Daily Papers

As of today, the best accuracy in line segment detection (LSD) is achieved by algorithms based on convolutional neural networks - CNNs. Unfortunately, these methods utilize deep, heavy networks and are slower than traditional model-based detectors. In this paper we build an accurate yet fast CNN- based detector, LSDNet, by incorporating a lightweight CNN into a classical LSD detector. Specifically, we replace the first step of the original LSD algorithm - construction of line segments heatmap and tangent field from raw image gradients - with a lightweight CNN, which is able to calculate more complex and rich features. The second part of the LSD algorithm is used with only minor modifications. Compared with several modern line segment detectors on standard Wireframe dataset, the proposed LSDNet provides the highest speed (among CNN-based detectors) of 214 FPS with a competitive accuracy of 78 Fh . Although the best-reported accuracy is 83 Fh at 33 FPS, we speculate that the observed accuracy gap is caused by errors in annotations and the actual gap is significantly lower. We point out systematic inconsistencies in the annotations of popular line detection benchmarks - Wireframe and York Urban, carefully reannotate a subset of images and show that (i) existing detectors have improved quality on updated annotations without retraining, suggesting that new annotations correlate better with the notion of correct line segment detection; (ii) the gap between accuracies of our detector and others diminishes to negligible 0.2 Fh , with our method being the fastest.

Multi-view computer vision pipelines typically rely on accurate sparse keypoints and robust descriptors. While incorporating line features has shown clear benefits for matching and pose estimation, existing point-line approaches remain inefficient: they detect points and lines separately, use increasingly heavy networks, and depend on CPU-bound heuristics that hinder real-time performance. We introduce a Unified Efficient Points and Lines (UPAL) feature extractor that jointly extracts keypoints, line segments, and feature descriptors within a single lightweight architecture. A shared backbone provides common representations that feed different branches for point and line features. Line segments are recovered through an accelerated post-processing stage, an enhanced and highly efficient variant of the LSD algorithm. UPAL matches or exceeds state-ofthe-art performance in both point and line applications while significantly reducing computational cost, achieving, for instance, a 4x speedup and 10x smaller memory footprint over the ALIKED + DeepLSD pipeline. Code is publicly available at https://github.com/francois141/upal.

We present Onesweep, a least-significant digit (LSD) radix sorting algorithm for large GPU sorting problems residing in global memory. Our parallel algorithm employs a method of single-pass prefix sum that only requires ~2n global read/write operations for each digit-binning iteration. This exhibits a significant reduction in last-level memory traffic versus contemporary GPU radix sorting implementations, where each iteration of digit binning requires two passes through the dataset totaling ~3n global memory operations. On the NVIDIA A100 GPU, our approach achieves 29.4 GKey/s when sorting 256M random 32-bit keys. Compared to CUB, the current state-of-the-art GPU LSD radix sort, our approach provides a speedup of ~1.5x. For 32-bit keys with varied distributions, our approach provides more consistent performance compared to HRS, the current state-of-the-art GPU MSD radix sort, and outperforms it in almost all cases.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at https://github.com/feiyangfu/LSD{https://github.com/feiyangfu/LSD}.

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for hallucination detection that analyzes the evolution of hidden-state semantics across transformer layers. Unlike prior methods that rely on multiple sampling passes or external verification sources, LSD operates intrinsically within the model's representational space. Using margin-based contrastive learning, LSD aligns hidden activations with ground-truth embeddings derived from a factual encoder, revealing a distinct separation in semantic trajectories: factual responses preserve stable alignment, while hallucinations exhibit pronounced semantic drift across depth. Evaluated on the TruthfulQA and synthetic factual-hallucination datasets, LSD achieves an F1-score of 0.92, AUROC of 0.96, and clustering accuracy of 0.89, outperforming SelfCheckGPT and Semantic Entropy baselines while requiring only a single forward pass. This efficiency yields a 5-20x speedup over sampling-based methods without sacrificing precision or interpretability. LSD offers a scalable, model-agnostic mechanism for real-time hallucination monitoring and provides new insights into the geometry of factual consistency within large language models.

Molecular structure elucidation involves deducing a molecule's structure from various types of spectral data, which is crucial in chemical experimental analysis. While large language models (LLMs) have shown remarkable proficiency in analyzing and reasoning through complex tasks, they still encounter substantial challenges in molecular structure elucidation. We identify that these challenges largely stem from LLMs' limited grasp of specialized chemical knowledge. In this work, we introduce a Knowledge-enhanced reasoning framework for Molecular Structure Elucidation (K-MSE), leveraging Monte Carlo Tree Search for test-time scaling as a plugin. Specifically, we construct an external molecular substructure knowledge base to extend the LLMs' coverage of the chemical structure space. Furthermore, we design a specialized molecule-spectrum scorer to act as a reward model for the reasoning process, addressing the issue of inaccurate solution evaluation in LLMs. Experimental results show that our approach significantly boosts performance, particularly gaining more than 20% improvement on both GPT-4o-mini and GPT-4o. Our code is available at https://github.com/HICAI-ZJU/K-MSE.

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

We introduce a frustratingly simple, super efficient and surprisingly effective decoding method, which we call Frustratingly Simple Decoding (FSD), for neural text generation. The idea behind FSD is straightforward: we build an anti-LM based on previously generated text and use this anti-LM to penalize future generation of what has been generated. The anti-LM can be implemented as simple as an n-gram language model or a vectorized variant. In this way, FSD introduces no extra model parameters and negligible computational overhead (FSD can be as fast as greedy search). Despite the simplicity, FSD is surprisingly effective; Experiments show that FSD can outperform the canonical methods to date (i.e., nucleus sampling) as well as several strong baselines that were proposed recently.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

We present a randomized O(n^{3.5})-time algorithm for computing optimal energetic paths for an electric car between all pairs of vertices in an n-vertex directed graph with positive and negative costs. The optimal energetic paths are finite and well-defined even if the graph contains negative-cost cycles. This makes the problem much more challenging than standard shortest paths problems. More specifically, for every two vertices s and~t in the graph, the algorithm computes α_B(s,t), the maximum amount of charge the car can reach~t with, if it starts at~s with full battery, i.e., with charge~B, where~B is the capacity of the battery. In the presence of negative-cost cycles, optimal paths are not necessarily simple. For dense graphs, our new O(n^{3.5}) time algorithm improves on a previous O(mn^{2})-time algorithm of Dorfman et al. [ESA 2023] for the problem. The cost of an arc is the amount of charge taken from the battery of the car when traversing the arc. The charge in the battery can never exceed the capacity~B of the battery and can never be negative. An arc of negative cost may correspond, for example, to a downhill road segment, while an arc with a positive cost may correspond to an uphill segment. A negative-cost cycle, if one exists, can be used in certain cases to charge the battery to its capacity. This makes the problem more interesting and more challenging. Negative-cost cycles may arise when certain road segments have magnetic charging strips, or when the electric car has solar panels. Combined with a result of Dorfman et al. [SOSA 2024], this also provides a randomized O(n^{3.5})-time algorithm for computing minimum-cost paths between all pairs of vertices in an n-vertex graph when the battery can be externally recharged, at varying costs, at intermediate vertices.

Recent advancements in Large Language Models (LLMs) have demonstrated their potential in planning and reasoning tasks, offering a flexible alternative to classical pathfinding algorithms. However, most existing studies focus on LLMs' independent reasoning capabilities and overlook the potential synergy between LLMs and traditional algorithms. To fill this gap, we propose a comprehensive evaluation benchmark GridRoute to assess how LLMs can take advantage of traditional algorithms. We also propose a novel hybrid prompting technique called Algorithm of Thought (AoT), which introduces traditional algorithms' guidance into prompting. Our benchmark evaluates six LLMs ranging from 7B to 72B parameters across various map sizes, assessing their performance in correctness, optimality, and efficiency in grid environments with varying sizes. Our results show that AoT significantly boosts performance across all model sizes, particularly in larger or more complex environments, suggesting a promising approach to addressing path planning challenges. Our code is open-sourced at https://github.com/LinChance/GridRoute.

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit that implements the algorithm consists of unitary gates whose locality is at most the locality of the objective function whose optimum is sought. The depth of the circuit grows linearly with p times (at worst) the number of constraints. If p is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing. If p grows with the input size a different strategy is proposed. We study the algorithm as applied to MaxCut on regular graphs and analyze its performance on 2-regular and 3-regular graphs for fixed p. For p = 1, on 3-regular graphs the quantum algorithm always finds a cut that is at least 0.6924 times the size of the optimal cut.

The Korean criminal justice system utilizes summary proceedings (guyaksik) to expedite high-volume minor infractions, such as simple driving under the influence (DUI), unlicensed driving, and minor traffic casualties. Although this mechanism improves judicial throughput, processing these cases creates a substantial administrative burden for prosecutors, driving the need for automated systems that can precisely translate unstructured legal text into deterministic statutory outcomes. While recent Large Language Models (LLMs) excel at semantic extraction, their probabilistic nature inherently limits their reliability in Legal Judgment Prediction tasks. Specifically, when confronted with the arithmetic constraints of legal statutes, LLMs can produce hallucinations. Given that legal accountability permits virtually no tolerance for stochastic errors, purely neural architectures remain limited in their direct judicial applications. To address these limitations, we propose a Neuro-Symbolic framework that bridges unstructured legal facts with formal verification. Our architecture restricts the LLM exclusively to semantic extraction, while offloading statutory fine calculations to a Satisfiability Modulo Theories solver. This division of labor reduces hallucination risks during computation. Furthermore, we incorporate a Human-in-the-Loop verification scheme to preserve professional legal oversight. We formalize the 2026 Sentencing Guidelines for Traffic Offenses within this pipeline, demonstrating a deterministic approach to supporting summary indictments.

Retrosynthetic planning is a critical task in organic chemistry which identifies a series of reactions that can lead to the synthesis of a target product. The vast number of possible chemical transformations makes the size of the search space very big, and retrosynthetic planning is challenging even for experienced chemists. However, existing methods either require expensive return estimation by rollout with high variance, or optimize for search speed rather than the quality. In this paper, we propose Retro*, a neural-based A*-like algorithm that finds high-quality synthetic routes efficiently. It maintains the search as an AND-OR tree, and learns a neural search bias with off-policy data. Then guided by this neural network, it performs best-first search efficiently during new planning episodes. Experiments on benchmark USPTO datasets show that, our proposed method outperforms existing state-of-the-art with respect to both the success rate and solution quality, while being more efficient at the same time.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

We investigate a relatively under-explored class of hybrid neurosymbolic models that integrate symbolic learning with neural reasoning to construct data generators meeting formal correctness criteria. In Symbolic Neural Generators (SNGs), symbolic learners examine logical specifications of feasible data from a small set of instances -- sometimes just one. Each specification in turn constrains the conditional information supplied to a neural-based generator, which rejects any instance violating the symbolic specification. Like other neurosymbolic approaches, SNG exploits the complementary strengths of symbolic and neural methods. The outcome of an SNG is a pair (H, X), where H is a symbolic description of feasible instances constructed from data, and X a set of generated new instances that satisfy the description. We introduce a semantics for such systems, based on the construction of appropriate base and fibre partially-ordered sets combined into an overall partial order. We implement an SNG combining a restricted form of Inductive Logic Programming (ILP) with a large language model (LLM) and evaluate it on early-stage drug design. Our main interest is the description and the set of potential inhibitor molecules generated by the SNG. On benchmark problems -- where drug targets are well understood -- SNG performance is statistically comparable to state-of-the-art methods. On exploratory problems with poorly understood targets, generated molecules exhibit binding affinities on par with leading clinical candidates. Experts further find the symbolic specifications useful as preliminary filters, with several generated molecules identified as viable for synthesis and wet-lab testing.

We study the behavior of an algorithm derived from the cavity method for the Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks networks and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the DHEA solver, a Branch and Cut Linear/Integer Programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two post-processing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require ``differentiable'' proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation. The code is available at https://github.com/masa-ue/SVDD{https://github.com/masa-ue/SVDD}.

A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et al. Science 2022], introduced an approach for learning properties of the ground state of an n-qubit gapped local Hamiltonian H from only n^{O(1)} data points sampled from Hamiltonians in the same phase of matter. This was subsequently improved by [Lewis et al. Nature Communications 2024], to O(log n) samples when the geometry of the n-qubit system is known. In this work, we introduce two approaches that achieve a constant sample complexity, independent of system size n, for learning ground state properties. Our first algorithm consists of a simple modification of the ML model used by Lewis et al. and applies to a property of interest known beforehand. Our second algorithm, which applies even if a description of the property is not known, is a deep neural network model. While empirical results showing the performance of neural networks have been demonstrated, to our knowledge, this is the first rigorous sample complexity bound on a neural network model for predicting ground state properties. We also perform numerical experiments that confirm the improved scaling of our approach compared to earlier results.

In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. The system's behavior is primarily driven by parameters such as instructions or tool definitions. Recent advancements enable end-to-end optimization of these parameters using an LLM. Notably, leveraging an LLM as an optimizer is particularly efficient because it avoids gradient computation and can generate complex code and instructions. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems. It covers archetypes of compound AI systems, approaches to LLM-based end-to-end optimization, and insights into future directions and broader impacts. Importantly, this survey uses concepts from program analysis to provide a unified view of how an LLM optimizer is prompted to optimize a compound AI system. The exhaustive list of paper is provided at https://github.com/linyuhongg/LLM-based-Optimization-of-Compound-AI-Systems.

Autonomous agents powered by language models (LMs) have demonstrated promise in their ability to perform decision-making tasks such as web automation. However, a key limitation remains: LMs, primarily optimized for natural language understanding and generation, struggle with multi-step reasoning, planning, and using environmental feedback when attempting to solve realistic computer tasks. Towards addressing this, we propose an inference-time search algorithm for LM agents to explicitly perform exploration and multi-step planning in interactive web environments. Our approach is a form of best-first tree search that operates within the actual environment space, and is complementary with most existing state-of-the-art agents. It is the first tree search algorithm for LM agents that shows effectiveness on realistic web tasks. On the challenging VisualWebArena benchmark, applying our search algorithm on top of a GPT-4o agent yields a 39.7% relative increase in success rate compared to the same baseline without search, setting a state-of-the-art success rate of 26.4%. On WebArena, search also yields a 28.0% relative improvement over a baseline agent, setting a competitive success rate of 19.2%. Our experiments highlight the effectiveness of search for web agents, and we demonstrate that performance scales with increased test-time compute. We conduct a thorough analysis of our results to highlight improvements from search, limitations, and promising directions for future work. Our code and models are publicly released at https://jykoh.com/search-agents.

Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectives can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations. Our code is available at http://github.com/zoom-wang112358/MOLLEO

Chemical similarity searches are widely used in-silico methods for identifying new drug-like molecules. These methods have historically relied on structure-based comparisons to compute molecular similarity. Here, we use a chemical language model to create a vector-based chemical search. We extend implementations by creating a prompt engineering strategy that utilizes two different chemical string representation algorithms: one for the query and the other for the database. We explore this method by reviewing the search results from five drug-like query molecules (penicillin G, nirmatrelvir, zidovudine, lysergic acid diethylamide, and fentanyl) and three dye-like query molecules (acid blue 25, avobenzone, and 2-diphenylaminocarbazole). We find that this novel method identifies molecules that are functionally similar to the query, indicated by the associated patent literature, and that many of these molecules are structurally distinct from the query, making them unlikely to be found with traditional chemical similarity search methods. This method may aid in the discovery of novel structural classes of molecules that achieve target functionality.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

We discuss an algorithm which produces the meaning of a sentence given meanings of its words, and its resemblance to quantum teleportation. In fact, this protocol was the main source of inspiration for this algorithm which has many applications in the area of Natural Language Processing.

Large language models are increasingly used as chemistry assistants, yet most chemistry benchmarks still score only final answers. This masks a critical failure mode: a model may output the correct molecule, product, or option while its reasoning violates chemical logic. Existing process-level evaluators are hard to scale because LLM judges and human step-level process annotation are costly, inconsistent, and vulnerable to hallucination. We introduce ChemCoTBench-V2, a rule-verifiable diagnostic benchmark for low-cost, auditable evaluation of structured, verifier-addressable chemical reasoning traces. It spans molecular understanding, molecule editing, molecular optimization, and reaction prediction, with 5,620 evaluation samples across 18 reporting tasks. Models must expose key intermediate steps in expert-designed templates, and those steps are checked with deterministic chemistry rules and, for closed-answer tasks, reference traces rather than another LLM judge. Open-ended molecular optimization is evaluated with oracle-verifiable state constraints rather than strict trace matching. The benchmark reports three separate signals: final-answer correctness, template adherence, and step-wise verifier correctness over expert-refined intermediate commitments. Experiments on frontier models reveal a persistent gap between final-answer success and structured-reasoning-state consistency: models often follow the requested format while failing chemical-step checks, or answer correctly with weak supporting reasoning. ChemCoTBench-V2 enables fine-grained model comparison and identifies the concrete step at which the trace first violates the verifier.

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 to introduce the study of algorithms which use predictions parsimoniously. We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

An important recurring pattern in scientific breakthroughs is a two-stage process: an initial phase of undirected experimentation that yields an unexpected finding, followed by a retrospective phase that explains why the finding works and situates it within existing theory. We present ResearchEVO, an end-to-end framework that computationally instantiates this discover-then-explain paradigm. The Evolution Phase employs LLM-guided bi-dimensional co-evolution -- simultaneously optimizing both algorithmic logic and overall architecture -- to search the space of code implementations purely by fitness, without requiring any understanding of the solutions it produces. The Writing Phase then takes the best-performing algorithm and autonomously generates a complete, publication-ready research paper through sentence-level retrieval-augmented generation with explicit anti-hallucination verification and automated experiment design. To our knowledge, ResearchEVO is the first system to cover this full pipeline end to end: no prior work jointly performs principled algorithm evolution and literature-grounded scientific documentation. We validate the framework on two cross-disciplinary scientific problems -- Quantum Error Correction using real Google quantum hardware data, and Physics-Informed Neural Networks -- where the Evolution Phase discovered human-interpretable algorithmic mechanisms that had not been previously proposed in the respective domain literatures. In both cases, the Writing Phase autonomously produced compilable LaTeX manuscripts that correctly grounded these blind discoveries in existing theory via RAG, with zero fabricated citations.

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

We give a deterministic O(mlog^{2/3}n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the O(m+nlog n) time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to an external modus operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. This mode escalates the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways, pioneering a new mode of in-context learning. By employing algorithmic examples, we exploit the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and stands on par with a recent multi-query strategy that employs an extensive tree search algorithm. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

Concerns about hallucinations in Large Language Models (LLMs) have been raised by researchers, yet their potential in areas where creativity is vital, such as drug discovery, merits exploration. In this paper, we come up with the hypothesis that hallucinations can improve LLMs in drug discovery. To verify this hypothesis, we use LLMs to describe the SMILES string of molecules in natural language and then incorporate these descriptions as part of the prompt to address specific tasks in drug discovery. Evaluated on seven LLMs and five classification tasks, our findings confirm the hypothesis: LLMs can achieve better performance with text containing hallucinations. Notably, Llama-3.1-8B achieves an 18.35% gain in ROC-AUC compared to the baseline without hallucination. Furthermore, hallucinations generated by GPT-4o provide the most consistent improvements across models. Additionally, we conduct empirical analyses and a case study to investigate key factors affecting performance and the underlying reasons. Our research sheds light on the potential use of hallucinations for LLMs and offers new perspectives for future research leveraging LLMs in drug discovery.

Modern optimization in experimental chemistry employs algorithmic search through black-box parameter spaces. Here we demonstrate that pre-trained knowledge in large language models (LLMs) fundamentally changes this paradigm. Using six fully enumerated categorical reaction datasets (768 - 5,684 experiments), we benchmark LLM-guided optimization (LLM-GO) against Bayesian optimization (BO) and random sampling. Frontier LLMs consistently match or exceed BO performance across five single-objective datasets, with advantages growing as parameter complexity increases and high-performing conditions become scarce (<5% of space). BO retains superiority only for explicit multi-objective trade-offs. To understand these contrasting behaviors, we introduce a topology-agnostic information theory framework quantifying sampling diversity throughout optimization campaigns. This analysis reveals that LLMs maintain systematically higher exploration entropy than BO across all datasets while achieving superior performance, with advantages most pronounced in solution-scarce parameter spaces where high-entropy exploration typically fails - suggesting that pre-trained domain knowledge enables more effective navigation of chemical parameter space rather than replacing structured exploration strategies. To enable transparent benchmarking and community validation, we release Iron Mind (https://gomes.andrew.cmu.edu/iron-mind), a no-code platform for side-by-side evaluation of human, algorithmic, and LLM optimization campaigns with public leaderboards and complete trajectories. Our findings establish that LLM-GO excels precisely where traditional methods struggle: complex categorical spaces requiring domain understanding rather than mathematical optimization.

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent variational algorithm used for solving combinatorial optimization problems such as the Max-Cut problem. A key challenge in QAOA lies in efficiently identifying suitable parameters (gamma, beta) that lead to high-quality solutions. In this paper, we propose a framework that combines Fully Informed Particle Swarm Optimization (FIPSO) with adaptive gradient correction using the Adam Optimizer to navigate the QAOA parameter space. This approach aims to avoid issues such as barren plateaus and convergence to local minima. The proposed algorithm is evaluated against two classes of graph instances, Erdos Renyi and Watts-Strogatz. Experimental results across multiple QAOA depths consistently demonstrate superior performance compared to random initialization, underscoring the effectiveness and robustness of the proposed optimization framework.

Large language models are increasingly used in scientific domains, especially for molecular understanding and analysis. However, existing models are affected by hallucination issues, resulting in errors in drug design and utilization. In this paper, we first analyze the sources of hallucination in LLMs for molecular comprehension tasks, specifically the knowledge shortcut phenomenon observed in the PubChem dataset. To evaluate hallucination in molecular comprehension tasks with computational efficiency, we introduce Mol-Hallu, a novel free-form evaluation metric that quantifies the degree of hallucination based on the scientific entailment relationship between generated text and actual molecular properties. Utilizing the Mol-Hallu metric, we reassess and analyze the extent of hallucination in various LLMs performing molecular comprehension tasks. Furthermore, the Hallucination Reduction Post-processing stage~(HRPP) is proposed to alleviate molecular hallucinations, Experiments show the effectiveness of HRPP on decoder-only and encoder-decoder molecular LLMs. Our findings provide critical insights into mitigating hallucination and improving the reliability of LLMs in scientific applications.

Recent advancements in large language models have opened new possibilities for generative molecular drug design. We present Chemlactica and Chemma, two language models fine-tuned on a novel corpus of 110M molecules with computed properties, totaling 40B tokens. These models demonstrate strong performance in generating molecules with specified properties and predicting new molecular characteristics from limited samples. We introduce a novel optimization algorithm that leverages our language models to optimize molecules for arbitrary properties given limited access to a black box oracle. Our approach combines ideas from genetic algorithms, rejection sampling, and prompt optimization. It achieves state-of-the-art performance on multiple molecular optimization benchmarks, including an 8% improvement on Practical Molecular Optimization compared to previous methods. We publicly release the training corpus, the language models and the optimization algorithm.

We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of ε-optimal goal-conditioned policies attaining all states that are incrementally reachable within L steps (in expectation) from a reference state s_0. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s_0 and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as O(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2}), where A is the number of actions, S_{L+ε} is the number of states that are incrementally reachable from s_0 in L+ε steps, and Γ_{L+ε} is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both ε and L at the cost of an extra Γ_{L+ε} factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an ε/c_{min}-optimal policy for any cost-sensitive shortest-path problem defined on the L-reachable states with minimum cost c_{min}. Finally, we report preliminary empirical results confirming our theoretical findings.

A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. Recent work of Gomes et al. [2019] on heuristic combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies. The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular it is found that natural evolution strategies can achieve approximation ratios competitive with widely used heuristic algorithms for Max-Cut, at the expense of increased computation time.

Retrosynthesis is one of the fundamental problems in organic chemistry. The task is to identify reactants that can be used to synthesize a specified product molecule. Recently, computer-aided retrosynthesis is finding renewed interest from both chemistry and computer science communities. Most existing approaches rely on template-based models that define subgraph matching rules, but whether or not a chemical reaction can proceed is not defined by hard decision rules. In this work, we propose a new approach to this task using the Conditional Graph Logic Network, a conditional graphical model built upon graph neural networks that learns when rules from reaction templates should be applied, implicitly considering whether the resulting reaction would be both chemically feasible and strategic. We also propose an efficient hierarchical sampling to alleviate the computation cost. While achieving a significant improvement of 8.1% over current state-of-the-art methods on the benchmark dataset, our model also offers interpretations for the prediction.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Finding new drugs is getting harder and harder. One of the hopes of drug discovery is to use machine learning models to predict molecular properties. That is why models for molecular property prediction are being developed and tested on benchmarks such as MoleculeNet. However, existing benchmarks are unrealistic and are too different from applying the models in practice. We have created a new practical Lo-Hi benchmark consisting of two tasks: Lead Optimization (Lo) and Hit Identification (Hi), corresponding to the real drug discovery process. For the Hi task, we designed a novel molecular splitting algorithm that solves the Balanced Vertex Minimum k-Cut problem. We tested state-of-the-art and classic ML models, revealing which works better under practical settings. We analyzed modern benchmarks and showed that they are unrealistic and overoptimistic. Review: https://openreview.net/forum?id=H2Yb28qGLV Lo-Hi benchmark: https://github.com/SteshinSS/lohi_neurips2023 Lo-Hi splitter library: https://github.com/SteshinSS/lohi_splitter

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

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets X_m of the set X_n (subset sum problem). Our algorithm has time complexity T=O(C_{n}^{k}) (k=[m/2], which significantly improves upon all known algorithms. This algorithm is applicable to all NP-complete problems. Moreover, the algorithm has memory complexity M=O(C_n^k), which makes our algorithm applicable to real-world problems. At first, we show how to use the algorithm for small dimensions m=4 ,5 ,6 ,7 ,8. After that we establish a general methodology for m>8. The main idea is to split the original set X_n (the algorithm becomes even faster with sorted sets) into smaller subsets and use parallel computing. This approach might be a significant breakthrough towards finding an efficient solution to NP-complete problems. As a result, it opens a way to prove the P versus NP problem (one of the seven Millennium Prize Problems).

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Chemical language models, combined with reinforcement learning (RL), have shown significant promise to efficiently traverse large chemical spaces for drug discovery. However, the performance of various RL algorithms and their best practices for practical drug discovery are still unclear. Here, starting from the principles of the REINFORCE algorithm, we investigate the effect of different components from RL theory including experience replay, hill-climbing, baselines to reduce variance, and alternative reward shaping. We propose a new regularization method more aligned to REINFORCE than current standard practices, and demonstrate how RL hyperparameters can be fine-tuned for effectiveness and efficiency. Lastly, we apply our learnings to practical drug discovery by demonstrating enhanced learning efficiency on frontier binding affinity models by using Boltz2 as a reward model. We share our RL models used in the ACEGEN repository, and hope the experiments here act as a guide to researchers applying RL to chemical language models for drug discovery.

Quantum architecture Search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS emphasize Multi-Layer Perceptron (MLP)-based deep Q-networks. However, their interpretability remains challenging due to the large number of learnable parameters and the complexities involved in selecting appropriate activation functions. In this work, to overcome these challenges, we utilize the Kolmogorov-Arnold Network (KAN) in the QAS algorithm, analyzing their efficiency in the task of quantum state preparation and quantum chemistry. In quantum state preparation, our results show that in a noiseless scenario, the probability of success is 2 to 5 times higher than MLPs. In noisy environments, KAN outperforms MLPs in fidelity when approximating these states, showcasing its robustness against noise. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating curriculum reinforcement learning with a KAN structure. This facilitates a more efficient design of parameterized quantum circuits by reducing the number of required 2-qubit gates and circuit depth. Further investigation reveals that KAN requires a significantly smaller number of learnable parameters compared to MLPs; however, the average time of executing each episode for KAN is higher.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Hallucination has been widely recognized to be a significant drawback for large language models (LLMs). There have been many works that attempt to reduce the extent of hallucination. These efforts have mostly been empirical so far, which cannot answer the fundamental question whether it can be completely eliminated. In this paper, we formalize the problem and show that it is impossible to eliminate hallucination in LLMs. Specifically, we define a formal world where hallucination is defined as inconsistencies between a computable LLM and a computable ground truth function. By employing results from learning theory, we show that LLMs cannot learn all of the computable functions and will therefore always hallucinate. Since the formal world is a part of the real world which is much more complicated, hallucinations are also inevitable for real world LLMs. Furthermore, for real world LLMs constrained by provable time complexity, we describe the hallucination-prone tasks and empirically validate our claims. Finally, using the formal world framework, we discuss the possible mechanisms and efficacies of existing hallucination mitigators as well as the practical implications on the safe deployment of LLMs.

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by min{mathcal{O}(R^2/ε^2), mathcal{O}(m)} to obtain an ε-approximation of the PPR vector, where m denotes the number of edges in the graph and R is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only mathcal{O}(1/sqrtα) such linear systems, where α is the damping factor. When 1/ε^2ll m, this implies the existence of an algorithm that computes an epsilon -approximation of the PPR vector with an overall time complexity of mathcal{O}left(R^2 / (sqrtαε^2)right), independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded, answers to unanswerable problems. We introduce TreeCut, a synthetic dataset that systematically generates infinite unanswerable math word problems and their answerable counterparts, by representing each question as a tree and removing chosen necessary conditions. Experiments show TreeCut effectively induce hallucinations in large language models, including GPT-4o and o3-mini, with rates of 64% and 44% in their respective worst-case scenarios under zero-shot setting. Further analysis highlights that deeper or more complex trees, composite item names, and removing necessary condition near the middle of a path all increase the likelihood of hallucinations, underscoring the persistent challenges LLMs face in identifying unanswerable math problems. The dataset generation code and sample data are available at https://github.com/j-bagel/treecut-math.

One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of strings. In this paper, we select a typical parallel LCS algorithm and integrate it into our large-scale string analysis algorithm library to support different types of large string analysis. Specifically, we take advantage of the high-level parallel language, Chapel, to integrate Lu and Liu's parallel LCS algorithm into Arkouda, an open-source framework. Through Arkouda, data scientists can easily handle large string analytics on the back-end high-performance computing resources from the front-end Python interface. The Chapel-enabled parallel LCS algorithm can identify the longest common subsequences of two strings, and experimental results are given to show how the number of parallel resources and the length of input strings can affect the algorithm's performance.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an Ntimes N matrix M, an N-dimensional vector emph{b}, and an initial vector emph{x}(0), obtain a target vector emph{x}(t) as a function of time t according to the constraint demph{x}(t)/dt=Memph{x}(t)+emph{b}. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4times4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

The efficient exploration of chemical space to design molecules with intended properties enables the accelerated discovery of drugs, materials, and catalysts, and is one of the most important outstanding challenges in chemistry. Encouraged by the recent surge in computer power and artificial intelligence development, many algorithms have been developed to tackle this problem. However, despite the emergence of many new approaches in recent years, comparatively little progress has been made in developing realistic benchmarks that reflect the complexity of molecular design for real-world applications. In this work, we develop a set of practical benchmark tasks relying on physical simulation of molecular systems mimicking real-life molecular design problems for materials, drugs, and chemical reactions. Additionally, we demonstrate the utility and ease of use of our new benchmark set by demonstrating how to compare the performance of several well-established families of algorithms. Surprisingly, we find that model performance can strongly depend on the benchmark domain. We believe that our benchmark suite will help move the field towards more realistic molecular design benchmarks, and move the development of inverse molecular design algorithms closer to designing molecules that solve existing problems in both academia and industry alike.

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm.

On-policy self-distillation, where a student is pulled toward a copy of itself conditioned on privileged context (e.g., a verified solution or feedback), offers a promising direction for advancing reasoning capability without a stronger external teacher. Yet in math reasoning the gains are inconsistent, even when the same approach succeeds elsewhere. A pointwise mutual information analysis traces the failure to the privileged context itself: it inflates the teacher's confidence on tokens already implied by the solution (structural connectives, verifiable claims) and deflates it on deliberation tokens ("Wait", "Let", "Maybe") that drive multi-step search. We propose Anti-Self-Distillation (AntiSD), which ascends a divergence between student and teacher rather than descending it: this reverses the per-token sign and yields a naturally bounded advantage in one step. An entropy-triggered gate disables the term once the teacher entropy collapses, completing a drop-in replacement for default self-distillation. Across five models from 4B to 30B parameters on math reasoning benchmarks, AntiSD reaches the GRPO baseline's accuracy in 2 to 10x fewer training steps and improves final accuracy by up to 11.5 points. AntiSD opens a path to scalable self-improvement, where a language model bootstraps its own reasoning through its training signal.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

The overwhelming majority of molecules remains unexplored. This is mostly due to the sheer number of them, which prohibits any enumeration of chemical space, the set of all such molecules. In practice, only subsets of chemical space are considered, but those subsets exhibit substantial bias, prohibiting data-driven characterization of chemical space itself. In this work, we provide a method produce unbiased representative random samples of chemical space without enumeration of constituent molecules and to estimate the number of molecules in any custom chemical space. The approach is applicable to molecules which can be represented as graph and runs efficiently even for molecules of 30 atoms. We use it to estimate the representativeness of current databases with respect to their underlying chemical space and to establish a necessary criterion for a lower bound of database sizes to be representative of an underlying chemical space.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based reasoning solutions usually suffer from significant performance degradation on huge evidence (tables). In addition, most existing methods struggle to reason over complex questions since the required information is scattered in different places. To alleviate the above challenges, we exploit large language models (LLMs) as decomposers for effective table-based reasoning, which (i) decompose huge evidence (a huge table) into sub-evidence (a small table) to mitigate the interference of useless information for table reasoning; and (ii) decompose complex questions into simpler sub-questions for text reasoning. Specifically, we first use the LLMs to break down the evidence (tables) involved in the current question, retaining the relevant evidence and excluding the remaining irrelevant evidence from the huge table. In addition, we propose a "parsing-execution-filling" strategy to alleviate the hallucination dilemma of the chain of thought by decoupling logic and numerical computation in each step. Extensive experiments show that our method can effectively leverage decomposed evidence and questions and outperforms the strong baselines on TabFact, WikiTableQuestion, and FetaQA datasets. Notably, our model outperforms human performance for the first time on the TabFact dataset.

Object hallucination has been an Achilles' heel which hinders the broader applications of large vision-language models (LVLMs). Object hallucination refers to the phenomenon that the LVLMs claim non-existent objects in the image. To mitigate the object hallucinations, instruction tuning and external model-based detection methods have been proposed, which either require large-scare computational resources or depend on the detection result of external models. However, there remains an under-explored field to utilize the LVLM itself to alleviate object hallucinations. In this work, we adopt the intuition that the LVLM tends to respond logically consistently for existent objects but inconsistently for hallucinated objects. Therefore, we propose a Logical Closed Loop-based framework for Object Hallucination Detection and Mitigation, namely LogicCheckGPT. In specific, we devise logical consistency probing to raise questions with logical correlations, inquiring about attributes from objects and vice versa. Whether their responses can form a logical closed loop serves as an indicator of object hallucination. As a plug-and-play method, it can be seamlessly applied to all existing LVLMs. Comprehensive experiments conducted on three benchmarks across four LVLMs have demonstrated significant improvements brought by our method, indicating its effectiveness and generality.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10\%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33\% to 35\% in our same setup. In particular, a 6\% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

Generative molecular design has moved from proof-of-concept to real-world applicability, as marked by the surge in very recent papers reporting experimental validation. Key challenges in explainability and sample efficiency present opportunities to enhance generative design to directly optimize expensive high-fidelity oracles and provide actionable insights to domain experts. Here, we propose Beam Enumeration to exhaustively enumerate the most probable sub-sequences from language-based molecular generative models and show that molecular substructures can be extracted. When coupled with reinforcement learning, extracted substructures become meaningful, providing a source of explainability and improving sample efficiency through self-conditioned generation. Beam Enumeration is generally applicable to any language-based molecular generative model and notably further improves the performance of the recently reported Augmented Memory algorithm, which achieved the new state-of-the-art on the Practical Molecular Optimization benchmark for sample efficiency. The combined algorithm generates more high reward molecules and faster, given a fixed oracle budget. Beam Enumeration shows that improvements to explainability and sample efficiency for molecular design can be made synergistic.

This paper studies the problem of solving complex chemistry problems with large language models (LLMs). Despite the extensive general knowledge in LLMs (such as GPT-4), they struggle with chemistry reasoning that requires faithful grounded reasoning with diverse chemical knowledge and an integrative understanding of chemical interactions. We propose InstructChem, a new structured reasoning approach that substantially boosts the LLMs' chemical reasoning capabilities. InstructChem explicitly decomposes the reasoning into three critical phrases, including chemical formulae generation by LLMs that offers the basis for subsequent grounded reasoning, step-by-step reasoning that makes multi-step derivations with the identified formulae for a preliminary answer, and iterative review-and-refinement that steers LLMs to progressively revise the previous phases for increasing confidence, leading to the final high-confidence answer. We conduct extensive experiments on four different chemistry challenges, including quantum chemistry, quantum mechanics, physical chemistry, and chemistry kinetics. Our approach significantly enhances GPT-4 on chemistry reasoning, yielding an 8% average absolute improvement and a 30% peak improvement. We further use the generated reasoning by GPT-4 to fine-tune smaller LMs (e.g., Vicuna) and observe strong improvement of the smaller LMs. This validates our approach and enables LLMs to generate high-quality reasoning.

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

Recently, the impressive performance of large language models (LLMs) on a wide range of tasks has attracted an increasing number of attempts to apply LLMs in drug discovery. However, molecule optimization, a critical task in the drug discovery pipeline, is currently an area that has seen little involvement from LLMs. Most of existing approaches focus solely on capturing the underlying patterns in chemical structures provided by the data, without taking advantage of expert feedback. These non-interactive approaches overlook the fact that the drug discovery process is actually one that requires the integration of expert experience and iterative refinement. To address this gap, we propose DrugAssist, an interactive molecule optimization model which performs optimization through human-machine dialogue by leveraging LLM's strong interactivity and generalizability. DrugAssist has achieved leading results in both single and multiple property optimization, simultaneously showcasing immense potential in transferability and iterative optimization. In addition, we publicly release a large instruction-based dataset called MolOpt-Instructions for fine-tuning language models on molecule optimization tasks. We have made our code and data publicly available at https://github.com/blazerye/DrugAssist, which we hope to pave the way for future research in LLMs' application for drug discovery.

Employing Large Language Models (LLMs) for semantic parsing has achieved remarkable success. However, we find existing methods fall short in terms of reliability and efficiency when hallucinations are encountered. In this paper, we address these challenges with a framework called QueryAgent, which solves a question step-by-step and performs step-wise self-correction. We introduce an environmental feedback-based self-correction method called ERASER. Unlike traditional approaches, ERASER leverages rich environmental feedback in the intermediate steps to perform selective and differentiated self-correction only when necessary. Experimental results demonstrate that QueryAgent notably outperforms all previous few-shot methods using only one example on GrailQA and GraphQ by 7.0 and 15.0 F1. Moreover, our approach exhibits superiority in terms of efficiency, including runtime, query overhead, and API invocation costs. By leveraging ERASER, we further improve another baseline (i.e., AgentBench) by approximately 10 points, revealing the strong transferability of our approach.

Masked diffusion language models decode by iteratively unmasking tokens, where the unmasking order defines an "order of thought" that strongly influences generation quality yet is typically chosen heuristically. We derive a tractable upper bound on the sequential decoding mismatch, measured by the Kullback-Leibler divergence and expressed in terms of the model's pathwise log-likelihood, with tightness under sufficient model expressivity. This bound induces a dense self-aware reward over ordered trajectories, casting order selection as a principled policy optimization problem with a frozen denoiser. We instantiate this idea as Self-Aware Scheduling (SAS), which learns a lightweight order policy using Group Relative Policy Optimization and applies seamlessly to both any-order and semi-autoregressive decoding. On Sudoku with 1B MDM, SAS improves puzzle accuracy from 82.0% (best heuristic schedule) to 91.8%, and reaches 97.5% with second-stage fine-tuning along learned trajectories. On mathematical reasoning with LLaDA-8B, SAS improves pass@1 on GSM8K from 64% to 76% and on MBPP from 39.5% to 41%, consistently matching or exceeding heuristic schedules across generation lengths and block sizes. Project page: https://jimmyxu123.github.io/SAS

Every chemical language model reading SMILES begins with a tokenizer, yet the field has inherited byte-pair encoding (BPE) from natural language with little scrutiny. In natural language, BPE's principal alternative, Unigram-LM, is known to build structurally different vocabularies. Whether that contrast survives in chemistry was open. We report a controlled comparison of BPE and Unigram-LM over a fixed 165-token chemistry base, at the small vocabulary sizes where token embeddings are learnable, across three corpus typologies (diverse, drug-like, natural-products) and both pre-tokenization boundary policies. The two do not converge. In all 22 matched conditions they build near-disjoint subword vocabularies: cross-algorithm Jaccard overlap on the learned pieces never exceeds 0.161, and at most 0.05 once weighted toward the high-frequency pieces a model updates most. Unigram-LM also segments held-out molecules into 29-41% more tokens; the arms largely agree on where to cut but not how deeply, so BPE's segmentation is a strict coarsening of Unigram-LM's on 80-99% of molecules. The separation holds across corpus, boundary, and vocabulary size, persisting even at eight times that scale. The subword algorithm is therefore a modeling decision, not a free default. The study trains no language models.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d^4) for the basis change plus O(d^3) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d^3) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.

To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on backward chaining, where the proof goal is recursively decomposed to subgoals by searching and applying rules. We argue that current LLM-based backward chaining systems (e.g. Least-to-most prompting and LAMBADA) are incomplete, as they omit crucial algorithmic components identified from the classic backward chaining algorithm in computational logic (SLD Resolution). To this end, we propose a novel backward chaining system, SymBa (Symbolic Backward Chaining), which integrates a symbolic solver and an LLM. In SymBa, the solver controls the proof process, and the LLM is only called when the solver requires new information to complete the proof. Empowered by completeness, SymBa achieves a significant improvement in seven deductive, relational, and arithmetic reasoning benchmarks compared to the baselines.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Molecular representation is a foundational element in our understanding of the physical world. Its importance ranges from the fundamentals of chemical reactions to the design of new therapies and materials. Previous molecular machine learning models have employed strings, fingerprints, global features, and simple molecular graphs that are inherently information-sparse representations. However, as the complexity of prediction tasks increases, the molecular representation needs to encode higher fidelity information. This work introduces a novel approach to infusing quantum-chemical-rich information into molecular graphs via stereoelectronic effects. We show that the explicit addition of stereoelectronic interactions significantly improves the performance of molecular machine learning models. Furthermore, stereoelectronics-infused representations can be learned and deployed with a tailored double graph neural network workflow, enabling its application to any downstream molecular machine learning task. Finally, we show that the learned representations allow for facile stereoelectronic evaluation of previously intractable systems, such as entire proteins, opening new avenues of molecular design.

A genetic algorithm is suitable for exploring large search spaces as it finds an approximate solution. Because of this advantage, genetic algorithm is effective in exploring vast and unknown space such as molecular search space. Though the algorithm is suitable for searching vast chemical space, it is difficult to optimize pharmacological properties while maintaining molecular substructure. To solve this issue, we introduce a genetic algorithm featuring a constrained molecular inverse design. The proposed algorithm successfully produces valid molecules for crossover and mutation. Furthermore, it optimizes specific properties while adhering to structural constraints using a two-phase optimization. Experiments prove that our algorithm effectively finds molecules that satisfy specific properties while maintaining structural constraints.

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks by using some given positive and negative trajectories for solving the complex task. We assume that the states are represented by first-order predicate logic using which we devise a novel algorithm to identify the subtasks. Then we employ a Large Language Model (LLM) to generate first-order logic rule templates for achieving each subtask. Such rules were then further fined tuned to a rule-based policy via an Inductive Logic Programming (ILP)-based RL agent. Through experiments, we verify the accuracy of our algorithm in detecting subtasks which successfully detect all of the subtasks correctly. We also investigated the quality of the common-sense rules produced by the language model to achieve the subtasks. Our experiments show that our LLM-guided rule template generation can produce rules that are necessary for solving a subtask, which leads to solving complex tasks with fewer assumptions about predefined first-order logic predicates of the environment.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

The problem of minimizing the maximum of N convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring O(Nepsilon^{-2/3} + epsilon^{-8/3}) queries to a first-order oracle to compute an epsilon-suboptimal point. On the other hand, quantum algorithms for optimization are rapidly advancing with speedups shown on many important optimization problems. In this paper, we conduct a systematic study for quantum algorithms and lower bounds for minimizing the maximum of N convex, Lipschitz functions. On one hand, we develop quantum algorithms with an improved complexity bound of O(Nepsilon^{-5/3} + epsilon^{-8/3}). On the other hand, we prove that quantum algorithms must take Omega(Nepsilon^{-2/3}) queries to a first order quantum oracle, showing that our dependence on N is optimal up to poly-logarithmic factors.

Organic reaction mechanisms are the stepwise elementary reactions by which reactants form intermediates and products, and are fundamental to understanding chemical reactivity and designing new molecules and reactions. Although large language models (LLMs) have shown promise in understanding chemical tasks such as synthesis design, it is unclear to what extent this reflects genuine chemical reasoning capabilities, i.e., the ability to generate valid intermediates, maintain chemical consistency, and follow logically coherent multi-step pathways. We address this by introducing oMeBench, the first large-scale, expert-curated benchmark for organic mechanism reasoning in organic chemistry. It comprises over 10,000 annotated mechanistic steps with intermediates, type labels, and difficulty ratings. Furthermore, to evaluate LLM capability more precisely and enable fine-grained scoring, we propose oMeS, a dynamic evaluation framework that combines step-level logic and chemical similarity. We analyze the performance of state-of-the-art LLMs, and our results show that although current models display promising chemical intuition, they struggle with correct and consistent multi-step reasoning. Notably, we find that using prompting strategy and fine-tuning a specialist model on our proposed dataset increases performance by 50% over the leading closed-source model. We hope that oMeBench will serve as a rigorous foundation for advancing AI systems toward genuine chemical reasoning.

This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.

Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive manual annotation, limiting their scale, or risk measuring memorization rather than genuine reasoning. To address this, we introduce an automated pipeline named A2RBench, encompassing generation, expansion, evaluation, and analysis. Specifically, in the generation stage, LLMs create diverse tasks demanding genuine reasoning; in the expansion stage, LLMs reuse validated rules and expand new input spaces to generate task variations, achieving scaling. However, such a process may cause hallucinations. To eliminate it, we further establish a theoretical framework and prove that programmatic verification--testing whether the inverse operation perfectly reverses the forward operation (cycle consistency)--guarantees a unique solution. Through extensive evaluations on mainstream LLMs, we find: (1) Current LLMs exhibit fundamental deficiencies in abstract reasoning, with top models significantly underperforming humans on a representative subset (39.8% vs. 68.5%). (2) Current LLMs fall far short of 2D and 1D in the complexity of generated 3D tasks, revealing their lack of understanding of high-dimensional tasks. (3) Counterintuitively, inputs with higher information complexity can simplify the reasoning process.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Reducing hallucination of Large Language Models (LLMs) is imperative for use in the sciences where reproducibility is crucial. However, LLMs inherently lack long-term memory, making it a nontrivial, ad hoc, and inevitably biased task to fine-tune them on domain-specific literature and data. Here we introduce LLaMP, a multimodal retrieval-augmented generation (RAG) framework of multiple data-aware reasoning-and-acting (ReAct) agents that dynamically interact with computational and experimental data on Materials Project (MP). Without fine-tuning, LLaMP demonstrates an ability to comprehend and integrate various modalities of materials science concepts, fetch relevant data stores on the fly, process higher-order data (such as crystal structures and elastic tensors), and summarize multi-step procedures for solid-state synthesis. We show that LLaMP effectively corrects errors in GPT-3.5's intrinsic knowledge, reducing a 5.21% MAPE on frequently-documented bandgaps and a significant 1103.54% MAPE on formation energies -- errors that GPT-3.5 seems to derive from mixed data sources. Additionally, LLaMP substantially reduces the hallucinated volumetric strain in a diamond cubic silicon structure from 66.3% to 0. The proposed framework offers an intuitive and nearly hallucination-free approach to exploring materials informatics and establishes a pathway for knowledge distillation and fine-tuning other language models. We envision the framework as a valuable component for scientific hypotheses and a foundation for future autonomous laboratories where multiple LLM agents communicate and cooperate with robotics to drive material synthesis and chemical reactions without hard-coded human logic and intervention.

Reasoning ability has become a central focus in the advancement of Large Reasoning Models (LRMs). Although notable progress has been achieved on several reasoning benchmarks such as MATH500 and LiveCodeBench, existing benchmarks for algorithmic reasoning remain limited, failing to answer a critical question: Do LRMs truly master algorithmic reasoning? To answer this question, we propose AlgBench, an expert-curated benchmark that evaluates LRMs under an algorithm-centric paradigm. AlgBench consists of over 3,000 original problems spanning 27 algorithms, constructed by ACM algorithmic experts and organized under a comprehensive taxonomy, including Euclidean-structured, non-Euclidean-structured, non-optimized, local-optimized, global-optimized, and heuristic-optimized categories. Empirical evaluations on leading LRMs (e.g., Gemini-3-Pro, DeepSeek-v3.2-Speciale and GPT-o3) reveal substantial performance heterogeneity: while models perform well on non-optimized tasks (up to 92%), accuracy drops sharply to around 49% on globally optimized algorithms such as dynamic programming. Further analysis uncovers strategic over-shifts, wherein models prematurely abandon correct algorithmic designs due to necessary low-entropy tokens. These findings expose fundamental limitations of problem-centric reinforcement learning and highlight the necessity of an algorithm-centric training paradigm for robust algorithmic reasoning.

Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories -- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.

Large language models (LLMs) have shown promise in automating scientific hypothesis generation, yet existing approaches primarily yield coarse-grained hypotheses lacking critical methodological and experimental details. We introduce and formally define the novel task of fine-grained scientific hypothesis discovery, which entails generating detailed, experimentally actionable hypotheses from coarse initial research directions. We frame this as a combinatorial optimization problem and investigate the upper limits of LLMs' capacity to solve it when maximally leveraged. Specifically, we explore four foundational questions: (1) how to best harness an LLM's internal heuristics to formulate the fine-grained hypothesis it itself would judge as the most promising among all the possible hypotheses it might generate, based on its own internal scoring-thus defining a latent reward landscape over the hypothesis space; (2) whether such LLM-judged better hypotheses exhibit stronger alignment with ground-truth hypotheses; (3) whether shaping the reward landscape using an ensemble of diverse LLMs of similar capacity yields better outcomes than defining it with repeated instances of the strongest LLM among them; and (4) whether an ensemble of identical LLMs provides a more reliable reward landscape than a single LLM. To address these questions, we propose a hierarchical search method that incrementally proposes and integrates details into the hypothesis, progressing from general concepts to specific experimental configurations. We show that this hierarchical process smooths the reward landscape and enables more effective optimization. Empirical evaluations on a new benchmark of expert-annotated fine-grained hypotheses from recent chemistry literature show that our method consistently outperforms strong baselines.

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication. The approach replaces expensive exact evaluation with fast heuristic scoring, including the new Greedy-Intersections strategy. The method runs many independent common subexpression elimination processes in parallel, exploring the search space through random pair substitutions and diverse selection strategies while sharing promising partial solutions. Tested on 164 ternary-coefficient schemes, the method achieves lower addition counts than the state-of-the-art Greedy-Potential on 103 schemes, matches it on 59, and is outperformed on 2. For most schemes, it gives equal or better results while being much faster, making it practical for algorithm exploration. All software and results are open source.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT li2024chain,merrill2023expresssive.

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.

Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the years. Recent advancements in evolutionary search with large language models (LLMs) have shown promise in accelerating the discovery of algorithms across various domains, particularly in mathematics and optimization. However, existing approaches treat the LLM as a static generator, missing the opportunity to update the model with the signal obtained from evolutionary exploration. In this work, we propose to augment LLM-based evolutionary search by continuously refining the search operator - the LLM - through reinforcement learning (RL) fine-tuning. Our method leverages evolutionary search as an exploration strategy to discover improved algorithms, while RL optimizes the LLM policy based on these discoveries. Our experiments on three combinatorial optimization tasks - bin packing, traveling salesman, and the flatpack problem - show that combining RL and evolutionary search improves discovery efficiency of improved algorithms, showcasing the potential of RL-enhanced evolutionary strategies to assist computer scientists and mathematicians for more efficient algorithm design.

Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully descriptive of the system, must facilitate the training process and must be invertible, so that one can extract the atomic configurations corresponding to the output of the model. In general, this last requirement is not automatically satisfied by the most efficient structural descriptors, namely the representation is not directly invertible. Such drawback severely limits our freedom of choice in selecting the most appropriate descriptors for the problem, and thus our flexibility to construct generative models. In this work, we present a general optimization method capable of inverting any local many-body descriptor of the chemical environment, back to a cartesian representation. The algorithm is then implemented together with the bispectrum representation of the local structure and demonstrated for a number of molecules. The scheme presented here, thus, represents a general approach to the inversion of structural descriptors, enabling the construction of efficient structural generative models.

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes in the ternary field (Z_T), where coefficients are restricted to {-1, 0, 1} to minimize naive additive complexity. The core of the method is a GPU-accelerated meta flip graph algorithm that maintains ternary safety through specialized arithmetic operations and sign symmetry breaking. Key results include new best ranks for the formats 4 times 5 times 12, 5 times 6 times 10, and 6 times 7 times 9, the independent discovery of 32 schemes in Z_T that match known optimal ranks (including 8 previously known only with rational coefficients), and 30 rank improvements in the binary field. The analysis of 164 known schemes shows that 92 can be implemented in Z_T, while 72 could not be found in the ternary field with current methods, defining the current boundaries of this approach. All software, results, and discovered schemes are provided as open-source.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Neural algorithmic reasoning is an emerging area of machine learning focusing on building models that can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms that are able to generalize to out-of-distribution data, in particular with significantly larger input sizes. Recent work on this problem has demonstrated the advantages of learning algorithms step-by-step, giving models access to all intermediate steps of the original algorithm. In this work, we instead focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We propose simple but effective architectural improvements and also build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRS Algorithmic Reasoning Benchmark and achieves new state-of-the-art results for several problems, including sorting, where we obtain significant improvements. Thus, learning without intermediate supervision is a promising direction for further research on neural reasoners.

AI is undergoing a paradigm shift, with breakthroughs achieved by systems orchestrating multiple large language models (LLMs) and other complex components. As a result, developing principled and automated optimization methods for compound AI systems is one of the most important new challenges. Neural networks faced a similar challenge in its early days until backpropagation and automatic differentiation transformed the field by making optimization turn-key. Inspired by this, we introduce TextGrad, a powerful framework performing automatic ``differentiation'' via text. TextGrad backpropagates textual feedback provided by LLMs to improve individual components of a compound AI system. In our framework, LLMs provide rich, general, natural language suggestions to optimize variables in computation graphs, ranging from code snippets to molecular structures. TextGrad follows PyTorch's syntax and abstraction and is flexible and easy-to-use. It works out-of-the-box for a variety of tasks, where the users only provide the objective function without tuning components or prompts of the framework. We showcase TextGrad's effectiveness and generality across a diverse range of applications, from question answering and molecule optimization to radiotherapy treatment planning. Without modifying the framework, TextGrad improves the zero-shot accuracy of GPT-4o in Google-Proof Question Answering from 51% to 55%, yields 20% relative performance gain in optimizing LeetCode-Hard coding problem solutions, improves prompts for reasoning, designs new druglike small molecules with desirable in silico binding, and designs radiation oncology treatment plans with high specificity. TextGrad lays a foundation to accelerate the development of the next-generation of AI systems.

Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the verifier LLM. This is unnecessarily restrictive as slight variations of the verifier's distribution, such as sampling with top-k or temperature, would also be acceptable. Typical acceptance sampling (TAS) alleviates this issue by accepting more tokens using entropy-based heuristics. However, this approach distorts the verifier distribution, potentially degrading output quality when the verifier encodes critical information. In this work, we formalize the speculative sampling algorithm through the lens of constrained optimization. Based on this formulation, we propose Cactus (constrained acceptance speculative sampling), a method that guarantees controlled divergence from the verifier distribution and increasing acceptance rates. Empirical results across a wide range of benchmarks confirm the effectiveness of our approach.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

Large Language Models (LLMs) have become an indispensable part of natural language processing tasks. However, autoregressive sampling has become an efficiency bottleneck. Multi-Draft Speculative Decoding (MDSD) is a recent approach where, when generating each token, a small draft model generates multiple drafts, and the target LLM verifies them in parallel, ensuring that the final output conforms to the target model distribution. The two main design choices in MDSD are the draft sampling method and the verification algorithm. For a fixed draft sampling method, the optimal acceptance rate is a solution to an optimal transport problem, but the complexity of this problem makes it difficult to solve for the optimal acceptance rate and measure the gap between existing verification algorithms and the theoretical upper bound. This paper discusses the dual of the optimal transport problem, providing a way to efficiently compute the optimal acceptance rate. For the first time, we measure the theoretical upper bound of MDSD efficiency for vocabulary sizes in the thousands and quantify the gap between existing verification algorithms and this bound. We also compare different draft sampling methods based on their optimal acceptance rates. Our results show that the draft sampling method strongly influences the optimal acceptance rate, with sampling without replacement outperforming sampling with replacement. Additionally, existing verification algorithms do not reach the theoretical upper bound for both without replacement and with replacement sampling. Our findings suggest that carefully designed draft sampling methods can potentially improve the optimal acceptance rate and enable the development of verification algorithms that closely match the theoretical upper bound.

Large Language Models (LLMs) have demonstrated strong capabilities across various domains, with recent advancements in challenging reasoning tasks such as mathematics and programming. However, solving reasoning tasks often requires long decoding chains (of thoughts), which incur O(N) time and memory consumption, where N is the chain length. To mitigate O(N) time and memory consumption, existing sparsity-based algorithms propose retaining only the most critical token's intermediate data (i.e., key-value cache) and discarding the rest. However, these existing algorithms struggle with the ``impossible trinity'' of accuracy, time, and memory. For example, the state-of-the-art algorithm, Quest, achieves high accuracy with O(L) time but O(N) memory (L is the cache budget, L ll N). To address this issue, in this paper, we identify a new attention pattern during the decode stage of reasoning tasks, where milestone tokens (analogous to lemmas in mathematical proofs) emerge, are utilized, and then become unimportant afterward. Based on this pattern, we propose a new algorithm named RaaS that identifies and retains milestone tokens only until they are no longer needed, achieving high accuracy with O(L) time and O(L) memory complexity.

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

While Vision-Language Models (VLMs) have demonstrated significant potential in chemical visual understanding, current models are predominantly optimized for direct visual question-answering tasks. This paradigm often results in "black-box" systems that fail to utilize the inherent capability of Large Language Models (LLMs) to infer underlying reaction mechanisms. In this work, we introduce ChemVLR, a chemical VLM designed to prioritize reasoning within the perception process. Unlike conventional chemical VLMs, ChemVLR analyzes visual inputs in a fine-grained manner by explicitly identifying granular chemical descriptors, such as functional groups, prior to generating answers. This approach ensures the production of explicit and interpretable reasoning paths for complex visual chemical problems. To facilitate this methodology, we implement a cross-modality reverse-engineering strategy, combined with a rigorous filtering pipeline, to curate a large-scale reasoning-and-captioning dataset comprising 760k high-quality samples across molecular and reaction tasks. Furthermore, we adopt a three-stage training framework that systemically builds model perception and reasoning capacity. Experiments demonstrate that ChemVLR achieves state-of-the-art (SOTA) performance, surpassing both leading proprietary models and domain-specific open-source baselines. We also provide comprehensive ablation studies to validate our training strategy and data generation designs. Code and model weights will be available at https://github.com/xxlllz/ChemVLR.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.