Daily Papers

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems - generalising to significantly larger problems than the ones seen during training - while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.

Active learning (AL) algorithms may achieve better performance with fewer data because the model guides the data selection process. While many algorithms have been proposed, there is little study on what the optimal AL algorithm looks like, which would help researchers understand where their models fall short and iterate on the design. In this paper, we present a simulated annealing algorithm to search for this optimal oracle and analyze it for several tasks. We present qualitative and quantitative insights into the behaviors of this oracle, comparing and contrasting them with those of various heuristics. Moreover, we are able to consistently improve the heuristics using one particular insight. We hope that our findings can better inform future active learning research. The code is available at https://github.com/YilunZhou/optimal-active-learning.

Recent improvements in text generation have leveraged human feedback to improve the quality of the generated output. However, human feedback is not always available, especially during inference. In this work, we propose an inference time optimization method FITO to use fine-grained actionable feedback in the form of error type, error location and severity level that are predicted by a learned error pinpoint model for iterative refinement. FITO starts with an initial output, then iteratively incorporates the feedback via a refinement model that generates an improved output conditioned on the feedback. Given the uncertainty of consistent refined samples at iterative steps, we formulate iterative refinement into a local search problem and develop a simulated annealing based algorithm that balances exploration of the search space and optimization for output quality. We conduct experiments on three text generation tasks, including machine translation, long-form question answering (QA) and topical summarization. We observe 0.8 and 0.7 MetricX gain on Chinese-English and English-German translation, 4.5 and 1.8 ROUGE-L gain at long form QA and topic summarization respectively, with a single iteration of refinement. With our simulated annealing algorithm, we see further quality improvements, including up to 1.7 MetricX improvements over the baseline approach.

The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared to long MD simulations. Our open-source implementation is available at https://github.com/lujiarui/Str2Str

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the noisy gradient descent ascent method which in the infinite particle limit gives rise to the {\em Mean-Field Gradient Descent Ascent} (GDA) dynamics on the space of probability measures. In this paper, we first study the convergence of a two-scale Mean-Field GDA dynamics for finding the MNE of the entropy-regularized objective. More precisely we show that for each finite temperature (or regularization parameter), the two-scale Mean-Field GDA with a suitable {\em finite} scale ratio converges exponentially to the unique MNE without assuming the convexity or concavity of the interaction potential. The key ingredient of our proof lies in the construction of new Lyapunov functions that dissipate exponentially along the Mean-Field GDA. We further study the simulated annealing of the Mean-Field GDA dynamics. We show that with a temperature schedule that decays logarithmically in time the annealed Mean-Field GDA converges to the MNE of the original unregularized objective.

Recent advances in multi-fingered robotic grasping have enabled fast 6-Degrees-Of-Freedom (DOF) single object grasping. Multi-finger grasping in cluttered scenes, on the other hand, remains mostly unexplored due to the added difficulty of reasoning over obstacles which greatly increases the computational time to generate high-quality collision-free grasps. In this work we address such limitations by introducing DDGC, a fast generative multi-finger grasp sampling method that can generate high quality grasps in cluttered scenes from a single RGB-D image. DDGC is built as a network that encodes scene information to produce coarse-to-fine collision-free grasp poses and configurations. We experimentally benchmark DDGC against the simulated-annealing planner in GraspIt! on 1200 simulated cluttered scenes and 7 real world scenes. The results show that DDGC outperforms the baseline on synthesizing high-quality grasps and removing clutter while being 5 times faster. This, in turn, opens up the door for using multi-finger grasps in practical applications which has so far been limited due to the excessive computation time needed by other methods.

In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.

As robots become more accessible outside of industrial settings, the need for reliable object grasping and manipulation grows significantly. In such dynamic environments it is expected that the robot is capable of reliably grasping and manipulating novel objects in different situations. In this work we present GraspCaps: a novel architecture based on Capsule Networks for generating per-point grasp configurations for familiar objects. In our work, the activation vector of each capsule in the deepest capsule layer corresponds to one specific class of object. This way, the network is able to extract a rich feature vector of the objects present in the point cloud input, which is then used for generating per-point grasp vectors. This approach should allow the network to learn specific grasping strategies for each of the different object categories. Along with GraspCaps we present a method for generating a large object grasping dataset using simulated annealing. The obtained dataset is then used to train the GraspCaps network. We performed an extensive set of experiments to assess the performance of the proposed approach regarding familiar object recognition accuracy and grasp success rate on challenging real and simulated scenarios.

This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA), and the other one based on neural network (NN). Empirical results on three classic CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA- and NN-based solvers. In particular, our SA algorithm reduces the runtime of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems. Our code is available at https://github.com/Shengyu-Feng/RLD4CO.

This paper proposes a novel mission planning platform, capable of efficiently deploying a team of UAVs to cover complex-shaped areas, in various remote sensing applications. Under the hood lies a novel optimization scheme for grid-based methods, utilizing Simulated Annealing algorithm, that significantly increases the achieved percentage of coverage and improves the qualitative features of the generated paths. Extensive simulated evaluation in comparison with a state-of-the-art alternative methodology, for coverage path planning (CPP) operations, establishes the performance gains in terms of achieved coverage and overall duration of the generated missions. On top of that, DARP algorithm is employed to allocate sub-tasks to each member of the swarm, taking into account each UAV's sensing and operational capabilities, their initial positions and any no-fly-zones possibly defined inside the operational area. This feature is of paramount importance in real-life applications, as it has the potential to achieve tremendous performance improvements in terms of time demanded to complete a mission, while at the same time it unlocks a wide new range of applications, that was previously not feasible due to the limited battery life of UAVs. In order to investigate the actual efficiency gains that are introduced by the multi-UAV utilization, a simulated study is performed as well. All of these capabilities are packed inside an end-to-end platform that eases the utilization of UAVs' swarms in remote sensing applications. Its versatility is demonstrated via two different real-life applications: (i) a photogrametry for precision agriculture and (ii) an indicative search and rescue for first responders missions, that were performed utilizing a swarm of commercial UAVs. The source code can be found at: https://github.com/savvas-ap/mCPP-optimized-DARP

We introduce NeuroSA, a neuromorphic architecture specifically designed to ensure asymptotic convergence to the ground state of an Ising problem using an annealing process that is governed by the physics of quantum mechanical tunneling using Fowler-Nordheim (FN). The core component of NeuroSA consists of a pair of asynchronous ON-OFF neurons, which effectively map classical simulated annealing (SA) dynamics onto a network of integrate-and-fire (IF) neurons. The threshold of each ON-OFF neuron pair is adaptively adjusted by an FN annealer which replicates the optimal escape mechanism and convergence of SA, particularly at low temperatures. To validate the effectiveness of our neuromorphic Ising machine, we systematically solved various benchmark MAX-CUT combinatorial optimization problems. Across multiple runs, NeuroSA consistently generates solutions that approach the state-of-the-art level with high accuracy (greater than 99%), and without any graph-specific hyperparameter tuning. For practical illustration, we present results from an implementation of NeuroSA on the SpiNNaker2 platform, highlighting the feasibility of mapping our proposed architecture onto a standard neuromorphic accelerator platform.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.