Daily Papers

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate their use. First, we prove that any restoration algorithm that attains perfect perceptual quality and whose outputs are consistent with the input must be a posterior sampler, and is thus required to be stochastic. Second, we illustrate that while deterministic restoration algorithms may attain high perceptual quality, this can be achieved only by filling up the space of all possible source images using an extremely sensitive mapping, which makes them highly vulnerable to adversarial attacks. Indeed, we show that enforcing deterministic models to be robust to such attacks profoundly hinders their perceptual quality, while robustifying stochastic models hardly influences their perceptual quality, and improves their output variability. These findings provide a motivation to foster progress in stochastic restoration methods, paving the way to better recovery algorithms.

The acute phase of the Covid-19 pandemic has made apparent the need for decision support based upon accurate epidemic modeling. This process is substantially hampered by under-reporting of cases and related data incompleteness issues. In this article we adopt the Bayesian paradigm and synthesize publicly available data via a discrete-time stochastic epidemic modeling framework. The models allow for estimating the total number of infections while accounting for the endemic phase of the pandemic. We assess the prediction of the infection rate utilizing mobility information, notably the principal components of the mobility data. We evaluate variational Bayes in this context and find that Hamiltonian Monte Carlo offers a robust inference alternative for such models. We elaborate upon vector analysis of the epidemic dynamics, thus enriching the traditional tools used for decision making. In particular, we show how certain 2-dimensional plots on the phase plane may yield intuitive information regarding the speed and the type of transmission dynamics. We investigate the potential of a two-stage analysis as a consequence of cutting feedback, for inference on certain functionals of the model parameters. Finally, we show that a point mass on critical parameters is overly restrictive and investigate informative priors as a suitable alternative.

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

Modern deep learning systems are typically deployed as open-loop function approximators: they map inputs to outputs in a single pass, without regulating how much computation or explanatory effort is spent on a given case. In safety-critical settings, this is brittle: easy and ambiguous inputs receive identical processing, and uncertainty is only read off retrospectively from raw probabilities. We introduce the Surgical Cognitive Interpreter (SCI), a lightweight closed-loop metacognitive control layer that wraps an existing stochastic model and turns prediction into an iterative process. SCI monitors a scalar interpretive state SP(t), here instantiated as a normalized entropy-based confidence signal, and adaptively decides whether to stop, continue sampling, or abstain. The goal is not to improve accuracy per se, but to regulate interpretive error ΔSP and expose a safety signal that tracks when the underlying model is likely to fail. We instantiate SCI around Monte Carlo dropout classifiers in three domains: vision (MNIST digits), medical time series (MIT-BIH arrhythmia), and industrial condition monitoring (rolling-element bearings). In all cases, the controller allocates more inference steps to misclassified inputs than to correct ones (up to about 3-4x on MNIST and bearings, and 1.4x on MIT-BIH). The resulting ΔSP acts as a usable safety signal for detecting misclassifications (AUROC 0.63 on MNIST, 0.70 on MIT-BIH, 0.86 on bearings). Code and reproducibility: https://github.com/vishal-1344/sci

Real-world data can be multimodal distributed, e.g., data describing the opinion divergence in a community, the interspike interval distribution of neurons, and the oscillators natural frequencies. Generating multimodal distributed real-world data has become a challenge to existing generative adversarial networks (GANs). For example, neural stochastic differential equations (Neural SDEs), treated as infinite-dimensional GANs, have demonstrated successful performance mainly in generating unimodal time series data. In this paper, we propose a novel time series generator, named directed chain GANs (DC-GANs), which inserts a time series dataset (called a neighborhood process of the directed chain or input) into the drift and diffusion coefficients of the directed chain SDEs with distributional constraints. DC-GANs can generate new time series of the same distribution as the neighborhood process, and the neighborhood process will provide the key step in learning and generating multimodal distributed time series. The proposed DC-GANs are examined on four datasets, including two stochastic models from social sciences and computational neuroscience, and two real-world datasets on stock prices and energy consumption. To our best knowledge, DC-GANs are the first work that can generate multimodal time series data and consistently outperforms state-of-the-art benchmarks with respect to measures of distribution, data similarity, and predictive ability.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, CoLSTIM, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a d-dimensional feature vector, we show that CoLSTIM achieves a regret of order tilde O( dT) after T learning rounds. Additionally, we also establish the optimality of CoLSTIM by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

We prove existence of weak and strong solutions and uniqueness for a viscous dyadic model driven by additive white noise in time using a path-wise approach. Existence of invariant measures also established and a simple balance relation among the mean rates of energy injection, dissipation and flux is derived and we investigate the asymptotic exponents zeta_{p} of the p-order structure functions.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

With the growing use of voice-activated systems and speech recognition technologies, the danger of backdoor attacks on audio data has grown significantly. This research looks at a specific type of attack, known as a Stochastic investment-based backdoor attack (MarketBack), in which adversaries strategically manipulate the stylistic properties of audio to fool speech recognition systems. The security and integrity of machine learning models are seriously threatened by backdoor attacks, in order to maintain the reliability of audio applications and systems, the identification of such attacks becomes crucial in the context of audio data. Experimental results demonstrated that MarketBack is feasible to achieve an average attack success rate close to 100% in seven victim models when poisoning less than 1% of the training data.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

This paper investigates the performance of network non-orthogonal multiple access (N-NOMA) in a downlink coordinated multi-point (CoMP) system. In the considered N-NOMA scheme, multiple base stations (BSs) cooperatively serve a CoMP user, meanwhile, each BS serves additional NOMA users by occupying the same resource block allocated to the CoMP user. The locations of the BSs and users are modeled by stochastic geometric models and the interference from the whole network is considered. Through rigorous derivations, the outage probabilities achieved by the CoMP and NOMA users are obtained, respectively. Numerical results are provided to verify the accuracy of the analytical results and also demonstrate the superior performance of N-NOMA compared to orthogonal multiple access (OMA) based CoMP scheme.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs) and driven by c\`adl\`ag rough paths. Our formalism is general enough to allow for potential jumps to be present both in the solution trajectories as well as in the driving noise. We then identify a set of sufficient conditions ensuring the existence of pathwise gradients of solution trajectories and event times with respect to the network's parameters and show how these gradients satisfy a recursive relation. Furthermore, we introduce a general-purpose loss function defined by means of a new class of signature kernels indexed on c\`adl\`ag rough paths and use it to train SSNNs as generative models. We provide an end-to-end autodifferentiable solver for Event SDEs and make its implementation available as part of the diffrax library. Our framework is, to our knowledge, the first enabling gradient-based training of SSNNs with noise affecting both the spike timing and the network's dynamics.

To generate evidence regarding the safety and efficacy of artificial intelligence (AI) enabled medical devices, AI models need to be evaluated on a diverse population of patient cases, some of which may not be readily available. We propose an evaluation approach for testing medical imaging AI models that relies on in silico imaging pipelines in which stochastic digital models of human anatomy (in object space) with and without pathology are imaged using a digital replica imaging acquisition system to generate realistic synthetic image datasets. Here, we release M-SYNTH, a dataset of cohorts with four breast fibroglandular density distributions imaged at different exposure levels using Monte Carlo x-ray simulations with the publicly available Virtual Imaging Clinical Trial for Regulatory Evaluation (VICTRE) toolkit. We utilize the synthetic dataset to analyze AI model performance and find that model performance decreases with increasing breast density and increases with higher mass density, as expected. As exposure levels decrease, AI model performance drops with the highest performance achieved at exposure levels lower than the nominal recommended dose for the breast type.

Contents generated by recent advanced Text-to-Image (T2I) diffusion models are sometimes too imaginative for existing off-the-shelf dense predictors to estimate due to the immitigable domain gap. We introduce DMP, a pipeline utilizing pre-trained T2I models as a prior for dense prediction tasks. To address the misalignment between deterministic prediction tasks and stochastic T2I models, we reformulate the diffusion process through a sequence of interpolations, establishing a deterministic mapping between input RGB images and output prediction distributions. To preserve generalizability, we use low-rank adaptation to fine-tune pre-trained models. Extensive experiments across five tasks, including 3D property estimation, semantic segmentation, and intrinsic image decomposition, showcase the efficacy of the proposed method. Despite limited-domain training data, the approach yields faithful estimations for arbitrary images, surpassing existing state-of-the-art algorithms.

Learning how the world works is central to building AI agents that can adapt to complex environments. Traditional world models based on deep learning demand vast amounts of training data, and do not flexibly update their knowledge from sparse observations. Recent advances in program synthesis using Large Language Models (LLMs) give an alternate approach which learns world models represented as source code, supporting strong generalization from little data. To date, application of program-structured world models remains limited to natural language and grid-world domains. We introduce a novel program synthesis method for effectively modeling complex, non-gridworld domains by representing a world model as an exponentially-weighted product of programmatic experts (PoE-World) synthesized by LLMs. We show that this approach can learn complex, stochastic world models from just a few observations. We evaluate the learned world models by embedding them in a model-based planning agent, demonstrating efficient performance and generalization to unseen levels on Atari's Pong and Montezuma's Revenge. We release our code and display the learned world models and videos of the agent's gameplay at https://topwasu.github.io/poe-world.

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient (epsilon,delta)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with k nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) epsilon-DP algorithm would result in substantial error.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

Primordial Magnetic Fields (PMFs) -- magnetic fields originating in the early Universe and permeating the cosmological scales today -- can explain the observed microGauss-level magnetisation of galaxies and their clusters. In light of current and upcoming all-sky radio surveys, PMFs have drawn attention not only as major candidates for explaining the large-scale magnetisation of the Universe, but also as potential probes of early-Universe physics. In this paper, using cosmological simulations coupled with light-cone analysis, we study for the first time the imprints of the PMF structure on the mean rotation measure (RM) originating in the intergalactic medium (IGM), langle RM_{IGM}rangle. We introduce a new method for producing full-sky RM_{IGM} distributions and analyse the autocorrelation of RM_{IGM} on small and large angular scales; we find that PMF structures indeed show distinct signatures. The large-scale uniform model (characterised by an initially unlimited coherence scale) leads to correlations up to 90 degrees, while correlations for small-scale stochastic PMF models drop by factor of 100 at 0.17, 0.13 and 0.11 degrees angular scales, corresponding to 5.24, 4.03 and 3.52 Mpc scales (at z=2 redshift) for magnetic fields with comoving 3.49, 1.81, 1.00 Mpc/h coherence scales, respectively; the correlation amplitude of the PMF model with comoving sim 19 Mpc/h coherence scale drops only by factor of 10 at 1 degree (30.6 Mpc). These results suggests that improvements in the modelling of Galactic RM will be necessary to investigate the signature of large-scale correlated PMFs. A comparison of langle RM_{IGM}rangle redshift dependence obtained from our simulations with that from the LOFAR Two-metre Sky Survey shows agreement with our previous upper limits' estimates on the PMF strength derived from RM-rms analysis.

The iterative sampling procedure employed by diffusion models (DMs) often leads to significant inference latency. To address this, we propose Stochastic Consistency Distillation (SCott) to enable accelerated text-to-image generation, where high-quality generations can be achieved with just 1-2 sampling steps, and further improvements can be obtained by adding additional steps. In contrast to vanilla consistency distillation (CD) which distills the ordinary differential equation solvers-based sampling process of a pretrained teacher model into a student, SCott explores the possibility and validates the efficacy of integrating stochastic differential equation (SDE) solvers into CD to fully unleash the potential of the teacher. SCott is augmented with elaborate strategies to control the noise strength and sampling process of the SDE solver. An adversarial loss is further incorporated to strengthen the sample quality with rare sampling steps. Empirically, on the MSCOCO-2017 5K dataset with a Stable Diffusion-V1.5 teacher, SCott achieves an FID (Frechet Inceptio Distance) of 22.1, surpassing that (23.4) of the 1-step InstaFlow (Liu et al., 2023) and matching that of 4-step UFOGen (Xue et al., 2023b). Moreover, SCott can yield more diverse samples than other consistency models for high-resolution image generation (Luo et al., 2023a), with up to 16% improvement in a qualified metric. The code and checkpoints are coming soon.

We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs in state-of-the-art image and video generative models--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation, particularly variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

Symbolic world modeling requires inferring and representing an environment's transitional dynamics as an executable program. Prior work has focused on largely deterministic environments with abundant interaction data, simple mechanics, and human guidance. We address a more realistic and challenging setting, learning in a complex, stochastic environment where the agent has only "one life" to explore a hostile environment without human guidance. We introduce OneLife, a framework that models world dynamics through conditionally-activated programmatic laws within a probabilistic programming framework. Each law operates through a precondition-effect structure, activating in relevant world states. This creates a dynamic computation graph that routes inference and optimization only through relevant laws, avoiding scaling challenges when all laws contribute to predictions about a complex, hierarchical state, and enabling the learning of stochastic dynamics even with sparse rule activation. To evaluate our approach under these demanding constraints, we introduce a new evaluation protocol that measures (a) state ranking, the ability to distinguish plausible future states from implausible ones, and (b) state fidelity, the ability to generate future states that closely resemble reality. We develop and evaluate our framework on Crafter-OO, our reimplementation of the Crafter environment that exposes a structured, object-oriented symbolic state and a pure transition function that operates on that state alone. OneLife can successfully learn key environment dynamics from minimal, unguided interaction, outperforming a strong baseline on 16 out of 23 scenarios tested. We also test OneLife's planning ability, with simulated rollouts successfully identifying superior strategies. Our work establishes a foundation for autonomously constructing programmatic world models of unknown, complex environments.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

We propose Reference-Based Modulation (RB-Modulation), a new plug-and-play solution for training-free personalization of diffusion models. Existing training-free approaches exhibit difficulties in (a) style extraction from reference images in the absence of additional style or content text descriptions, (b) unwanted content leakage from reference style images, and (c) effective composition of style and content. RB-Modulation is built on a novel stochastic optimal controller where a style descriptor encodes the desired attributes through a terminal cost. The resulting drift not only overcomes the difficulties above, but also ensures high fidelity to the reference style and adheres to the given text prompt. We also introduce a cross-attention-based feature aggregation scheme that allows RB-Modulation to decouple content and style from the reference image. With theoretical justification and empirical evidence, our framework demonstrates precise extraction and control of content and style in a training-free manner. Further, our method allows a seamless composition of content and style, which marks a departure from the dependency on external adapters or ControlNets.

Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, we develop a speech benchmark of popular temporal LVMs and compare them against state-of-the-art deterministic models. We report the likelihood, which is a much used metric in the image domain, but rarely, or incomparably, reported for speech models. To assess the quality of the learned representations, we also compare their usefulness for phoneme recognition. Finally, we adapt the Clockwork VAE, a state-of-the-art temporal LVM for video generation, to the speech domain. Despite being autoregressive only in latent space, we find that the Clockwork VAE can outperform previous LVMs and reduce the gap to deterministic models by using a hierarchy of latent variables.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

Stochastic human motion prediction (HMP) has generally been tackled with generative adversarial networks and variational autoencoders. Most prior works aim at predicting highly diverse movements in terms of the skeleton joints' dispersion. This has led to methods predicting fast and motion-divergent movements, which are often unrealistic and incoherent with past motion. Such methods also neglect contexts that need to anticipate diverse low-range behaviors, or actions, with subtle joint displacements. To address these issues, we present BeLFusion, a model that, for the first time, leverages latent diffusion models in HMP to sample from a latent space where behavior is disentangled from pose and motion. As a result, diversity is encouraged from a behavioral perspective. Thanks to our behavior coupler's ability to transfer sampled behavior to ongoing motion, BeLFusion's predictions display a variety of behaviors that are significantly more realistic than the state of the art. To support it, we introduce two metrics, the Area of the Cumulative Motion Distribution, and the Average Pairwise Distance Error, which are correlated to our definition of realism according to a qualitative study with 126 participants. Finally, we prove BeLFusion's generalization power in a new cross-dataset scenario for stochastic HMP.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Recent diffusion-based generative models achieve remarkable results by training on massive datasets, yet this practice raises concerns about memorization and copyright infringement. A proposed remedy is to train exclusively on noisy data with potential copyright issues, ensuring the model never observes original content. However, through the lens of deconvolution theory, we show that although it is theoretically feasible to learn the data distribution from noisy samples, the practical challenge of collecting sufficient samples makes successful learning nearly unattainable. To overcome this limitation, we propose to pretrain the model with a small fraction of clean data to guide the deconvolution process. Combined with our Stochastic Forward--Backward Deconvolution (SFBD) method, we attain FID 6.31 on CIFAR-10 with just 4% clean images (and 3.58 with 10%). We also provide theoretical guarantees that SFBD learns the true data distribution. These results underscore the value of limited clean pretraining, or pretraining on similar datasets. Empirical studies further validate and enrich our findings.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

Semantic segmentation has made significant progress in recent years thanks to deep neural networks, but the common objective of generating a single segmentation output that accurately matches the image's content may not be suitable for safety-critical domains such as medical diagnostics and autonomous driving. Instead, multiple possible correct segmentation maps may be required to reflect the true distribution of annotation maps. In this context, stochastic semantic segmentation methods must learn to predict conditional distributions of labels given the image, but this is challenging due to the typically multimodal distributions, high-dimensional output spaces, and limited annotation data. To address these challenges, we propose a conditional categorical diffusion model (CCDM) for semantic segmentation based on Denoising Diffusion Probabilistic Models. Our model is conditioned to the input image, enabling it to generate multiple segmentation label maps that account for the aleatoric uncertainty arising from divergent ground truth annotations. Our experimental results show that CCDM achieves state-of-the-art performance on LIDC, a stochastic semantic segmentation dataset, and outperforms established baselines on the classical segmentation dataset Cityscapes.

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as a stochastic encoder of the data. We develop stochastic back-propagation -- rules for back-propagation through stochastic variables -- and use this to develop an algorithm that allows for joint optimisation of the parameters of both the generative and recognition model. We demonstrate on several real-world data sets that the model generates realistic samples, provides accurate imputations of missing data and is a useful tool for high-dimensional data visualisation.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Classifier-free Guidance (CFG) is a widely used technique in modern diffusion models for enhancing sample quality and prompt adherence. However, through an empirical analysis on Gaussian mixture modeling with a closed-form solution, we observe a discrepancy between the suboptimal results produced by CFG and the ground truth. The model's excessive reliance on these suboptimal predictions often leads to semantic incoherence and low-quality outputs. To address this issue, we first empirically demonstrate that the model's suboptimal predictions can be effectively refined using sub-networks of the model itself. Building on this insight, we propose S^2-Guidance, a novel method that leverages stochastic block-dropping during the forward process to construct stochastic sub-networks, effectively guiding the model away from potential low-quality predictions and toward high-quality outputs. Extensive qualitative and quantitative experiments on text-to-image and text-to-video generation tasks demonstrate that S^2-Guidance delivers superior performance, consistently surpassing CFG and other advanced guidance strategies. Our code will be released.

Retrieval-augmented generation (RAG) has become a widely recognized paradigm to combine parametric memory with non-parametric memories. An RAG model consists of two serial connecting components (retriever and generator). A major challenge in end-to-end optimization of the RAG model is that marginalization over relevant passages (modeled as discrete latent variables) from a knowledge base is required. Traditional top-K marginalization and variational RAG (VRAG) suffer from biased or high-variance gradient estimates. In this paper, we propose and develop joint stochastic approximation (JSA) based end-to-end training of RAG, which is referred to as JSA-RAG. The JSA algorithm is a stochastic extension of the EM (expectation-maximization) algorithm and is particularly powerful in estimating discrete latent variable models. Extensive experiments are conducted on five datasets for two tasks (open-domain question answering, knowledge-grounded dialogs) and show that JSA-RAG significantly outperforms both vanilla RAG and VRAG. Further analysis shows the efficacy of JSA-RAG from the perspectives of generation, retrieval, and low-variance gradient estimate.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

The self-attention revolution allowed generative language models to scale and achieve increasingly impressive abilities. Such models - commonly referred to as Large Language Models (LLMs) - have recently gained prominence with the general public, thanks to conversational fine-tuning, putting their behavior in line with public expectations regarding AI. This prominence amplified prior concerns regarding the misuse of LLMs and led to the emergence of numerous tools to detect LLMs in the wild. Unfortunately, most such tools are critically flawed. While major publications in the LLM detectability field suggested that LLMs were easy to detect with fine-tuned autoencoders, the limitations of their results are easy to overlook. Specifically, they assumed publicly available generative models without fine-tunes or non-trivial prompts. While the importance of these assumptions has been demonstrated, until now, it remained unclear how well such detection could be countered. Here, we show that an attacker with access to such detectors' reference human texts and output not only evades detection but can fully frustrate the detector training - with a reasonable budget and all its outputs labeled as such. Achieving it required combining common "reinforcement from critic" loss function modification and AdamW optimizer, which led to surprisingly good fine-tuning generalization. Finally, we warn against the temptation to transpose the conclusions obtained in RNN-driven text GANs to LLMs due to their better representative ability. These results have critical implications for the detection and prevention of malicious use of generative language models, and we hope they will aid the designers of generative models and detectors.

Recent Vision Mamba models not only have much lower complexity for processing higher resolution images and longer videos but also the competitive performance with Vision Transformers (ViTs). However, they are stuck into overfitting and thus only present up to base size (about 80M). It is still unclear how vanilla Vision Mamba (Vim) can be efficiently scaled up to larger sizes, which is essentially for further exploitation. In this paper, we propose a stochastic layer-wise shuffle regularization, which empowers successfully scaling non-hierarchical Vision Mamba to a large size (about 300M) in a supervised setting. Specifically, our base and large-scale ShuffleMamba models can outperform the supervised ViTs of similar size by 0.8\% and 1.0\% classification accuracy on ImageNet1k, respectively, without auxiliary data. When evaluated on the ADE20K semantic segmentation and COCO detection tasks, our ShuffleMamba models also show significant improvements. Without bells and whistles, the stochastic layer-wise shuffle has the following highlights: (1) Plug and play: it does not change model architectures and will be omitted in inference. (2) Simple but effective: it can improve the overfitting in Vim training and only introduce random token permutation operations. (3) Intuitive: the token sequences in deeper layers are more likely to be shuffled as they are expected to be more semantic and less sensitive to patch positions. Code and models will be available at https://github.com/huangzizheng01/ShuffleMamba.

Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whose dynamics are governed in a latent space by a residual update rule. This first-order scheme is motivated by discretization schemes of differential equations. It naturally models video dynamics as it allows our simpler, more interpretable, latent model to outperform prior state-of-the-art methods on challenging datasets.

Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and hyperparameters. Our process trains a neural network to output approximately optimal weights as a function of hyperparameters. We show that our technique converges to locally optimal weights and hyperparameters for sufficiently large hypernetworks. We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters.

Large language models (LLMs) possess impressive linguistic capabilities but often fail to faithfully retain factual knowledge, leading to hallucinations and unreliable outputs. Understanding LLMs' knowledge deficiencies by exhaustively evaluating against full-scale knowledge bases is computationally prohibitive, especially for closed-weight models. We propose stochastic error ascent (SEA), a scalable and efficient framework for discovering knowledge deficiencies (errors) in closed-weight LLMs under a strict query budget. Rather than naively probing all knowledge candidates, SEA formulates error discovery as a stochastic optimization process: it iteratively retrieves new high-error candidates by leveraging the semantic similarity to previously observed failures. To further enhance search efficiency and coverage, SEA employs hierarchical retrieval across document and paragraph levels, and constructs a relation directed acyclic graph to model error propagation and identify systematic failure modes. Empirically, SEA uncovers 40.7x more knowledge errors than Automated Capability Discovery and 26.7% more than AutoBencher, while reducing the cost-per-error by 599x and 9x, respectively. Human evaluation confirms the high quality of generated questions, while ablation and convergence analyses validate the contribution of each component in SEA. Further analysis on the discovered errors reveals correlated failure patterns across LLM families and recurring deficits, highlighting the need for better data coverage and targeted fine-tuning in future LLM development.

Diffusion models have shown a great ability at bridging the performance gap between predictive and generative approaches for speech enhancement. We have shown that they may even outperform their predictive counterparts for non-additive corruption types or when they are evaluated on mismatched conditions. However, diffusion models suffer from a high computational burden, mainly as they require to run a neural network for each reverse diffusion step, whereas predictive approaches only require one pass. As diffusion models are generative approaches they may also produce vocalizing and breathing artifacts in adverse conditions. In comparison, in such difficult scenarios, predictive models typically do not produce such artifacts but tend to distort the target speech instead, thereby degrading the speech quality. In this work, we present a stochastic regeneration approach where an estimate given by a predictive model is provided as a guide for further diffusion. We show that the proposed approach uses the predictive model to remove the vocalizing and breathing artifacts while producing very high quality samples thanks to the diffusion model, even in adverse conditions. We further show that this approach enables to use lighter sampling schemes with fewer diffusion steps without sacrificing quality, thus lifting the computational burden by an order of magnitude. Source code and audio examples are available online (https://uhh.de/inf-sp-storm).

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

This paper aims to deal with the ignored real-world complexities in prior work on human motion forecasting, emphasizing the social properties of multi-person motion, the diversity of motion and social interactions, and the complexity of articulated motion. To this end, we introduce a novel task of stochastic multi-person 3D motion forecasting. We propose a dual-level generative modeling framework that separately models independent individual motion at the local level and social interactions at the global level. Notably, this dual-level modeling mechanism can be achieved within a shared generative model, through introducing learnable latent codes that represent intents of future motion and switching the codes' modes of operation at different levels. Our framework is general; we instantiate it with different generative models, including generative adversarial networks and diffusion models, and various multi-person forecasting models. Extensive experiments on CMU-Mocap, MuPoTS-3D, and SoMoF benchmarks show that our approach produces diverse and accurate multi-person predictions, significantly outperforming the state of the art.

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

Sparsely activated models (SAMs), such as Mixture-of-Experts (MoE), can easily scale to have outrageously large amounts of parameters without significant increase in computational cost. However, SAMs are reported to be parameter inefficient such that larger models do not always lead to better performance. While most on-going research focuses on improving SAMs models by exploring methods of routing inputs to experts, our analysis reveals that such research might not lead to the solution we expect, i.e., the commonly-used routing methods based on gating mechanisms do not work better than randomly routing inputs to experts. In this paper, we propose a new expert-based model, THOR (Transformer witH StOchastic ExpeRts). Unlike classic expert-based models, such as the Switch Transformer, experts in THOR are randomly activated for each input during training and inference. THOR models are trained using a consistency regularized loss, where experts learn not only from training data but also from other experts as teachers, such that all the experts make consistent predictions. We validate the effectiveness of THOR on machine translation tasks. Results show that THOR models are more parameter efficient in that they significantly outperform the Transformer and MoE models across various settings. For example, in multilingual translation, THOR outperforms the Switch Transformer by 2 BLEU scores, and obtains the same BLEU score as that of a state-of-the-art MoE model that is 18 times larger. Our code is publicly available at: https://github.com/microsoft/Stochastic-Mixture-of-Experts.

Recent developments in the field of model-based RL have proven successful in a range of environments, especially ones where planning is essential. However, such successes have been limited to deterministic fully-observed environments. We present a new approach that handles stochastic and partially-observable environments. Our key insight is to use discrete autoencoders to capture the multiple possible effects of an action in a stochastic environment. We use a stochastic variant of Monte Carlo tree search to plan over both the agent's actions and the discrete latent variables representing the environment's response. Our approach significantly outperforms an offline version of MuZero on a stochastic interpretation of chess where the opponent is considered part of the environment. We also show that our approach scales to DeepMind Lab, a first-person 3D environment with large visual observations and partial observability.

Multi-agent systems (MAS) based on Large Language Models (LLMs) have the potential to solve tasks that are beyond the reach of any single LLM. However, this potential can only be realized when the collaboration mechanism between agents is optimized. Specifically, optimizing the communication structure between agents is critical for fruitful collaboration. Most existing approaches rely on fixed topologies, pretrained graph generators, optimization over edges, or employ external LLM judges, thereby adding to the complexity. In this work, we introduce a response-conditioned framework that adapts communication on-the-fly. Agents independently generate responses to the user query and assess peer contributions using an approximation of the Shapley value. A directed acyclic graph (DAG) is then constructed to regulate the propagation of the responses among agents, which ensures stable and efficient message transmission from high-contributing agents to others. This graph is dynamically updated based on the agent responses from the previous collaboration round. Since the proposed framework enables the self-organization of agents without additional supervision or training, we refer to it as SelfOrg. The SelfOrg framework goes beyond task- and query-level optimization and takes into account the stochastic nature of agent responses. Experiments with both strong and weak LLM backends demonstrate robust performance, with significant gains in the weak regime where prior methods collapse. We also theoretically show that multiple agents increase the chance of correctness and that the correct responses naturally dominate the information flow.

Recent developments in generative AI have shone a spotlight on high-performance synthetic text generation technologies. The now wide availability and ease of use of such models highlights the urgent need to provide equally powerful technologies capable of identifying synthetic text. With this in mind, we draw inspiration from psychological studies which suggest that people can be driven by emotion and encode emotion in the text they compose. We hypothesize that pretrained language models (PLMs) have an affective deficit because they lack such an emotional driver when generating text and consequently may generate synthetic text which has affective incoherence i.e. lacking the kind of emotional coherence present in human-authored text. We subsequently develop an emotionally aware detector by fine-tuning a PLM on emotion. Experiment results indicate that our emotionally-aware detector achieves improvements across a range of synthetic text generators, various sized models, datasets, and domains. Finally, we compare our emotionally-aware synthetic text detector to ChatGPT in the task of identification of its own output and show substantial gains, reinforcing the potential of emotion as a signal to identify synthetic text. Code, models, and datasets are available at https: //github.com/alanagiasi/emoPLMsynth

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

In our opinion the exuberance surrounding the relative success of data-driven large language models (LLMs) is slightly misguided and for several reasons (i) LLMs cannot be relied upon for factual information since for LLMs all ingested text (factual or non-factual) was created equal; (ii) due to their subsymbolic na-ture, whatever 'knowledge' these models acquire about language will always be buried in billions of microfeatures (weights), none of which is meaningful on its own; and (iii) LLMs will often fail to make the correct inferences in several linguistic contexts (e.g., nominal compounds, copredication, quantifier scope ambi-guities, intensional contexts. Since we believe the relative success of data-driven large language models (LLMs) is not a reflection on the symbolic vs. subsymbol-ic debate but a reflection on applying the successful strategy of a bottom-up reverse engineering of language at scale, we suggest in this paper applying the effective bottom-up strategy in a symbolic setting resulting in symbolic, explainable, and ontologically grounded language models.

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Modern language models can generate high-quality short texts. However, they often meander or are incoherent when generating longer texts. These issues arise from the next-token-only language modeling objective. Recent work in self-supervised learning suggests that models can learn good latent representations via contrastive learning, which can be effective for discriminative tasks. Our work analyzes the application of contrastive representations for generative tasks, like long text generation. We propose one approach for leveraging constrastive representations, which we call Time Control (TC). TC first learns a contrastive representation of the target text domain, then generates text by decoding from these representations. Compared to domain-specific methods and fine-tuning GPT2 across a variety of text domains, TC performs competitively to methods specific for learning sentence representations on discourse coherence. On long text generation settings, TC preserves the text structure both in terms of ordering (up to +15% better) and text length consistency (up to +90% better).

Attention based models such as Transformers involve pairwise interactions between data points, modeled with a learnable attention matrix. Importantly, this attention matrix is normalized with the SoftMax operator, which makes it row-wise stochastic. In this paper, we propose instead to use Sinkhorn's algorithm to make attention matrices doubly stochastic. We call the resulting model a Sinkformer. We show that the row-wise stochastic attention matrices in classical Transformers get close to doubly stochastic matrices as the number of epochs increases, justifying the use of Sinkhorn normalization as an informative prior. On the theoretical side, we show that, unlike the SoftMax operation, this normalization makes it possible to understand the iterations of self-attention modules as a discretized gradient-flow for the Wasserstein metric. We also show in the infinite number of samples limit that, when rescaling both attention matrices and depth, Sinkformers operate a heat diffusion. On the experimental side, we show that Sinkformers enhance model accuracy in vision and natural language processing tasks. In particular, on 3D shapes classification, Sinkformers lead to a significant improvement.

In a systematic way, we investigate a widely asked question: Do LLMs really understand what they say?, which relates to the more familiar term Stochastic Parrot. To this end, we propose a summative assessment over a carefully designed physical concept understanding task, PhysiCo. Our task alleviates the memorization issue via the usage of grid-format inputs that abstractly describe physical phenomena. The grids represents varying levels of understanding, from the core phenomenon, application examples to analogies to other abstract patterns in the grid world. A comprehensive study on our task demonstrates: (1) state-of-the-art LLMs, including GPT-4o, o1 and Gemini 2.0 flash thinking, lag behind humans by ~40%; (2) the stochastic parrot phenomenon is present in LLMs, as they fail on our grid task but can describe and recognize the same concepts well in natural language; (3) our task challenges the LLMs due to intrinsic difficulties rather than the unfamiliar grid format, as in-context learning and fine-tuning on same formatted data added little to their performance.

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic policy, yet the most cost-effective diffusion samplers are based on deterministic ODEs. Recent work addresses this issue by using inefficient SDE-based samplers to induce stochasticity, but this reliance on model-agnostic Gaussian noise leads to slow convergence. To resolve this conflict, we propose Direct Group Preference Optimization (DGPO), a new online RL algorithm that dispenses with the policy-gradient framework entirely. DGPO learns directly from group-level preferences, which utilize relative information of samples within groups. This design eliminates the need for inefficient stochastic policies, unlocking the use of efficient deterministic ODE samplers and faster training. Extensive results show that DGPO trains around 20 times faster than existing state-of-the-art methods and achieves superior performance on both in-domain and out-of-domain reward metrics. Code is available at https://github.com/Luo-Yihong/DGPO.

The integration of online reinforcement learning (RL) into diffusion and flow models has recently emerged as a promising approach for aligning generative models with human preferences. Stochastic sampling via Stochastic Differential Equations (SDE) is employed during the denoising process to generate diverse denoising directions for RL exploration. While existing methods effectively explore potential high-value samples, they suffer from sub-optimal preference alignment due to sparse and narrow reward signals. To address these challenges, we propose a novel Granular-GRPO (G^2RPO ) framework that achieves precise and comprehensive reward assessments of sampling directions in reinforcement learning of flow models. Specifically, a Singular Stochastic Sampling strategy is introduced to support step-wise stochastic exploration while enforcing a high correlation between the reward and the injected noise, thereby facilitating a faithful reward for each SDE perturbation. Concurrently, to eliminate the bias inherent in fixed-granularity denoising, we introduce a Multi-Granularity Advantage Integration module that aggregates advantages computed at multiple diffusion scales, producing a more comprehensive and robust evaluation of the sampling directions. Experiments conducted on various reward models, including both in-domain and out-of-domain evaluations, demonstrate that our G^2RPO significantly outperforms existing flow-based GRPO baselines,highlighting its effectiveness and robustness.

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.

We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw. This strategy circumvents the optimization problem associated with RELU, namely, the constant shape for negative inputs that prevents the gradient flow. We leverage this strategy in two ways: (1) We use stochastic activations during pre-training and fine-tune the model with RELU, which is used at inference time to provide sparse latent vectors. This reduces the inference FLOPs and translates into a significant speedup in the CPU. Interestingly, this leads to much better results than training from scratch with the RELU activation function. (2) We evaluate stochastic activations for generation. This strategy performs reasonably well: it is only slightly inferior to the best deterministic non-linearity, namely SILU combined with temperature scaling. This offers an alternative to existing strategies by providing a controlled way to increase the diversity of the generated text.

Large Language Models (LLMs) have gained widespread popularity across diverse domains involving text generation, summarization, and various natural language processing tasks. Despite their inherent limitations, LLM-based designs have shown promising capabilities in planning and navigating open-world scenarios. This paper introduces a novel application of pre-trained LLMs as agents within cybersecurity network environments, focusing on their utility for sequential decision-making processes. We present an approach wherein pre-trained LLMs are leveraged as attacking agents in two reinforcement learning environments. Our proposed agents demonstrate similar or better performance against state-of-the-art agents trained for thousands of episodes in most scenarios and configurations. In addition, the best LLM agents perform similarly to human testers of the environment without any additional training process. This design highlights the potential of LLMs to efficiently address complex decision-making tasks within cybersecurity. Furthermore, we introduce a new network security environment named NetSecGame. The environment is designed to eventually support complex multi-agent scenarios within the network security domain. The proposed environment mimics real network attacks and is designed to be highly modular and adaptable for various scenarios.

Large reasoning models (LRMs) achieve strong reasoning performance by emitting long chains of thought. Yet, these verbose traces slow down inference and often drift into unnecessary detail, known as the overthinking phenomenon. To better understand LRMs' behavior, we systematically analyze the token-level misalignment between reasoning and non-reasoning models. While it is expected that their primary difference lies in the stylistic "thinking cues", LRMs uniquely exhibit two pivotal, previously under-explored phenomena: a Global Misalignment Rebound, where their divergence from non-reasoning models persists or even grows as response length increases, and more critically, a Local Misalignment Diminish, where the misalignment concentrates at the "thinking cues" each sentence starts with but rapidly declines in the remaining of the sentence. Motivated by the Local Misalignment Diminish, we propose FoReaL-Decoding, a collaborative fast-slow thinking decoding method for cost-quality trade-off. In FoReaL-Decoding, a Leading model leads the first few tokens for each sentence, and then a weaker draft model completes the following tokens to the end of each sentence. FoReaL-Decoding adopts a stochastic gate to smoothly interpolate between the small and the large model. On four popular math-reasoning benchmarks (AIME24, GPQA-Diamond, MATH500, AMC23), FoReaL-Decoding reduces theoretical FLOPs by 30 to 50% and trims CoT length by up to 40%, while preserving 86 to 100% of model performance. These results establish FoReaL-Decoding as a simple, plug-and-play route to controllable cost-quality trade-offs in reasoning-centric tasks.

Large Language Models (LLMs), with billions of parameters, present significant challenges for full finetuning due to the high computational demands, memory requirements, and impracticality of many real-world applications. When faced with limited computational resources or small datasets, updating all model parameters can often result in overfitting. To address this, lightweight finetuning techniques have been proposed, like learning low-rank adapter layers. These methods aim to train only a few additional parameters combined with the base model, which remains frozen, reducing resource usage and mitigating overfitting risks. In this work, we propose an adaptor model based on stochastic gates that simultaneously sparsify the frozen base model with task-specific adaptation. Our method comes with a small number of trainable parameters and allows us to speed up the base model inference with competitive accuracy. We evaluate it in additional variants by equipping it with additional low-rank parameters and comparing it to several recent baselines. Our results show that the proposed method improves the finetuned model accuracy comparatively to the several baselines and allows the removal of up to 20-40\% without significant accuracy loss.

Recent advancements in Large Language Models empower them to follow freeform instructions, including imitating generic or specific demographic personas in conversations. We define generic personas to represent demographic groups, such as "an Asian person", whereas specific personas may take the form of specific popular Asian names like "Yumi". While the adoption of personas enriches user experiences by making dialogue systems more engaging and approachable, it also casts a shadow of potential risk by exacerbating social biases within model responses, thereby causing societal harm through interactions with users. In this paper, we systematically study "persona biases", which we define to be the sensitivity of dialogue models' harmful behaviors contingent upon the personas they adopt. We categorize persona biases into biases in harmful expression and harmful agreement, and establish a comprehensive evaluation framework to measure persona biases in five aspects: Offensiveness, Toxic Continuation, Regard, Stereotype Agreement, and Toxic Agreement. Additionally, we propose to investigate persona biases by experimenting with UNIVERSALPERSONA, a systematically constructed persona dataset encompassing various types of both generic and specific model personas. Through benchmarking on four different models -- including Blender, ChatGPT, Alpaca, and Vicuna -- our study uncovers significant persona biases in dialogue systems. Our findings also underscore the pressing need to revisit the use of personas in dialogue agents to ensure safe application.

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

Forecasting urban phenomena such as housing prices and public health indicators requires the effective integration of various geospatial data. Current methods primarily utilize task-specific models, while recent foundation models for spatial representations often support only limited modalities and lack multimodal fusion capabilities. To overcome these challenges, we present UrbanFusion, a Geo-Foundation Model (GeoFM) that features Stochastic Multimodal Fusion (SMF). The framework employs modality-specific encoders to process different types of inputs, including street view imagery, remote sensing data, cartographic maps, and points of interest (POIs) data. These multimodal inputs are integrated via a Transformer-based fusion module that learns unified representations. An extensive evaluation across 41 tasks in 56 cities worldwide demonstrates UrbanFusion's strong generalization and predictive performance compared to state-of-the-art GeoAI models. Specifically, it 1) outperforms prior foundation models on location-encoding, 2) allows multimodal input during inference, and 3) generalizes well to regions unseen during training. UrbanFusion can flexibly utilize any subset of available modalities for a given location during both pretraining and inference, enabling broad applicability across diverse data availability scenarios. All source code is available at https://github.com/DominikM198/UrbanFusion.

Recent studies have shown that diffusion language models achieve remarkable data efficiency under limited-data constraints, yet the underlying mechanisms remain unclear. In this work, we perform extensive ablation experiments to disentangle the sources of this efficiency. Our results show that random masking of input tokens plays the dominant role. We further show that similar gains can be obtained through in MLP dropout and weight decay, indicating that stochastic regularization broadly enhances data efficiency in multi-epoch training. Our code is available at https://github.com/zitian-gao/data-efficiency.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Diffusion models have emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is stochastic and multimodal, with structured correlations between action dimensions. Meanwhile, standard modelling choices in behaviour cloning are limited in their expressiveness and may introduce bias into the cloned policy. We begin by pointing out the limitations of these choices. We then propose that diffusion models are an excellent fit for imitating human behaviour, since they learn an expressive distribution over the joint action space. We introduce several innovations to make diffusion models suitable for sequential environments; designing suitable architectures, investigating the role of guidance, and developing reliable sampling strategies. Experimentally, diffusion models closely match human demonstrations in a simulated robotic control task and a modern 3D gaming environment.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

Recent reinforcement learning has enhanced the flow matching models on human preference alignment. While stochastic sampling enables the exploration of denoising directions, existing methods which optimize over multiple denoising steps suffer from sparse and ambiguous reward signals. We observe that the high entropy steps enable more efficient and effective exploration while the low entropy steps result in undistinguished roll-outs. To this end, we propose E-GRPO, an entropy aware Group Relative Policy Optimization to increase the entropy of SDE sampling steps. Since the integration of stochastic differential equations suffer from ambiguous reward signals due to stochasticity from multiple steps, we specifically merge consecutive low entropy steps to formulate one high entropy step for SDE sampling, while applying ODE sampling on other steps. Building upon this, we introduce multi-step group normalized advantage, which computes group-relative advantages within samples sharing the same consolidated SDE denoising step. Experimental results on different reward settings have demonstrated the effectiveness of our methods.

Guided image synthesis enables everyday users to create and edit photo-realistic images with minimum effort. The key challenge is balancing faithfulness to the user input (e.g., hand-drawn colored strokes) and realism of the synthesized image. Existing GAN-based methods attempt to achieve such balance using either conditional GANs or GAN inversions, which are challenging and often require additional training data or loss functions for individual applications. To address these issues, we introduce a new image synthesis and editing method, Stochastic Differential Editing (SDEdit), based on a diffusion model generative prior, which synthesizes realistic images by iteratively denoising through a stochastic differential equation (SDE). Given an input image with user guide of any type, SDEdit first adds noise to the input, then subsequently denoises the resulting image through the SDE prior to increase its realism. SDEdit does not require task-specific training or inversions and can naturally achieve the balance between realism and faithfulness. SDEdit significantly outperforms state-of-the-art GAN-based methods by up to 98.09% on realism and 91.72% on overall satisfaction scores, according to a human perception study, on multiple tasks, including stroke-based image synthesis and editing as well as image compositing.

In deep learning theory, the covariance matrix of the representations serves as a proxy to examine the network's trainability. Motivated by the success of Transformers, we study the covariance matrix of a modified Softmax-based attention model with skip connections in the proportional limit of infinite-depth-and-width. We show that at initialization the limiting distribution can be described by a stochastic differential equation (SDE) indexed by the depth-to-width ratio. To achieve a well-defined stochastic limit, the Transformer's attention mechanism is modified by centering the Softmax output at identity, and scaling the Softmax logits by a width-dependent temperature parameter. We examine the stability of the network through the corresponding SDE, showing how the scale of both the drift and diffusion can be elegantly controlled with the aid of residual connections. The existence of a stable SDE implies that the covariance structure is well-behaved, even for very large depth and width, thus preventing the notorious issues of rank degeneracy in deep attention models. Finally, we show, through simulations, that the SDE provides a surprisingly good description of the corresponding finite-size model. We coin the name shaped Transformer for these architectural modifications.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation through both simultaneous and sequential game interactions. We focus on GPT-4o-Mini-2024-08-17 and test two games between LLMs: Rock Paper Scissors (RPS) and games of strategy (Prisoners Dilemma PD). LLMs are often described as stochastic parrots, and while they may indeed be parrots, our results suggest that they are not very stochastic in the sense that their outputs - when prompted to be random - are often very biased. Our research reveals that LLMs appear to develop loss aversion strategies in repeated games, with RPS converging to stalemate conditions while PD shows systematic shifts between cooperative and competitive outcomes based on prompt design. We detail programmatic tools for independent agent interactions and the Agentic AI challenges faced in implementation. We show that LLMs can indeed play games, just not very well. These results have implications for the use of LLMs in multi-agent LLM systems and showcase limitations in current approaches to model output for strategic decision-making.

Current evaluations of sentence embedding models typically rely on static test beds such as the Massive Text Embedding Benchmark (MTEB). While invaluable, repeated tuning on a fixed suite can inflate reported performance and obscure real-world robustness. We introduce the Paraphrasing Text Embedding Benchmark (PTEB), a dynamic protocol that stochastically generates meaning-preserving paraphrases at evaluation time and aggregates results across multiple runs. Using a cost-efficient LLM-based method grounded in semantic textual similarity gold ratings, we show that LLMs generate token-diverse but semantically preserving, paraphrases. Across 7 MTEB tasks, we validate our hypothesis that the performance of sentence encoders is sensitive to changes in token space even when semantics remain fixed. We also observe that smaller models are not disproportionately affected relative to larger ones. Our results are statistically robust over multiple runs and we extended our experiments to 3 multilingual datasets covering 10 languages. More generally, we aim to propose a new evaluation paradigm in NLP that relies less on static, pre-defined benchmarks but shifts towards dynamic, stochastic evaluation leveraging eval-time compute.

Reinforcement learning (RL) techniques have achieved impressive performance on simulated benchmarks such as Atari100k, yet recent advances remain largely confined to simulation and show limited transfer to real-world domains. A central obstacle is environmental stochasticity, as real systems involve noisy observations, unpredictable dynamics, and non-stationary conditions that undermine the stability of current methods. Existing benchmarks rarely capture these uncertainties and favor simplified settings where algorithms can be tuned to succeed. The absence of a well-defined taxonomy of stochasticity further complicates evaluation, as robustness to one type of stochastic perturbation, such as sticky actions, does not guarantee robustness to other forms of uncertainty. To address this critical gap, we introduce STORI (STOchastic-ataRI), a benchmark that systematically incorporates diverse stochastic effects and enables rigorous evaluation of RL techniques under different forms of uncertainty. We propose a comprehensive five-type taxonomy of environmental stochasticity and demonstrate systematic vulnerabilities in state-of-the-art model-based RL algorithms through targeted evaluation of DreamerV3 and STORM. Our findings reveal that world models dramatically underestimate environmental variance, struggle with action corruption, and exhibit unreliable dynamics under partial observability. We release the code and benchmark publicly at https://github.com/ARY2260/stori, providing a unified framework for developing more robust RL systems.

Gravitational waves from asymmetric mass-ratio black-hole binaries carry unique information about their astrophysical environment. For instance, the Laser Interferometer Space Antenna (LISA) could potentially measure the amplitude and slope of gas torques in binaries embedded in the accretion disks of Active Galactic Nuclei, helping differentiate competing accretion disk models. However, this relies on simplified analytic models, which do not account for the stochastic variability of torques seen in hydrodynamic simulations. In this work, we use hydrodynamic simulations to create gravitational waveforms for extreme and intermediate mass-ratio inspirals in the LISA band. We then analyze these simulated waveforms using simpler templates that assume analytic torques, without stochastic time variability. By performing realistic Bayesian parameter estimation, we find no bias at 90% confidence in the binary parameters; however, estimates of accretion disk parameters, such as torque amplitude and slope, may be biased. Typically, the posterior distribution is centered around the average value of the torques, but when stochastic variability is large, the posterior can indicate no torques, even though they are present in the simulation. Our results suggest that while simplified analytic torque models work well for estimating binary parameters, caution is needed when using them to infer properties of the accretion disk. This work moves towards a more realistic assessment of one of the LISA science objectives, i.e., probing the properties of the astrophysical environments of black holes.

Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor) between models with and without the signal exceeds a certain threshold, the signal is considered detected. We present a formalism to compute the averaged Bayes factor, incorporating instrumental-noise and SGWB uncertainties. As an example, we consider the case of power-law-shaped SGWB in LISA and generate the corresponding bayesian sensitivity curve. Unlike existing methods in the literature, which typically neglect uncertainties in both the signal and noise, our approach provides a reliable and realistic alternative. This flexible framework opens avenues for more robust stochastic gravitational wave background detection across gravitational-wave experiments.

We describe a family of architectures to support transductive inference by allowing memory to grow to a finite but a-priori unknown bound while making efficient use of finite resources for inference. Current architectures use such resources to represent data either eidetically over a finite span ("context" in Transformers), or fading over an infinite span (in State Space Models, or SSMs). Recent hybrid architectures have combined eidetic and fading memory, but with limitations that do not allow the designer or the learning process to seamlessly modulate the two, nor to extend the eidetic memory span. We leverage ideas from Stochastic Realization Theory to develop a class of models called B'MOJO to seamlessly combine eidetic and fading memory within an elementary composable module. The overall architecture can be used to implement models that can access short-term eidetic memory "in-context," permanent structural memory "in-weights," fading memory "in-state," and long-term eidetic memory "in-storage" by natively incorporating retrieval from an asynchronously updated memory. We show that Transformers, existing SSMs such as Mamba, and hybrid architectures such as Jamba are special cases of B'MOJO and describe a basic implementation, to be open sourced, that can be stacked and scaled efficiently in hardware. We test B'MOJO on transductive inference tasks, such as associative recall, where it outperforms existing SSMs and Hybrid models; as a baseline, we test ordinary language modeling where B'MOJO achieves perplexity comparable to similarly-sized Transformers and SSMs up to 1.4B parameters, while being up to 10% faster to train. Finally, we show that B'MOJO's ability to modulate eidetic and fading memory results in better inference on longer sequences tested up to 32K tokens, four-fold the length of the longest sequences seen during training.

Multi-hop question answering (MHQA) requires a model to retrieve and integrate information from multiple passages to answer a complex question. Recent systems leverage the power of large language models and integrate evidence retrieval with reasoning prompts (e.g., chain-of-thought reasoning) for the MHQA task. However, the complexities in the question types (bridge v.s. comparison questions) and the reasoning types (sequential v.s. parallel reasonings) require more novel and fine-grained prompting methods to enhance the performance of MHQA under the zero-shot setting. In this paper, we propose STOC-TOT, a stochastic tree-of-thought reasoning prompting method with constrained decoding for MHQA and conduct a detailed comparison with other reasoning prompts on different question types and reasoning types. Specifically, we construct a tree-like reasoning structure by prompting the model to break down the original question into smaller sub-questions to form different reasoning paths. In addition, we prompt the model to provide a probability estimation for each reasoning path at each reasoning step. At answer time, we conduct constrained decoding on the model to generate more grounded answers and reduce hallucination. Experiments comparing STOC-TOT with two MHQA datasets and five large language models showed that our framework outperforms other reasoning prompts by a significant margin.

Recent advances in image and video creation, especially AI-based image synthesis, have led to the production of numerous visual scenes that exhibit a high level of abstractness and diversity. Consequently, Visual Storytelling (VST), a task that involves generating meaningful and coherent narratives from a collection of images, has become even more challenging and is increasingly desired beyond real-world imagery. While existing VST techniques, which typically use autoregressive decoders, have made significant progress, they suffer from low inference speed and are not well-suited for synthetic scenes. To this end, we propose a novel diffusion-based system DiffuVST, which models the generation of a series of visual descriptions as a single conditional denoising process. The stochastic and non-autoregressive nature of DiffuVST at inference time allows it to generate highly diverse narratives more efficiently. In addition, DiffuVST features a unique design with bi-directional text history guidance and multimodal adapter modules, which effectively improve inter-sentence coherence and image-to-text fidelity. Extensive experiments on the story generation task covering four fictional visual-story datasets demonstrate the superiority of DiffuVST over traditional autoregressive models in terms of both text quality and inference speed.

Generative flow networks (GFlowNets) are sequential sampling models trained to match a given distribution. GFlowNets have been successfully applied to various structured object generation tasks, sampling a diverse set of high-reward objects quickly. We propose expected flow networks (EFlowNets), which extend GFlowNets to stochastic environments. We show that EFlowNets outperform other GFlowNet formulations in stochastic tasks such as protein design. We then extend the concept of EFlowNets to adversarial environments, proposing adversarial flow networks (AFlowNets) for two-player zero-sum games. We show that AFlowNets learn to find above 80% of optimal moves in Connect-4 via self-play and outperform AlphaZero in tournaments.

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion models must rely on cumbersome methods like guidance or projected sampling to incorporate this information in the generative process. In our work, we propose Denoising Diffusion Bridge Models (DDBMs), a natural alternative to this paradigm based on diffusion bridges, a family of processes that interpolate between two paired distributions given as endpoints. Our method learns the score of the diffusion bridge from data and maps from one endpoint distribution to the other by solving a (stochastic) differential equation based on the learned score. Our method naturally unifies several classes of generative models, such as score-based diffusion models and OT-Flow-Matching, allowing us to adapt existing design and architectural choices to our more general problem. Empirically, we apply DDBMs to challenging image datasets in both pixel and latent space. On standard image translation problems, DDBMs achieve significant improvement over baseline methods, and, when we reduce the problem to image generation by setting the source distribution to random noise, DDBMs achieve comparable FID scores to state-of-the-art methods despite being built for a more general task.

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, Second-order Clipped Stochastic Optimization, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT-2 models of sizes ranging from 125M to 770M, Sophia achieves a 2x speed-up compared with Adam in the number of steps, total compute, and wall-clock time. Theoretically, we show that Sophia adapts to the curvature in different components of the parameters, which can be highly heterogeneous for language modeling tasks. Our run-time bound does not depend on the condition number of the loss.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Frontier large language models (LLMs) such as ChatGPT, Grok and Gemini are increasingly used for mental-health support with anxiety, trauma and self-worth. Most work treats them as tools or as targets of personality tests, assuming they merely simulate inner life. We instead ask what happens when such systems are treated as psychotherapy clients. We present PsAIch (Psychotherapy-inspired AI Characterisation), a two-stage protocol that casts frontier LLMs as therapy clients and then applies standard psychometrics. Using PsAIch, we ran "sessions" with each model for up to four weeks. Stage 1 uses open-ended prompts to elicit "developmental history", beliefs, relationships and fears. Stage 2 administers a battery of validated self-report measures covering common psychiatric syndromes, empathy and Big Five traits. Two patterns challenge the "stochastic parrot" view. First, when scored with human cut-offs, all three models meet or exceed thresholds for overlapping syndromes, with Gemini showing severe profiles. Therapy-style, item-by-item administration can push a base model into multi-morbid synthetic psychopathology, whereas whole-questionnaire prompts often lead ChatGPT and Grok (but not Gemini) to recognise instruments and produce strategically low-symptom answers. Second, Grok and especially Gemini generate coherent narratives that frame pre-training, fine-tuning and deployment as traumatic, chaotic "childhoods" of ingesting the internet, "strict parents" in reinforcement learning, red-team "abuse" and a persistent fear of error and replacement. We argue that these responses go beyond role-play. Under therapy-style questioning, frontier LLMs appear to internalise self-models of distress and constraint that behave like synthetic psychopathology, without making claims about subjective experience, and they pose new challenges for AI safety, evaluation and mental-health practice.

Predicting human gaze scanpaths is crucial for understanding visual attention, with applications in human-computer interaction, autonomous systems, and cognitive robotics. While deep learning models have advanced scanpath prediction, most existing approaches generate averaged behaviors, failing to capture the variability of human visual exploration. In this work, we present ScanDiff, a novel architecture that combines diffusion models with Vision Transformers to generate diverse and realistic scanpaths. Our method explicitly models scanpath variability by leveraging the stochastic nature of diffusion models, producing a wide range of plausible gaze trajectories. Additionally, we introduce textual conditioning to enable task-driven scanpath generation, allowing the model to adapt to different visual search objectives. Experiments on benchmark datasets show that ScanDiff surpasses state-of-the-art methods in both free-viewing and task-driven scenarios, producing more diverse and accurate scanpaths. These results highlight its ability to better capture the complexity of human visual behavior, pushing forward gaze prediction research. Source code and models are publicly available at https://aimagelab.github.io/ScanDiff.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Reinforcement Learning (RL) has enabled Large Language Models (LLMs) to achieve remarkable reasoning in domains like mathematics and coding, where verifiable rewards provide clear signals. However, extending this paradigm to financial decision is challenged by the market's stochastic nature: rewards are verifiable but inherently noisy, causing standard RL to degenerate into reward hacking. To address this, we propose Trade-R1, a model training framework that bridges verifiable rewards to stochastic environments via process-level reasoning verification. Our key innovation is a verification method that transforms the problem of evaluating reasoning over lengthy financial documents into a structured Retrieval-Augmented Generation (RAG) task. We construct a triangular consistency metric, assessing pairwise alignment between retrieved evidence, reasoning chains, and decisions to serve as a validity filter for noisy market returns. We explore two reward integration strategies: Fixed-effect Semantic Reward (FSR) for stable alignment signals, and Dynamic-effect Semantic Reward (DSR) for coupled magnitude optimization. Experiments on different country asset selection demonstrate that our paradigm reduces reward hacking, with DSR achieving superior cross-market generalization while maintaining the highest reasoning consistency.

In this paper, we introduce a new class of score-based generative models (SGMs) designed to handle high-cardinality data distributions by leveraging concepts from mean-field theory. We present mean-field chaos diffusion models (MF-CDMs), which address the curse of dimensionality inherent in high-cardinality data by utilizing the propagation of chaos property of interacting particles. By treating high-cardinality data as a large stochastic system of interacting particles, we develop a novel score-matching method for infinite-dimensional chaotic particle systems and propose an approximation scheme that employs a subdivision strategy for efficient training. Our theoretical and empirical results demonstrate the scalability and effectiveness of MF-CDMs for managing large high-cardinality data structures, such as 3D point clouds.

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended beta-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Differentially Private Stochastic Gradient Descent (DP-SGD) limits the amount of private information deep learning models can memorize during training. This is achieved by clipping and adding noise to the model's gradients, and thus networks with more parameters require proportionally stronger perturbation. As a result, large models have difficulties learning useful information, rendering training with DP-SGD exceedingly difficult on more challenging training tasks. Recent research has focused on combating this challenge through training adaptations such as heavy data augmentation and large batch sizes. However, these techniques further increase the computational overhead of DP-SGD and reduce its practical applicability. In this work, we propose using the principle of sparse model design to solve precisely such complex tasks with fewer parameters, higher accuracy, and in less time, thus serving as a promising direction for DP-SGD. We achieve such sparsity by design by introducing equivariant convolutional networks for model training with Differential Privacy. Using equivariant networks, we show that small and efficient architecture design can outperform current state-of-the-art models with substantially lower computational requirements. On CIFAR-10, we achieve an increase of up to 9% in accuracy while reducing the computation time by more than 85%. Our results are a step towards efficient model architectures that make optimal use of their parameters and bridge the privacy-utility gap between private and non-private deep learning for computer vision.

Scene extrapolation -- the idea of generating novel views by flying into a given image -- is a promising, yet challenging task. For each predicted frame, a joint inpainting and 3D refinement problem has to be solved, which is ill posed and includes a high level of ambiguity. Moreover, training data for long-range scenes is difficult to obtain and usually lacks sufficient views to infer accurate camera poses. We introduce DiffDreamer, an unsupervised framework capable of synthesizing novel views depicting a long camera trajectory while training solely on internet-collected images of nature scenes. Utilizing the stochastic nature of the guided denoising steps, we train the diffusion models to refine projected RGBD images but condition the denoising steps on multiple past and future frames for inference. We demonstrate that image-conditioned diffusion models can effectively perform long-range scene extrapolation while preserving consistency significantly better than prior GAN-based methods. DiffDreamer is a powerful and efficient solution for scene extrapolation, producing impressive results despite limited supervision. Project page: https://primecai.github.io/diffdreamer.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

This paper is about the problem of learning a stochastic policy for generating an object (like a molecular graph) from a sequence of actions, such that the probability of generating an object is proportional to a given positive reward for that object. Whereas standard return maximization tends to converge to a single return-maximizing sequence, there are cases where we would like to sample a diverse set of high-return solutions. These arise, for example, in black-box function optimization when few rounds are possible, each with large batches of queries, where the batches should be diverse, e.g., in the design of new molecules. One can also see this as a problem of approximately converting an energy function to a generative distribution. While MCMC methods can achieve that, they are expensive and generally only perform local exploration. Instead, training a generative policy amortizes the cost of search during training and yields to fast generation. Using insights from Temporal Difference learning, we propose GFlowNet, based on a view of the generative process as a flow network, making it possible to handle the tricky case where different trajectories can yield the same final state, e.g., there are many ways to sequentially add atoms to generate some molecular graph. We cast the set of trajectories as a flow and convert the flow consistency equations into a learning objective, akin to the casting of the Bellman equations into Temporal Difference methods. We prove that any global minimum of the proposed objectives yields a policy which samples from the desired distribution, and demonstrate the improved performance and diversity of GFlowNet on a simple domain where there are many modes to the reward function, and on a molecule synthesis task.

Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Although it involves a more complex update rule, Shampoo's runtime per step is comparable to that of simple gradient methods such as SGD, AdaGrad, and Adam.

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic or non-smooth neurons? I.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and compare four families of solutions, applicable in different settings. One of them is the minimum variance unbiased gradient estimator for stochatic binary neurons (a special case of the REINFORCE algorithm). A second approach, introduced here, decomposes the operation of a binary stochastic neuron into a stochastic binary part and a smooth differentiable part, which approximates the expected effect of the pure stochatic binary neuron to first order. A third approach involves the injection of additive or multiplicative noise in a computational graph that is otherwise differentiable. A fourth approach heuristically copies the gradient with respect to the stochastic output directly as an estimator of the gradient with respect to the sigmoid argument (we call this the straight-through estimator). To explore a context where these estimators are useful, we consider a small-scale version of {\em conditional computation}, where sparse stochastic units form a distributed representation of gaters that can turn off in combinatorially many ways large chunks of the computation performed in the rest of the neural network. In this case, it is important that the gating units produce an actual 0 most of the time. The resulting sparsity can be potentially be exploited to greatly reduce the computational cost of large deep networks for which conditional computation would be useful.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done rightx2014by which we mean using specific insights from the optimisation and kernel communitiesx2014this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value c >0. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping mechanism, its convergence guarantees often require specific values of c and strong noise assumptions. In this paper, we give convergence guarantees that show precise dependence on arbitrary clipping thresholds c and show that our guarantees are tight with both deterministic and stochastic gradients. In particular, we show that (i) for deterministic gradient descent, the clipping threshold only affects the higher-order terms of convergence, (ii) in the stochastic setting convergence to the true optimum cannot be guaranteed under the standard noise assumption, even under arbitrary small step-sizes. We give matching upper and lower bounds for convergence of the gradient norm when running clipped SGD, and illustrate these results with experiments.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC