Heuristics

We present a systematic empirical study of prompt engineering for formal mathematical reasoning in the context of the SAIR Equational Theories Stage 1 competition. The task requires deciding whether one equational law implies another over all magmas -- a problem that is undecidable in general but decidable for FALSE via finite model search. Over five weeks, we designed, tested, and analyzed more than 40 prompt variants, ranging from 0 to 4,878 bytes, across four evaluation splits and three language models (gpt-oss-120b, Llama 3.3 70B, Gemma 4 31B). Our central finding is a single-prompt ceiling: despite substantial engineering effort, balanced hard accuracy plateaus in an empirical saturation region of approximately 60--79% for gpt-oss-120b, compared to a 59.75% no-cheatsheet baseline. We identify three mechanisms underlying this ceiling: (1) the mathematical undecidability of the TRUE case limits what any finite prompt can encode; (2) complex rule systems decrease performance on weaker models (Llama 3.3 70B collapses to 0% TRUE recall with prompts exceeding 2KB); and (3) prompt ordering effects interact with model attention in fragile, non-monotonic ways. Our best submission (AN45c, 2,252 bytes) achieves 79.25% accuracy on hard3 (n=400; 95% CI: [75.0%, 82.9%]), with TRUE recall of 95.9% and FALSE recall of 63.4%, representing a +19.5 percentage-point improvement over the no-cheatsheet baseline (59.75%). We release all prompt variants, evaluation scripts, and results at https://github.com/israelcazares/sair-prompt-engineering

In this article, we generalize Unbounded Minimax, the state-of-the-art search algorithm for zero sums two-player games with perfect information to the framework of multiplayer games with perfect information. We experimentally show that this generalized algorithm also achieves better performance than the main multiplayer search algorithms.

When does an LLM controller outperform rule-based traversal for knowledge graph exploration? We study this question through RLM-on-KG, a retrieval system that treats an LLM as an autonomous navigator over an RDF-encoded mention graph for grounded question answering. Unlike GraphRAG pipelines that rely on offline LLM indexing, RLM-on-KG performs entity-first, multi-hop exploration at query time using deterministic graph construction and a fixed tool set. Our central finding is a conditional advantage: the value of LLM control depends on evidence scatter and tool-calling sophistication. The paper's core claim is LLM control versus heuristic traversal, not a generic win over GraphRAG. On GraphRAG-Bench Novel (519 questions), Gemini 2.0 Flash achieves +2.47 pp F1 over a rule-based heuristic baseline (p < 0.0001), but only +0.16 pp over a GraphRAG-local variant (not significant). With a stronger controller, Claude Haiku 4.5, the gain over heuristic grows to +4.37 pp (p < 0.001) and extends to a +2.42 pp significant improvement over GraphRAG-local (p < 0.001). The gain is largest when gold evidence is scattered across 6-10 chunks (+3.21 pp) and smallest for concentrated evidence (+1.85 pp). Cross-scale validation on MuSiQue confirms that the LLM-over-heuristic advantage transfers, with expected attenuation on smaller per-question graphs. The core architectural insight is the separation of candidate discovery from ranking: the LLM adds value through exploration breadth, while final evidence selection is best handled by pure vector re-ranking. Beyond retrieval, exploration traces provide a proposed stress-test harness for structured data quality, yielding diagnostics for coverage, connectivity, provenance, and queryability.

Agent \texttt{skills} are structured collections of instructions, tools, and supporting resources that help large language model (LLM) agents perform particular classes of tasks. Empirical evidence shows that the design of \texttt{skills} can materially affect agent task performance, yet systematically optimizing \texttt{skills} remains challenging. Since a \texttt{skill} comprises instructions, tools, and supporting resources in a structured way, optimizing it requires jointly determining both the structure of these components and the content each component contains. This gives rise to a complex decision space with strong interdependence across structure and components. We therefore represent these two coupled decisions as \texttt{skill} structure and component content, and formulate \texttt{skill} optimization as a bilevel optimization problem. We propose a bilevel optimization framework in which an outer loop employs Monte Carlo Tree Search to determine the \texttt{skill} structure, while an inner loop refines the component content within the structure selected by the outer loop. In both loops, we employ LLMs to assist the optimization procedure. We evaluate the proposed framework on an open-source Operations Research Question Answering dataset, and the experimental results suggest that the bilevel optimization framework improves the performance of the agents with the optimized \texttt{skill}.

Large Language Models (LLMs) have shown promising progress for generating Register Transfer Level (RTL) hardware designs, largely because they can rapidly propose alternative architectural realizations. However, single-shot LLM generation struggles to consistently produce designs that are both functionally correct and power-efficient. This paper proposes HYPERHEURIST, a simulated annealing-based control framework that treats LLM-generated RTL as intermediate candidates rather than final designs. The suggested system not only focuses on functionality correctness but also on Power-Performance-Area (PPA) optimization. In the first phase, RTL candidates are filtered through compilation, structural checks, and simulation to identify functionally valid designs. PPA optimization is restricted to RTL designs that have already passed compilation and simulation. Evaluated across eight RTL benchmarks, this staged approach yields more stable and repeatable optimization behavior than single-pass LLM-generated RTL.

Coverage path planning on irregular hexagonal grids is relevant to maritime surveillance, search and rescue and environmental monitoring, yet classical methods are often compared on small ad hoc examples or on rectangular grids. This paper presents a reproducible benchmark of deterministic single-vehicle coverage path planning heuristics on irregular hexagonal graphs derived from synthetic but maritime-motivated areas of interest. The benchmark contains 10,000 Hamiltonian-feasible instances spanning compact, elongated, and irregular morphologies, 17 heuristics from seven families, and a common evaluation protocol covering Hamiltonian success, complete-coverage success, revisits, path length, heading changes, and CPU latency. Across the released dataset, heuristics with explicit shortest-path reconnection solve the relaxed coverage task reliably but almost never produce zero-revisit tours. Exact Depth-First Search confirms that every released instance is Hamiltonian-feasible. The strongest classical Hamiltonian baseline is a Warnsdorff variant that uses an index-based tie-break together with a terminal-inclusive residual-degree policy, reaching 79.0% Hamiltonian success. The dominant design choice is not tie-breaking alone, but how the residual degree is defined when the endpoint is reserved until the final move. This shows that underreported implementation details can materially affect performance on sparse geometric graphs with bottlenecks. The benchmark is intended as a controlled testbed for heuristic analysis rather than as a claim of operational optimality at fleet scale.

Visual token pruning methods effectively mitigate the quadratic computational growth caused by processing high-resolution images and video frames in vision-language models (VLMs). However, existing approaches rely on predefined pruning configurations without determining whether they achieve computation-performance optimality. In this work, we introduce , a novel framework that formulates visual token pruning as a Pareto configuration optimization problem to automatically identify optimal configurations. Our approach employs continuous relaxation and straight-through estimators to enable gradient-based search, solved via the Augmented Lagrangian method. Extensive experiments across 8 visual benchmarks demonstrate that effectively approximates the empirical Pareto frontier obtained through grid search and generalizes well across various pruning methods and VLM architectures. Furthermore, through learnable kernel functions, we investigate layer-wise pruning patterns and reveal that multi-step progressive pruning captures VLMs' hierarchical compression structure, achieving superior accuracy-efficiency trade-offs compared to single-layer approaches.

Purpose: Adaptive skip modules can improve medical image segmentation, but searching for them is computationally costly. Implantable Adaptive Cells (IACs) are compact NAS modules inserted into U-Net skip connections, reducing the search space compared with full-network NAS. However, the original IAC framework still requires a 200-epoch differentiable search for each backbone and dataset. Methods: We analyzed the temporal behavior of operations and edges within IAC cells during differentiable search on public medical image segmentation benchmarks. We found that operations selected in the final discrete cell typically emerge among the strongest candidates early in training, and their architecture parameters stabilize well before the final epoch. Based on this, we propose a Jensen--Shannon-divergence-based stability criterion that tracks per-edge operation-importance distributions and progressively prunes low-importance operations during search. The accelerated framework is called IAC-LTH. Results: Across four public benchmarks (ACDC, BraTS, KiTS, AMOS), several 2-D U-Net backbones, and a 2-D nnU-Net pipeline, IAC-LTH discovers IAC cells whose patient-level segmentation performance matches and sometimes slightly exceeds that of cells found by the original full-length search, while reducing wall-clock NAS cost by 3.7x to 16x across datasets and backbones. These results are consistent across architectures, benchmarks, and both non-augmented and augmented training settings, while preserving the gains of IAC-equipped U-Nets over strong attention-based and dense-skip baselines. Conclusion: Competitive IAC architectures can be identified from early-stabilizing operations without running the full search, making adaptive skip-module design more practical for medical image segmentation under realistic computational constraints.

Monte-Carlo Tree Search (MCTS) is a fundamental sampling-based search algorithm widely used for online planning in sequential decision-making domains. Despite its success in driving recent advances in artificial intelligence, understanding the behavior of MCTS agents remains a challenge for both developers and users. This difficulty stems from the complex search trees produced through the simulation of numerous future states and their intricate relationships. A known weakness of standard MCTS is its reliance on highly selective tree construction, which may lead to the omission of crucial moves and a vulnerability to tactical traps. To resolve this, we incorporate shallow, full-width Minimax search into the rollout phase of multi-agent MCTS to enhance strategic depth. Furthermore, to demystify the resulting decision-making logic, we introduce \textsf{M2-PALE} (MCTS--Minimax Process-Aided Linguistic Explanations). This framework employs process mining techniques, specifically the Alpha Miner, iDHM, and Inductive Miner algorithms, to extract underlying behavioral workflows from agent execution traces. These process models are then synthesized by LLMs to generate human-readable causal and distal explanations. We demonstrate the efficacy of our approach in a small-scale checkers environment, establishing a scalable foundation for interpreting hybrid agents in increasingly complex strategic domains.

Reinforcement learning (RL) paradigms have demonstrated strong performance on reasoning-intensive tasks such as code generation. However, limited trajectory diversity often leads to diminishing returns, which constrains the achievable performance ceiling. Search-enhanced RL alleviates this issue by introducing structured exploration, which remains constrained by the single-agent policy priors. Meanwhile, leveraging multiple interacting policies can acquire more diverse exploratory signals, but existing approaches are typically decoupled from structured search. We propose \textbf{MARS$^2$} (Multi-Agent Reinforced Tree-Search Scaling), a unified RL framework in which multiple independently-optimized agents collaborate within a shared tree-structured search environment. MARS$^2$ models the search tree as a learnable multi-agent interaction environment, enabling heterogeneous agents to collaboratively generate and refine candidate solutions within a shared search topology. To support effective learning, we introduce a path-level group advantage formulation based on tree-consistent reward shaping, which facilitates effective credit assignment across complex search trajectories. Experiments on code generation benchmarks show that MARS$^2$ consistently improves performance across diverse model combinations and training settings, demonstrating the effectiveness of coupling multi-agent collaboration with tree search for enhancing reinforcement learning. Our code is publicly available at https://github.com/TsinghuaC3I/MARTI.

Co-design is a high-dimensional search problem in the robot morphology and control design space. Efficient search requires exploiting the structure shaped by their interaction. To understand this structure, we analyze the landscapes of soft locomotion and manipulation tasks. We identify three patterns consistent across regions of their co-design spaces: 1) Within a region, quality varies along a low-dimensional manifold, with minimal variation orthogonal to it, reducing the effective search space dimensionality. 2) In higher-quality regions, the variance in quality is spread across more dimensions, necessitating search to expand dimensionality as quality improves. 3) In higher-quality regions, quality varies along joint morphology-control dimensions, requiring search along them. Using these insights, we devise an efficient co-design algorithm that yields 36% better co-designs than state-of-the-art baselines. We examine their exploration patterns and show that these baselines required an order of magnitude more function evaluations to find co-designs of comparable quality. Finally, we ablate our algorithm to verify that exploiting the identified structure was the key to efficient co-design.

Tree-based speculative decoding accelerates autoregressive generation by verifying a branching tree of draft tokens in a single target-model forward pass. However, existing methods prioritize maximizing token-level likelihood or the number of accepted tokens while ignoring a critical ``efficiency paradox'': the computational overhead of drafting and verifying big trees can grow super-linearly, particularly at scale. This often leads to negative wall-clock speedup when batch sizes increase or hardware saturation limits are reached. To address this, we propose SMART, a system-aware marginal analysis framework for runtime tree construction. SMART reformulates tree expansion as a hardware-aware optimization problem that directly maximizes end-to-end speedup. By applying a principled marginal benefit--cost rule at inference time, SMART expands a node only when its marginal benefit--cost ratio exceeds the tree-level speedup. SMART is training-free and serves as a plug-and-play controller for existing frameworks like MSD and EAGLE. Extensive evaluations across three MLLMs (e.g., LLaVA, Qwen2-VL) and four LLMs (e.g., Llama-3.1, DeepSeek-R1) demonstrate that SMART consistently outperforms state-of-the-art baselines. It delivers an average additional speedup of 20.0% for MLLMs and 15.4% for LLMs across compute-bound batching regimes and diverse GPU architectures without performance loss.

We introduce the penalised Saito functional $\mathfrak S_{λ,β}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$. It measures the alignment of a candidate Saito determinant with the defining polynomial while penalising the failure of the candidate derivations to be logarithmic. We prove that the functional takes values in $[0,1]$, vanishes exactly when $\mathcal{A}$ is free with exponents $(1,d_1,d_2)$, and lies strictly between $0$ and $1$ otherwise. For fixed $(d_1,d_2)$, it is upper semicontinuous on the reduced configuration space, continuous at arrangements free with the prescribed pair, and converges as $λ\to\infty$ to the corresponding binary freeness test. We use a numerical approximation of this functional, together with a small $b_2$-shell term, to guide fixed-cardinality line-replacement searches over $\mathbb{Q}$ and selected quadratic extensions. Numerical values are used only to select candidates; every reported arrangement is certified in exact arithmetic using Saito's criterion. At the current snapshot, the certified database contains $6{,}146$ representatives with distinct Weisfeiler--Leman fingerprints and cardinalities up to $n=28$. Among them, $3{,}012$ have multiplicity gap $ε(\mathcal{A})=d_1-m(\mathcal{A})\geq2$, including lower-bound-extremal examples with $ε=7$. These non-supersolvable arrangements provide test cases for studying realisation spaces and the persistence of freeness among realisations of the same intersection lattice, in connection with Terao's conjecture.

Maximum inner product search (MIPS) is a crucial subroutine in machine learning, requiring the identification of a vector taken within a database (the keys) that best aligns with a given query. We propose amortized MIPS: a regression-based approach that trains neural networks to directly predict MIPS solutions, amortizing the cost of repeatedly solving MIPS for queries drawn from a known distribution over a fixed key database. Our key insight is that the MIPS value function is the \emph{support} function of the set of keys, a well-studied convex function whose gradient yields the optimal key. This motivates two complementary amortized models: SupportNet, an input-convex neural network trained to regress the support function, and KeyNet, a vector-valued network that directly regresses the optimal key. SupportNet can serve as a cluster router, steering queries toward relevant database partitions, while KeyNet can be used as a drop-in replacement for the original query, fed directly to off-the-shelf indexing pipelines. Our experiments on the BEIR benchmark show that, for document embeddings, learned \SupportNet{}s and \KeyNet{}s significantly improve IVF match rates when accounting for compute effort, whether measured in FLOPs, number of probes, or wall-clock time. Our code is available at: https://github.com/apple/ml-amips.

Learned top-K search improves the accuracy-latency trade-off of graph-based vector search, but existing methods are designed for a fixed K: serving production workloads with varying K values requires preprocessing cost proportional to the number of distinct Ks served - prohibitive in practice. This paper shows that learned search can support arbitrary K with the preprocessing cost of a single top-1 model. The key idea is to reduce top-K learned search to repeated masked top-1 refinement, which works because the distance-reduction trajectory for discovering the next top-1 vector is largely invariant to the number of results already found. We therefore train the model on trajectory features that remain effective under masking. To make repeated refinement robust and efficient, OMEGA counters error accumulation across iterations with rank-wise confidence allocation, and skips unnecessary model invocations with a statistical forecast of recall from partial results. Across nine dataset-scale configurations, OMEGA meets the 0.95 recall target with one K-independent model. Under the lowest-preprocessing configuration of each learned baseline,it reduces mean latency by 7-36% versus DARTH, 3-25% versus MultiK-DARTH, and 8-21% versus LAET on BIGANN, BIGANN-1B, DEEP, and three production workloads. On GIST, Text2Image, and MS MARCO, its latency remains within 9% of DARTH and MultiK-DARTH. On production traces, OMEGA further reduces total serving and preprocessing computation by up to 28%.

Accurate time series forecasting underpins decision-making in many domains, yetconventional ML development often faces data scarcity, distribution shift, anddiminishing returns from manual iteration. We propose Self-Evolving Agent forTime Series Algorithms (SEATS), a framework that autonomously generates, val-idates, and optimizes forecasting algorithm code through an iterative self-evolutionloop. Our design combines three mechanisms: (1) Metric-Advantage MCTS(MA-MCTS), which replaces fixed rewards with a statistically normalized advan-tage score for search guidance, (2) code review with running prompt refinement,so every successfully executed solution is reviewed and the running prompt encodescorrective patterns for later iterations, and (3) global steerable reasoning, whichcompares each evaluated node to global best- and worst-performing solutions forcross-trajectory transfer. A MAP-Elites archive maintains architectural diversity.Across four datasets and two metrics, SEATS wins seven of eight comparisonsagainst strong baselines TimeMixer, Timer, and SEMixer

We consider the optimization problem of an expensive-to-evaluate black-box function, in which we can obtain noisy function values in parallel. For this problem, parallel Bayesian optimization (PBO) is a promising approach, which aims to optimize with fewer function evaluations by selecting a diverse input set for parallel evaluation. However, existing PBO methods suffer from poor practical performance or lack theoretical guarantees. In this study, we propose a PBO method, called randomized kriging believer (KB), based on a well-known KB heuristic and inheriting the advantages of the original KB: low computational complexity, a simple implementation, versatility across various BO methods, and applicability to asynchronous parallelization. Furthermore, we show that our randomized KB achieves Bayesian expected regret guarantees. We demonstrate the effectiveness of the proposed method through experiments, including those on real-data emulators.

Graph neural networks are usually treated as auxiliaries for combinatorial optimization: they imitate algorithms, guide search, or supply scores to classical procedures. We show that this auxiliary role is not intrinsic. A GNN can itself be a heuristic. For the Euclidean Travelling Salesman Problem, we train a non-autoregressive GNN with no labels, rewards, sequential decoding, search, or local improvement. A differentiable Hamiltonian-cycle objective is the only supervision. The trained model produces a complete tour in one forward pass, while dropout and snapshots from a single training trajectory provide solution diversity without engineered moves. The heuristic is therefore learned, not programmed. It is also fast: batched inference remains in the millisecond regime on GPUs. Experiments on TSP100, TSP200, and TSP500 show that the model consistently improves over nearest-neighbor greedy baselines. These results identify unsupervised GNNs as a class of fast learned heuristics for combinatorial optimization.

Ball Mapper summarizes a finite metric dataset by covering the sample with closed balls centered at selected landmarks and connecting landmarks whose balls share observations. Its construction therefore depends critically on repeated fixed radius range queries, yet the effect of replacing exact queries by approximate search has not been systematically characterized. We formulate Ball Mapper through an abstract range query procedure that separates the mathematical construction from the search backend used to realize it. Under fixed ordering, exact procedures preserve the landmark sequence, cover, graph, and membership-based colorings. For approximate procedures, we derive deterministic bounds on covering radius and landmark separation under additive and multiplicative query errors, prove inclusions for the induced nerve, characterize edge survival through witness redundancy for conservative approximations, and bound perturbations of mean vertex colorings. The accompanying implementation provides independent exact reference backends together with exhaustive and approximate search methods under a common closed ball convention. Experiments on Gaussian, mixture, and noisy curve data across three seeds show that approximation fidelity depends strongly on geometry and that edges supported by multiple witnesses are substantially more robust to missed memberships. At 20,000 observations, the approximate indexes did not outperform exhaustive FAISS Flat search. The results therefore establish a framework for controlled approximation rather than a universal speed advantage, and identify the geometric and combinatorial quantities that govern when approximate range search preserves the Ball Mapper summary.

LLM services need to offer a family of models spanning different capability--cost trade-offs to accommodate diverse user preferences. Model merging offers a practical way to construct such a model family by combining a reasoning-enhanced model with an instruction-tuned model. Compared with model-level merging, layer-wise merging offers finer control over the capability--cost trade-off by assigning different merge weights to individual layers. However, it introduces two practical challenges: the layer-wise search space is high-dimensional, and existing methods rarely exploit informative signals from the source models; moreover, the highly variable runtime of LLM evaluations makes synchronous batch optimization inefficient by leaving GPU resources idle while waiting for slow evaluations. To address these challenges, we propose Asynchronous Prior-Guided Bayesian Model Merging (AP-BMM), which formulates layer-wise merging as a multi-objective optimization problem to approximate a Pareto set of merged LLMs, yielding a family of Pareto-optimal merged models with diverse capability--cost trade-offs. AP-BMM leverages parameter and activation discrepancies between the source models to guide the early layer-wise search, employs asynchronous pending-aware Bayesian optimization to maximize GPU utilization through asynchronous evaluations and to select high-quality candidates via pending awareness, and applies lightweight ranking over an oversized candidate pool to improve Pareto-front coverage. Under fixed evaluation budgets, AP-BMM achieves higher hypervolume (HV) and broader Pareto-front coverage than synchronous layer-wise and representative model-level merging methods, while reducing wall-clock time through higher GPU utilization.

Monte Carlo Tree Search is a cornerstone algorithm for online planning, and its root-parallel variant is widely used when wall clock time is limited but best performance is desired. In environments with continuous action spaces, how to best aggregate statistics from different threads is an important yet underexplored question. In this work, we introduce a method that uses Gaussian Process Regression to obtain value estimates for promising actions that were not trialed in the environment. We perform a systematic evaluation across 6 different domains, demonstrating that our approach outperforms existing aggregation strategies while requiring a modest increase in inference time.

Make-on-demand combinatorial synthesis libraries (CSLs) like Enamine REAL have significantly enabled drug discovery efforts. However, their large size presents a challenge for virtual screening, where the goal is to identify the top compounds in a library according to a computational objective (e.g., optimizing docking score) subject to computational constraints under a limited computational budget. For current library sizes -- numbering in the tens of billions of compounds -- and scoring functions of interest, a routine virtual screening campaign may be limited to scoring fewer than 0.1% of the available compounds, leaving potentially many high scoring compounds undiscovered. Furthermore, as constraints (and sometimes objectives) change during the course of a virtual screening campaign, existing virtual screening algorithms typically offer little room for amortization. We propose the approximate-but-exhaustive search protocol for CSLs, or APEX. APEX utilizes a neural network surrogate that exploits the structure of CSLs in the prediction of objectives and constraints to make full enumeration on a consumer GPU possible in under a minute, allowing for exact retrieval of approximate top-k sets. To demonstrate APEX's capabilities, we develop a benchmark CSL comprised of more than 10 million compounds, all of which have been annotated with their docking scores on five medically relevant targets along with physicohemical properties measured with RDKit such that, for any objective and set of constraints, the ground truth top-k compounds can be identified and compared against the retrievals from any virtual screening algorithm. We show APEX's consistently strong performance both in retrieval accuracy and runtime compared to alternative methods.

Inference-time search over multi-agent systems (MAS) wastes compute when it cannot identify which agent's intermediate message advanced progress. We present the Multi-Agent System Process Reward Model (MASPRM), which scores routed transcripts (ordered sequences of messages between agents) and acts as an inference controller for step-level beam search (SBS) and Monte Carlo Tree Search (MCTS). MASPRM is trained from multi-agent MCTS rollouts labeled only with terminal outcome rewards, without human step-level annotations. We evaluate on GSM8K, MATH, MMLU, and LogiQA. Under matched scorer size and comparable MCTS budget, MASPRM exceeds a size-matched ORM by $+2.0$ to $+3.0$ points at 1.5B and $+4.1$ to $+14.5$ at 7B across all four benchmarks, with additional scorer-scaling gains over policy likelihood at 7B (avg $+13.4$ under MCTS). MASPRM also improves ranking quality, reducing Hit@1 to Hit@5 gaps by up to $10.3$ points, with the largest gains under stepwise search that uses intermediate decisions. Code: https://github.com/milad1378yz/MASPRM

Approximate Nearest-Neighbor Search (ANNS) pipelines for high-dimensional neural embeddings spend the bulk of their query time in candidate verification, making it the primary bottleneck in the search process. In this paper, we present PANORAMA, a state-of-the-art refinement technique that accelerates verification by exploiting the inherent spectral decay of these embeddings. Using PCA to compact signal energy, PANORAMA evaluates candidate distances incrementally, computing at each step a strict lower bound on the full-vector distance and dynamically pruning candidates the moment this bound exceeds the running k-th nearest neighbor distance. While PCA's concentration of variance facilitates pruning, it breaks the uniform-variance assumption required by Product Quantization (PQ); we resolve this with a variance-shaping step that redistributes energy across subvectors, rendering accretive refinement compatible with quantized indexes. Optimized for modern memory hierarchies via vectorized bulk-pruning and cache-conscious data layouts, PANORAMA has been upstreamed into the FAISS library across major index families (IVFPQ/Flat, HNSW, and Refine). PANORAMA achieves higher QPS at any target recall with a cost that provably scales inversely with dataset spectral decay, delivering end-to-end speedups of up to 28.9x and outperforming probabilistic methods across all recall bands.

Determining where to execute the manipulation policy is a fundamental challenge in mobile manipulation. Most approaches have formulated this as a geometric search problem, prioritizing physical reachability. However, given the high sensitivity of modern learning-based manipulation policies, geometric criteria alone are insufficient. Optimal performance requires base positioning that is aware of the policy's preference. While recent works have attempted to address this, they remain limited in practicality due to reliance on pre-built scene reconstruction and slow inference. In this work, we introduce N2M that systematically reformulates the approach to base positioning problem, naturally overcoming limitations of previous methods. Our key insight is that policy preferences are inherent to the local scene structure and can be effectively learned from the policy rollouts. Technically, we propose a novel viewpoint augmentation strategy that enables the model to learn robust, viewpoint-invariant pose preferences with remarkable data efficiency. Extensive experiments demonstrate that N2M achieves state-of-the-art performance, outperforming both non-policy-aware baselines and recent policy-aware alternatives. Furthermore, we provide a comprehensive analysis highlighting N2M's broad applicability, generalization capabilities, and data efficiency. Project website: https://clvrai.github.io/N2M/

With respect to improving the reasoning accuracy of LLMs, the representative reinforcement learning (RL) method - Group Relative Policy Optimization (GRPO) - has achieved critical success, yet it still suffers from the issue of insignificant reward signals. This paper introduces ReST-RL, a unified Reinforced Self-Training (ReST) policy-value framework that reconnects policy optimization and value-guided search to improve LLM reasoning ability. Firstly, ReST-GRPO adopts an optimized ReST-style algorithm to reshape the policy-induced trajectory distribution by increasing the reward variance of GRPO sampling and exposing the policy to more informative partial states, thereby improving training efficiency and effectiveness. Then, we further introduce a decoding optimization method, VM-MCTS, which trains a Value Model (VM) from self-collected Monte-Carlo Tree Search (MCTS) targets and deploys it through an adapted MCTS algorithm to provide precise process signals and verification scores, further enhancing reasoning accuracy. These two stages are internally dependent - ReST-GRPO yields higher-quality trajectories for value learning with VM-MCTS, which in turn enables more effective inference-time search. We validate our framework on multiple coding benchmarks (e.g., APPS, BigCodeBench, and HumanEval), where it significantly outperforms other reinforcement training baselines (naive GRPO, DAPO, and ReST-DPO), as well as decoding and verification baselines (e.g., PRM-BoN and ORM-MCTS), indicating its power to strengthen LLM reasoning capability. Moreover, we further evaluate ReST-RL on out-of-domain math and science reasoning tasks, where it achieves improved performance without target-domain tuning and favorable end-to-end efficiency trade-offs, providing preliminary transfer evidence beyond our primary coding domain.

Many robotic tasks, such as inverse kinematics, motion planning, and contact-rich manipulation, can be formulated as optimization problems. Solving these problems requires addressing inherent nonlinear kinematics, complex contact dynamics, long-horizon correlations, and multi-modal optimization landscapes, each posing distinct challenges for state-of-the-art optimizers. While existing methods tackle these issues through problem-specific strategies, such specialization inherently limits cross-task generalization, requires heavy engineering effort in problem reformulation, and hinders multi-task autonomy. Monte Carlo Tree Search (MCTS) offers a compelling framework that generalizes across diverse robotic tasks via strategic exploration of the solution space. However, it typically suffers from combinatorial complexity when applied naively, resulting in slow convergence and excessive storage space in high-dimensional domains. To address this limitation, we propose Tensor Train Tree Search (TTTS), which leverages tensor factorization to exploit implicit correlations among different branches within the decision tree. By utilizing the resulting compact, linear-complexity representation, TTTS significantly reduces both computation and storage overhead, thereby enabling highly efficient global decision making. Experimental results across inverse kinematics, motion planning around obstacles, legged robot manipulation, multi-stage motion planning, and bimanual whole-body manipulation demonstrate the efficiency of TTTS for generalized robot optimization over a diverse set of tasks.

Heuristics are a central component of deterministic planning, particularly in domain-independent settings where general applicability is prioritized over task-specific tuning. This work revisits that paradigm in light of recent advances in large language models (LLMs), which enable the automatic synthesis of heuristics directly from problem definitions -- bypassing the need for handcrafted domain knowledge. We present a method that employs LLMs to generate problem-specific heuristic functions from planning tasks specified through successor generators, goal tests, and initial states written in a general-purpose programming language. These heuristics are compiled and integrated into standard heuristic search algorithms, such as greedy best-first search. Our approach achieves competitive, and in many cases state-of-the-art, performance across a broad range of established planning benchmarks. Moreover, it enables the solution of problems that are difficult to express in traditional formalisms, including those with complex numeric constraints or custom transition dynamics. We provide an extensive empirical evaluation that characterizes the strengths and limitations of the approach across diverse planning settings, demonstrating its effectiveness.

Novelty search (NS) aims to uncover diverse system behaviors through simulation or experiment without requiring a pre-specified scalar objective. This capability is especially relevant to modern discovery problems in chemistry, materials science, and molecular design, where researchers often seek broad coverage of attainable property space rather than a single optimum and where each evaluation may require a costly computation or experiment. For such expensive black-box settings, we propose BEACON, a sample-efficient NS strategy inspired by Bayesian optimization principles. BEACON models the input-to-outcome mapping using multi-output Gaussian processes and selects new inputs by scoring how far plausible posterior outcomes lie from a denoised archive of previously observed outcomes. This gives a distance-based novelty acquisition that accounts for predictive uncertainty and observational noise while operating directly in continuous outcome space, rather than requiring direct optimization over a discretized partition of behaviors. By leveraging efficient posterior sampling together with scalable high-dimensional Gaussian process models, the proposed framework can be extended to settings with large data sets and high-dimensional design variables. We demonstrate BEACON on established benchmark problems together with real-world case studies in materials and molecular discovery. Across these settings, BEACON consistently discovers broader sets of distinct behaviors than several competing baselines under limited evaluation budgets.

Imperfect Information Games (IIGs) are used to model games under uncertainty or lack complete information. Counterfactual Regret Minimization (CFR) is one of the most successful families of algorithms for IIGs. The integration of skill-based strategy learning with CFR could potentially mirror more human-like decision-making and improve learning on complex IIGs. It enables the learning of a hierarchical strategy, wherein low-level components represent skills for solving subgames and the high-level component manages the transition between skills. In this paper, we introduce the first hierarchical version of Deep CFR (HDCFR), an innovative method that boosts learning efficiency in tasks involving extensively large state spaces and deep game trees. Notably, HDCFR enables learning with predefined (human) expertise and extracting skills transferable to similar tasks. We first present the algorithm and establish its theory in a tabular setting, including hierarchical CFR update rules and a variance-reduced Monte Carlo sampling extension for the model-free setting, where backtracking is infeasible. We then extend HDCFR to large-scale tasks via deep learning objectives that match the tabular targets under exact function fitting. Code: https://anonymous.4open.science/r/HDCFR_RUN-677B.

Transfer learning involves taking information and insight from one problem domain and applying it to a new problem domain. Although widely used in practice, theory for transfer learning remains less well-developed. To address this, we prove several novel results related to transfer learning, showing the need to carefully select which sets of information to transfer and the need for dependence between transferred information and target problems. Furthermore, we prove how the degree of probabilistic change in an algorithm using transfer learning places an upper bound on the amount of improvement possible. These results build on the algorithmic search framework for machine learning, allowing the results to apply to a wide range of learning problems using transfer.

Can an agent learn a numerical search strategy through executable practice and then transfer that strategy as text? We study low-budget black-box optimization, where unaided language models remain well below strong classical optimizers. During development, an agent repeatedly writes and evaluates optimizer programs. It then distills the resulting program and practice record once into a 197-word primary Harness A, which is frozen before evaluation. Harness A reduces Gemini Flash regret by 48% in an independent $N=30$ study ($p<.001$), enters the GP-BO performance range on the practice family, and lowers mean regret on all three held-out BBOB landscapes. The same text improves every tested Gemini executor and transfers to Claude Sonnet, reducing regret by 43% and 49% ($p\leq.005$). An independent end-to-end replication produces Harness B, a different program and text at the same performance tier. The same framework also attains the lowest regret on a sealed YouTube reward-tuning production benchmark. Executable practice is thus a viable way to discover a search policy, and language a portable medium for deploying it.

Generative Flow Networks (GFlowNets) have shown promising potential to generate high-scoring candidates with probability proportional to their rewards. As existing GFlowNets freely explore in state space, they encounter significant convergence challenges when scaling to large state spaces. Addressing this issue, this paper proposes to restrict the exploration of actor. A planner is introduced to partition the entire state space into overlapping partial state spaces. Given their limited size, these partial state spaces allow the actor to efficiently identify subregions with higher rewards. A heuristic strategy is introduced to switch partial regions thus preventing the actor from wasting time exploring fully explored or low-reward partial regions. By iteratively exploring these partial state spaces, the actor learns to converge towards the high-reward subregions within the entire state space. Experiments on several widely used datasets demonstrate that \modelname converges faster than existing works on large state spaces. Furthermore, \modelname not only generates candidates with higher rewards but also significantly improves their diversity.