In this paper, we first show that increases in beam size of even just small-sized LLM (1B-7B parameters) require an extensive GPU resource consumption, leading to up to 80% of recurring crashes due to memory overloads in LLM-based APR. Seemingly simple solutions to reduce memory consumption are (1) to quantize LLM models, i.e., converting the weights of a LLM from high-precision values to lower-precision ones. and (2) to make beam search sequential, i.e., forwarding each beam through the model sequentially and then concatenate them back into a single model output. However, we show that these approaches still do not work via both theoretical analysis and experiments. To address this, we introduce FLAMES, a novel LLM-based APR technique that employs semantic-guided patch generation to enhance repair effectiveness and memory efficiency. Unlike conventional methods that rely on beam search, FLAMES utilizes greedy decoding to enhance memory efficiency while steering the search to more potentially good repair candidates via a semantic-guided best-first search algorithm. At each decoding step, FLAMES uses semantic feedback from test validation such as the number of passing and failing test cases to select the most promising token to explore further. Our empirical evaluation on the Defects4J and HumanEval-Java datasets shows that FLAMES not only substantially reduces memory consumption by up to 83% compared to conventional LLM-based APR, but also accelerates the repair process. Remarkably, FLAMES successfully generated 133 and 103 correct fixes for 333 and 163 bugs in the Defects4J and HumanEval-Java datasets, respectively. This suggests that FLAMES is not only more efficient but also outperforms state-of-the-art techniques, fixing at least 10 and 11 more bugs than SOTA baselines in the Defects4J and HumanEval-Java datasets, respectively.

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. The major learning paradigm is expert iteration, which necessitates a pre-defined dataset comprising numerous mathematical problems. In this process, LLMs attempt to prove problems within the dataset and iteratively refine their capabilities through self-training on the proofs they discover. We propose to use large scale LEAN problem datasets Lean-workbook for expert iteration with more than 20,000 CPU days. During expert iteration, we found log-linear trends between solved problem amount with proof length and CPU usage. We train a critic model to select relatively easy problems for policy models to make trials and guide the model to search for deeper proofs. InternLM2.5-StepProver achieves open-source state-of-the-art on MiniF2F, Lean-Workbook-Plus, ProofNet, and Putnam benchmarks. Specifically, it achieves a pass of 65.9% on the MiniF2F-test and proves (or disproves) 17.0% of problems in Lean-Workbook-Plus which shows a significant improvement compared to only 9.5% of problems proved when Lean-Workbook-Plus was released. We open-source our models and searched proofs at https://github.com/InternLM/InternLM-Math and https://huggingface.co/datasets/internlm/Lean-Workbook.

Cooperative path planning, a crucial aspect of multi-agent systems research, serves a variety of sectors, including military, agriculture, and industry. Many existing algorithms, however, come with certain limitations, such as simplified kinematic models and inadequate support for multiple group scenarios. Focusing on the planning problem associated with a nonholonomic Ackermann model for Unmanned Ground Vehicles (UGV), we propose a leaderless, hierarchical Search-Based Cooperative Motion Planning (SCMP) method. The high-level utilizes a binary conflict search tree to minimize runtime, while the low-level fabricates kinematically feasible, collision-free paths that are shape-constrained. Our algorithm can adapt to scenarios featuring multiple groups with different shapes, outlier agents, and elaborate obstacles. We conduct algorithm comparisons, performance testing, simulation, and real-world testing, verifying the effectiveness and applicability of our algorithm. The implementation of our method will be open-sourced at https://github.com/WYCUniverStar/SCMP.

We study agents acting in an unknown environment where the agent's goal is to find a robust policy. We consider robust policies as policies that achieve high cumulative rewards for all possible environments. To this end, we consider agents minimizing the maximum regret over different environment parameters, leading to the study of minimax regret. This research focuses on deriving information-theoretic bounds for minimax regret in Markov Decision Processes (MDPs) with a finite time horizon. Building on concepts from supervised learning, such as minimum excess risk (MER) and minimax excess risk, we use recent bounds on the Bayesian regret to derive minimax regret bounds. Specifically, we establish minimax theorems and use bounds on the Bayesian regret to perform minimax regret analysis using these minimax theorems. Our contributions include defining a suitable minimax regret in the context of MDPs, finding information-theoretic bounds for it, and applying these bounds in various scenarios.

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.

This paper addresses two tasks: (i) fixed-size objects such as hay bales are to be identified in an aerial image for a given reference image of the object, and (ii) variable-size patches such as areas on fields requiring spot spraying or other handling are to be identified in an image for a given small-scale reference image. Both tasks are related. The second differs in that identified sub-images similar to the reference image are further clustered before patches contours are determined by solving a traveling salesman problem. Both tasks are complex in that the exact number of similar sub-images is not known a priori. The main discussion of this paper is presentation of an acceleration mechanism for sub-image search that is based on a transformation of an image to multivariate time series along the RGB-channels and subsequent segmentation to reduce the 2D search space in the image. Two variations of the acceleration mechanism are compared to exhaustive search on diverse synthetic and real-world images. Quantitatively, proposed method results in solve time reductions of up to 2 orders of magnitude, while qualitatively delivering comparative visual results. Proposed method is neural network-free and does not use any image pre-processing.

Gboard Decoder produces suggestions by looking for paths that best match input touch points on the context aware search space, which is backed by the language Finite State Transducers (FST). The language FST is currently an N-gram language model (LM). However, N-gram LMs, limited in context length, are known to have sparsity problem under device model size constraint. In this paper, we propose \textbf{Neural Search Space} which substitutes the N-gram LM with a Neural Network LM (NN-LM) and dynamically constructs the search space during decoding. Specifically, we integrate the long range context awareness of NN-LM into the search space by converting its outputs given context, into the language FST at runtime. This involves language FST structure redesign, pruning strategy tuning, and data structure optimizations. Online experiments demonstrate improved quality results, reducing Words Modified Ratio by [0.26\%, 1.19\%] on various locales with acceptable latency increases. This work opens new avenues for further improving keyboard decoding quality by enhancing neural LM more directly.

In multi-armed bandits, the tasks of reward maximization and pure exploration are often at odds with each other. The former focuses on exploiting arms with the highest means, while the latter may require constant exploration across all arms. In this work, we focus on good arm identification (GAI), a practical bandit inference objective that aims to label arms with means above a threshold as quickly as possible. We show that GAI can be efficiently solved by combining a reward-maximizing sampling algorithm with a novel nonparametric anytime-valid sequential test for labeling arm means. We first establish that our sequential test maintains error control under highly nonparametric assumptions and asymptotically achieves the minimax optimal e-power, a notion of power for anytime-valid tests. Next, by pairing regret-minimizing sampling schemes with our sequential test, we provide an approach that achieves minimax optimal stopping times for labeling arms with means above a threshold, under an error probability constraint. Our empirical results validate our approach beyond the minimax setting, reducing the expected number of samples for all stopping times by at least 50% across both synthetic and real-world settings.

We explored the Patrol Security Game (PSG), a robotic patrolling problem modeled as an extensive-form Stackelberg game, where the attacker determines the timing, location, and duration of their attack. Our objective is to devise a patrolling schedule with an infinite time horizon that minimizes the attacker's payoff. We demonstrated that PSG can be transformed into a combinatorial minimax problem with a closed-form objective function. By constraining the defender's strategy to a time-homogeneous first-order Markov chain (i.e., the patroller's next move depends solely on their current location), we proved that the optimal solution in cases of zero penalty involves either minimizing the expected hitting time or return time, depending on the attacker model, and that these solutions can be computed efficiently. Additionally, we observed that increasing the randomness in the patrol schedule reduces the attacker's expected payoff in high-penalty cases. However, the minimax problem becomes non-convex in other scenarios. To address this, we formulated a bi-criteria optimization problem incorporating two objectives: expected maximum reward and entropy. We proposed three graph-based algorithms and one deep reinforcement learning model, designed to efficiently balance the trade-off between these two objectives. Notably, the third algorithm can identify the optimal deterministic patrol schedule, though its runtime grows exponentially with the number of patrol spots. Experimental results validate the effectiveness and scalability of our solutions, demonstrating that our approaches outperform state-of-the-art baselines on both synthetic and real-world crime datasets.

Text generation commonly relies on greedy and beam decoding that limit the search space and degrade output quality. Minimum Bayes Risk (MBR) decoding can mitigate this problem by utilizing automatic evaluation metrics and model-generated pseudo-references. Previous studies have conducted empirical analyses to reveal the improvement by MBR decoding, and reported various observations. However, despite these observations, the theoretical relationship between them remains uncertain. To address this, we present a novel theoretical interpretation of MBR decoding from the perspective of bias-diversity decomposition. We decompose errors in the estimated quality of generated hypotheses in MBR decoding into two key factors: bias, which reflects the closeness between utility functions and human evaluations, and diversity, which represents the variation in the estimated quality of utility functions. Our theoretical analysis reveals the difficulty in simultaneously improving both bias and diversity, and highlights the effectiveness of increasing diversity to enhance MBR decoding performance. This analysis verifies the alignment between our theoretical insights and the empirical results reported in previous work. Furthermore, to support our theoretical findings, we propose a new metric, pseudo-bias, which approximates the bias term using gold references. We also introduce a new MBR approach, Metric-augmented MBR (MAMBR), which increases diversity by adjusting the behavior of utility functions without altering the pseudo-references. Experimental results across multiple NLP tasks show that the decomposed terms in the bias-diversity decomposition correlate well with performance, and that MAMBR improves text generation quality by modifying utility function behavior. Our code will be available at https://github.com/naist-nlp/mbr-bias-diversity.