotate the image and code; we then build stepwise updates that mirror the incremental addition of primitives. On this data, we train an LLM with supervised fine-tuning that exposes its chain-of-thought as intermediate reasoning, improving robustness and reducing errors and hallucinations. Experiments against state-of-the-art baselines show that SVGThinker produces more stable, editable, and higher-quality SVGs while preserving the structural advantages of vector graphics. Unlike image-based methods, our outputs enable precise and hierarchical editing, opening new directions for design, content creation, and automated graphics generation.

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required.

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

Recognizing symbols in architectural CAD drawings is critical for various advanced engineering applications. In this paper, we propose a novel CAD data annotation engine that leverages intrinsic attributes from systematically archived CAD drawings to automatically generate high-quality annotations, thus significantly reducing manual labeling efforts. Utilizing this engine, we construct ArchCAD-400K, a large-scale CAD dataset consisting of 413,062 chunks from 5538 highly standardized drawings, making it over 26 times larger than the largest existing CAD dataset. ArchCAD-400K boasts an extended drawing diversity and broader categories, offering line-grained annotations. Furthermore, we present a new baseline model for panoptic symbol spotting, termed Dual-Pathway Symbol Spotter (DPSS). It incorporates an adaptive fusion module to enhance primitive features with complementary image features, achieving state-of-the-art performance and enhanced robustness. Extensive experiments validate the effectiveness of DPSS, demonstrating the value of ArchCAD-400K and its potential to drive innovation in architectural design and construction.

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.

Scalable Vector Graphics (SVG) are ubiquitous in modern 2D interfaces due to their ability to scale to different resolutions. However, despite the success of deep learning-based models applied to rasterized images, the problem of vector graphics representation learning and generation remains largely unexplored. In this work, we propose a novel hierarchical generative network, called DeepSVG, for complex SVG icons generation and interpolation. Our architecture effectively disentangles high-level shapes from the low-level commands that encode the shape itself. The network directly predicts a set of shapes in a non-autoregressive fashion. We introduce the task of complex SVG icons generation by releasing a new large-scale dataset along with an open-source library for SVG manipulation. We demonstrate that our network learns to accurately reconstruct diverse vector graphics, and can serve as a powerful animation tool by performing interpolations and other latent space operations. Our code is available at https://github.com/alexandre01/deepsvg.

The neural Hawkes process (Mei & Eisner, 2017) is a generative model of irregularly spaced sequences of discrete events. To handle complex domains with many event types, Mei et al. (2020a) further consider a setting in which each event in the sequence updates a deductive database of facts (via domain-specific pattern-matching rules); future events are then conditioned on the database contents. They show how to convert such a symbolic system into a neuro-symbolic continuous-time generative model, in which each database fact and the possible event has a time-varying embedding that is derived from its symbolic provenance. In this paper, we modify both models, replacing their recurrent LSTM-based architectures with flatter attention-based architectures (Vaswani et al., 2017), which are simpler and more parallelizable. This does not appear to hurt our accuracy, which is comparable to or better than that of the original models as well as (where applicable) previous attention-based methods (Zuo et al., 2020; Zhang et al., 2020a).

Albeit being a prevalent architecture searching approach, differentiable architecture search (DARTS) is largely hindered by its substantial memory cost since the entire supernet resides in the memory. This is where the single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. Nonetheless, we discover a critical issue of single-path DARTS that has not been primarily noticed. Namely, it also suffers from severe performance collapse since too many parameter-free operations like skip connections are derived, just like DARTS does. In this paper, we propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure. First, we disentangle the topology search from the operation search to make searching and evaluation consistent. We then adopt Gumbel-Top2 reparameterization and gradient accumulation to robustify the unwieldy bi-level optimization. We verify ROME extensively across 15 benchmarks to demonstrate its effectiveness and robustness.

Neural Architecture Search (NAS) has demonstrated its power on various AI accelerating platforms such as Field Programmable Gate Arrays (FPGAs) and Graphic Processing Units (GPUs). However, it remains an open problem, how to integrate NAS with Application-Specific Integrated Circuits (ASICs), despite them being the most powerful AI accelerating platforms. The major bottleneck comes from the large design freedom associated with ASIC designs. Moreover, with the consideration that multiple DNNs will run in parallel for different workloads with diverse layer operations and sizes, integrating heterogeneous ASIC sub-accelerators for distinct DNNs in one design can significantly boost performance, and at the same time further complicate the design space. To address these challenges, in this paper we build ASIC template set based on existing successful designs, described by their unique dataflows, so that the design space is significantly reduced. Based on the templates, we further propose a framework, namely NASAIC, which can simultaneously identify multiple DNN architectures and the associated heterogeneous ASIC accelerator design, such that the design specifications (specs) can be satisfied, while the accuracy can be maximized. Experimental results show that compared with successive NAS and ASIC design optimizations which lead to design spec violations, NASAIC can guarantee the results to meet the design specs with 17.77%, 2.49x, and 2.32x reductions on latency, energy, and area and with 0.76% accuracy loss. To the best of the authors' knowledge, this is the first work on neural architecture and ASIC accelerator design co-exploration.

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence, capable of processing and understanding extensive human knowledge to enhance problem-solving across various domains. This paper explores the potential of LLMs to drive the discovery of symbolic solutions within scientific and engineering disciplines, where such solutions are crucial for advancing theoretical and practical applications. We propose a novel framework that utilizes LLMs in an evolutionary search methodology, augmented by a dynamic knowledge library that integrates and refines insights in an open-ended manner. This approach aims to tackle the dual challenges of efficiently navigating complex symbolic representation spaces and leveraging both existing and newly generated knowledge to foster open-ended innovation. By enabling LLMs to interact with and expand upon a knowledge library, we facilitate the continuous generation of novel solutions in diverse forms such as language, code, and mathematical expressions. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing AI in the perpetual pursuit of scientific and engineering breakthroughs. We have open-sourced our code and data, please visit https://github.com/pgg3/CoEvo for more information.

Vision transformers have shown unprecedented levels of performance in tackling various visual perception tasks in recent years. However, the architectural and computational complexity of such network architectures have made them challenging to deploy in real-world applications with high-throughput, low-memory requirements. As such, there has been significant research recently on the design of efficient vision transformer architectures. In this study, we explore the generation of fast vision transformer architecture designs via generative architecture search (GAS) to achieve a strong balance between accuracy and architectural and computational efficiency. Through this generative architecture search process, we create TurboViT, a highly efficient hierarchical vision transformer architecture design that is generated around mask unit attention and Q-pooling design patterns. The resulting TurboViT architecture design achieves significantly lower architectural computational complexity (>2.47times smaller than FasterViT-0 while achieving same accuracy) and computational complexity (>3.4times fewer FLOPs and 0.9% higher accuracy than MobileViT2-2.0) when compared to 10 other state-of-the-art efficient vision transformer network architecture designs within a similar range of accuracy on the ImageNet-1K dataset. Furthermore, TurboViT demonstrated strong inference latency and throughput in both low-latency and batch processing scenarios (>3.21times lower latency and >3.18times higher throughput compared to FasterViT-0 for low-latency scenario). These promising results demonstrate the efficacy of leveraging generative architecture search for generating efficient transformer architecture designs for high-throughput scenarios.

Modern Vision-Language Models (VLMs) have achieved impressive performance in various tasks, yet they often struggle with compositional reasoning, the ability to decompose and recombine concepts to solve novel problems. While neuro-symbolic approaches offer a promising direction, they are typically constrained by crisp logical execution or predefined predicates, which limit flexibility. In this work, we introduce NePTune, a neuro-symbolic framework that overcomes these limitations through a hybrid execution model that integrates the perception capabilities of foundation vision models with the compositional expressiveness of symbolic reasoning. NePTune dynamically translates natural language queries into executable Python programs that blend imperative control flow with soft logic operators capable of reasoning over VLM-generated uncertainty. Operating in a training-free manner, NePTune, with a modular design, decouples perception from reasoning, yet its differentiable operations support fine-tuning. We evaluate NePTune on multiple visual reasoning benchmarks and various domains, utilizing adversarial tests, and demonstrate a significant improvement over strong base models, as well as its effective compositional generalization and adaptation capabilities in novel environments.

We introduce Motif-2-12.7B, a new open-weight foundation model that pushes the efficiency frontier of large language models by combining architectural innovation with system-level optimization. Designed for scalable language understanding and robust instruction generalization under constrained compute budgets, Motif-2-12.7B builds upon Motif-2.6B with the integration of Grouped Differential Attention (GDA), which improves representational efficiency by disentangling signal and noise-control attention pathways. The model is pre-trained on 5.5 trillion tokens spanning diverse linguistic, mathematical, scientific, and programming domains using a curriculum-driven data scheduler that gradually changes the data composition ratio. The training system leverages the MuonClip optimizer alongside custom high-performance kernels, including fused PolyNorm activations and the Parallel Muon algorithm, yielding significant throughput and memory efficiency gains in large-scale distributed environments. Post-training employs a three-stage supervised fine-tuning pipeline that successively enhances general instruction adherence, compositional understanding, and linguistic precision. Motif-2-12.7B demonstrates competitive performance across diverse benchmarks, showing that thoughtful architectural scaling and optimized training design can rival the capabilities of much larger models.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

While Multimodal Large Language Models (MLLMs) excel at general vision-language tasks, visuospatial cognition - reasoning about spatial layouts, relations, and dynamics - remains a significant challenge. Existing models often lack the necessary architectural components and specialized training data for fine-grained spatial understanding. We introduce ViCA2 (Visuospatial Cognitive Assistant 2), a novel MLLM designed to enhance spatial reasoning. ViCA2 features a dual vision encoder architecture integrating SigLIP for semantics and Hiera for spatial structure, coupled with a token ratio control mechanism for efficiency. We also developed ViCA-322K, a new large-scale dataset with over 322,000 spatially grounded question-answer pairs for targeted instruction tuning. On the challenging VSI-Bench benchmark, our ViCA2-7B model achieves a state-of-the-art average score of 56.8, significantly surpassing larger open-source models (e.g., LLaVA-NeXT-Video-72B, 40.9) and leading proprietary models (Gemini-1.5 Pro, 45.4). This demonstrates the effectiveness of our approach in achieving strong visuospatial intelligence with a compact model. We release ViCA2, its codebase, and the ViCA-322K dataset to facilitate further research.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .