Beam Search

Robots operating in physical environments make control decisions based on uncertain sensor measurements, which can lead to unsafe or suboptimal actions. Runtime monitors that check their behavior against safety specifications must represent this uncertainty soundly. Zonotopes are a widely used representation, but continuously incorporating new measurements grows their order unboundedly, so monitors must periodically apply an over-approximating reduction. The choice of the reduction method substantially affects the zonotope's precision, yet existing approaches typically utilize a fixed method throughout the run, even though the optimal choice depends on the current state. This paper presents a Predictive Zonotope Reduction (PZR) approach, which frames reducer selection as an optimal control problem and solves it using beam-search model predictive control. Policy distillation into a small neural policy further provides substantially higher execution speed than model predictive control while maintaining improved performance, enabling uncertainty-aware runtime monitoring on resource-constrained real-time systems. We implement our approach in the RLola runtime monitoring framework and evaluate it on a 5-degree-of-freedom robotic arm simulated in MuJoCo, with sensor uncertainty modeled according to ISO 5725. Experiments on a Raspberry Pi 5 show that dynamic reduction significantly lowers false-positive rates in monitoring compared with static reduction strategies.

Generative retrieval has demonstrated significant success by unifying representation learning and search into a single sequence-to-sequence generation task. However, extending this paradigm to cross-modal retrieval reveals a critical challenge arising from the inherent information asymmetry across different modalities, such as the gap between concise text queries and dense visual candidates. This structural mismatch causes the autoregressive decoder to suffer from forced hallucination when generating identifiers via standard trie-constrained beam search, where the model is severely penalized for failing to guess fine-grained details absent from the query, allowing irrelevant candidates to hijack top rankings. To address this issue, we propose Wildcard Inference with Dynamic Expansion (WIDE). WIDE employs Adaptive Entropy Thresholding (AET) to calibrate layer-specific uncertainty boundaries offline. During the decoding generation phase, Asymmetry-aware Wildcard Decoding (AWD) detects semantic blind spots and emits wildcards instead of forced deterministic identifiers, dynamically expanding the search space without incurring log-probability penalties. Finally, Blind-Spot Re-ranking (BSR) evaluates the expanded candidate pool using a hybrid scoring mechanism that combines discrete generation confidence with continuous semantic similarity. Extensive experiments on the M-BEIR benchmark demonstrate that WIDE outperforms state-of-the-art generative retrieval methods, effectively suppressing forced hallucination while maintaining compact index structures.

We present a training-free method for multi-modal trajectory prediction that achieves comparable accuracy to a 57M-parameter transformer while requiring no GPU and zero learned parameters. The method builds a transition table of historical state-to-next position pairs and retrieves neighbors using a product kernel over spatial proximity, bearing, speed, and temporal context. Two inference modes operate over this shared representation: diversity-penalized sampling produces trajectories covering distinct plausible routes, while beam search finds the highest-likelihood path. On the TrAISformer benchmark (Danish Maritime AIS), our method achieves competitive accuracy at full data availability and dramatically outperforms the transformer in data-scarce regimes---remaining stable down to 10% of training data where TrAISformer degrades catastrophically. This enables deployment in new geographic regions from an order of magnitude less historical data.

Autoregressive semantic ID recommenders are constrained by expensive beam-search decoding, which limits the practical length of item identifiers. Parallel generation methods alleviate this bottleneck by predicting all semantic ID tokens simultaneously, enabling longer IDs. However, existing semantic ID methods still rely on manually predefined and homogeneous ID structures, where both the number of semantic slots and the codebook size of each slot are treated as fixed hyperparameters. This ignores the heterogeneous capacity demands of different semantic subspaces and may allocate prediction capacity to slots with limited utility. We show that uniformly expanding semantic slots can provide limited gains, indicating redundant capacity in homogeneous semantic IDs. We propose InforID, a lightweight adaptive semantic target construction framework for parallel generative recommendation. InforID allocates a fixed capacity budget across candidate semantic slots, thereby jointly determining the effective ID length and slot-specific codebook sizes. Experiments demonstrate improved recommendation accuracy under comparable capacity budgets while preserving one-step parallel prediction.

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from \emph{how much} compute to spend, to \emph{where} to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes \emph{thought-level beam search}. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7% absolute accuracy gain on HMMT-24 and +3.3% on AIME-25 over pruning baselines, delivers $>2\times$ higher throughput on trace completion, and reduces total token consumption by up to 68.5% relative to standard parallel sampling.

This study addresses the Variable Gapped Longest Common Subsequence Problem (VGLCSP), a variant of the classical longest common subsequence problem with additional gap constraints and applications in sequence alignment and time-series analysis. While the two-sequence version has been widely studied using dynamic programming, the generalized multi-sequence form is usually solved with beam search-based heuristics, whose hand-crafted designs often lack robustness. To overcome this limitation, we propose a learning-based approach for automatically designing more effective data-driven heuristics. The heuristics are represented by a neural network with predefined architecture, whose weights are optimized by a genetic algorithm within a neuro-evolutionary framework. The learning process alternates between weight optimization and evaluation within an iterative multi-source beam search procedure, a state-of-the-art method for the problem. Rather than constructing solutions directly, the neural network learns to guide the search process, producing a neuro-evolved heuristic. We further introduce an ensemble heuristic that combines the scores of learned and the best-performing hand-crafted heuristic. Integrated into the iterative multi-source beam search framework, the resulting hybrid approach outperforms existing methods on both synthetic benchmark instances and newly introduced real-world instances with data-driven gap constraints.

Large language models (LLMs) have made automated heuristic design (AHD) increasingly practical by generating executable heuristic code from task descriptions and evaluator feedback. Yet under a limited query and evaluation budget, search efficiency depends critically on a pre-generation decision. Before each LLM query and black-box evaluation, the system must choose which archived heuristics to reuse as parents and which generation operator should transform them. Existing methods typically choose such actions with predefined rules, leaving the expected outcome of each concrete operator-parent action only indirectly modeled. Therefore, we propose \emph{\fullmethod{}} (\method{}), a surrogate-guided action-selection module for operator-parent selection in LLM-based AHD. \method{} guides the LLM code-generation process by scoring pre-generation actions with two complementary surrogates. Specifically, a transition surrogate is proposed to predict the latent distribution of the child representation induced by an operator-parent action, while an instance-conditioned utility surrogate is proposed to estimate the expected performance of sampled child latents. Moreover, we propose an uncertainty-aware acquisition rule that combines predicted utility, utility uncertainty, and transition uncertainty to select the next LLM generation action. Across a diverse heuristic-design suite, \method{} is competitive with strong LLM-AHD baselines, and ablation and action-selection analyses suggest that its behavior goes beyond simple archive ranking or fixed operator preferences.

We study the coupled objective J_K^WOR = E_{S ~ PL-WOR_K}[max_{i in S} R_i]: the expected maximum reward of a size-K Plackett-Luce draw without replacement, the law of Gumbel-Top-K / Stochastic Beam Search decoding. This estimand differs from the conventional i.i.d. objective J_K^iid = E[max_{i<=K} R_i] targeted by existing sample-reuse Max@K estimators, and reusing their i.i.d. weights under the coupled sampler is provably biased (a closed-form three-item instance gives E[g_iid] = (4/5) grad J_K^WOR exactly; pass@K under the coupled sampler is the binary-reward special case). Generic joint-score REINFORCE is already unbiased for J_K^WOR; what it lacks is sample reuse. Our contribution is to instantiate standard rank-conditioned Horvitz-Thompson estimation for the J_K^WOR subset total: from one Gumbel-Top-n pool (n>K) and its observed priority threshold we build an estimator that reuses all C(n,K) embedded K-subsets, unbiased with an unbiased exact score-function surrogate gradient, plus a reward-sorted Max-specific dynamic program that collapses the C(n,K)-term subset sum (with K!-cost set probabilities) exactly to a one-dimensional integral. A fixed-Q quadrature evaluation costs O(n log n + nKQ) arithmetic and is numerically, not algebraically, exact; no epsilon-approximation rate is certified. Each nonzero degree-K Horvitz-Thompson term has finite second moment exactly when n >= 2K; under the same assumptions the full surrogate gradient has finite second moment whenever n >= 2K (sharpness there is open). At K=1 the construction recovers classical priority sampling. All quantities require only the values and differentiable computation graphs of the n+1 drawn items' probabilities, so finite structured sequence policies sampled by exact SBS are covered. A certified finite-Q quadrature bound and countably infinite support remain open. Validation code is included as ancillary files.

Constrained decoding is essential in generative retrieval, where document identifiers generated directly from a query must exactly match a predefined library of valid IDs. At scale, decoding is often constrained using a trie with beam search but most implementations run on CPU. Limited parallelism then makes trie traversal and candidate validation a serving bottleneck as beam width grows. We present FlashTrie, which addresses this limitation by optimizing constrained beam search on GPUs. It introduces an integer-aware succinct trie layout that uses bit compression to reduce memory footprint while keeping the full index in GPU high-bandwidth memory reducing memory stalls, and a cooperative CUDA kernel that performs beam expansion, validation, and pruning entirely on-device without per-step host orchestration. It further replaces CPU-style irregular lookup and heap maintenance with GPU-aware parallel primitives, improving warp utilization and reducing divergence. Together, these designs significantly reduce decoding latency and increase throughput while preserving retrieval quality. On a library of 800M keywords with beam widths up to 1000, FlashTrie reduces trie-search latency to under 3 ms, achieving up to 24x speedup over a highly optimized multi-threaded CPU baseline. These improvements enable FlashTrie to scale beam sizes by up to 5x in latency-critical applications such as sponsored search. In a large-scale online A/B experiment on a popular commercial search engine, it delivers a statistically significant +0.71% revenue lift, enabling real-time constrained decoding at a scale previously feasible only offline. The FlashTrie code will be publicly released after the review process.

Optimizing composite stacking sequences to match continuous targets (e.g., Lamination or Buckling Parameters) with discrete manufacturing constraints represents a challenging combinatorial inverse problem that regularly occurs in composite design especially when numerical optimization approaches are used (bi-step, bi-level configurations). In multipanel configurations, this complexity is further intensified by blending, a global compatibility/continuity requirement between the different panel stackings. This study presents SeqGPT, a conditional Transformer agent developed to replace computationally expensive iterative methods. To ensure both global continuity and manufacturing feasibility by construction, we implemented a hybrid neurosymbolic decoding strategy. SeqGPT predicts a conditional distribution that guides a Constrained Beam Search, where any branch violating blending rules is strictly pruned. Numerical experiments on the 18-panel horseshoe benchmark demonstrate that SeqGPT generates solutions near-instantaneously with buckling performance comparable to evolutionary methods, offering a significant speed-up compared to the state of the art.

In many decision-making scenarios, acquiring information incurs different costs. We consider the problem of constructing a deterministic evaluation strategy that minimizes the expected cost of evaluating a propositional formula under variable costs and a probability distribution over truth assignments. We present a branch-and-bound algorithm with variable-selection heuristics, pruning, and caching. To the best of our knowledge, it is the first practical exact algorithm for this level of generality. Experiments on random instances demonstrate scalability and quantify the efficiency-quality trade-off of a greedy beam-search variant. We additionally evaluate a structured heart-disease diagnosis instance. Finally, we prove that the problem is $\#P$-hard and contained in $\mathrm{PSPACE}$.

Modern retrieval increasingly relies on dense and learned-sparse neural models that are effective but require encoding the entire corpus into a specialized index, rebuilt whenever the model changes. Lexical retrievers like BM25 stay efficient and transparent on a standard inverted index that need not change as models evolve, but suffer from vocabulary mismatch. LLM query rewriting can help, yet prompted rewriters emit well-formed but retrieval-ineffective or harmful-terms, and training against a retrieval reward gives only delayed, sequence-level supervision that obscures which terms helped. We introduce STORM (Stepwise Token Optimization with Reward-guided beaM search), a self-supervised framework for lexical query expansion. STORM trains the rewriter through generation guided by retrieval metrics: at each step, candidate expansions are scored against the BM25 index and low-reward continuations pruned, turning the retrieval reward into a token-level signal that concentrates exploration on retrieval-effective vocabulary. Across TREC DL and BEIR, STORM lets 0.6B-8B backbones match or surpass competitive LLM rewriters while retrieving as fast as plain BM25; at 8B it rivals far larger proprietary rewriters. It further transfers zero-shot to 18 languages (MIRACL), beating dedicated multilingual dense retrievers on average, making STORM a competitive, infrastructure-light alternative to dense neural retrieval.

We ask whether structural properties of intermediate grid states predict whether a symbolic ARC-AGI solver will succeed, framed as a test of conditional mutual information I(X;Y|task) > 0. Across 44,800 runs spanning two architecturally distinct solvers (beam search and Stochastic DFS), 400 ARC tasks, 28 configurations per solver, and both training and evaluation splits, hand-crafted grid descriptors measured at 50% trajectory completion discriminate successful from failed runs within the same task (mean within-task best-feature AUC = 0.885, p < 0.001 under within-task label permutation). Most predictive content lies along a single grid-complexity axis. The result generalizes across solver architectures: a feature selected on one solver predicts success on the other with AUC 0.747-0.762 in all four transfer directions (p < 0.001, leakage controlled). On a pre-registered held-out set of 41 reliable tasks, the frozen feature n_components_final achieves AUC = 0.765 (95% CI [0.717, 0.810], p < 0.001), robust under task-clustered bootstrap resampling and cross-solver task collapsing. The signal is not explained by solver capacity (configuration-residualized AUC = 0.927 and 0.896 for beam search and SDFS, p < 0.001) and is only weakly coupled to score trajectories (R^2 approximately 0). Early stopping at 50% completion reduces beam-search compute by 33.6% while retaining 98.9% of solves; degenerate-trajectory detection reduces SDFS compute by 65.3% with no solve loss. Finally, on 229 of 400 evaluation tasks the DSL primitive library produces no valid transition from the input grid. This 0-step collapse is invariant to search budget and universally failed by beam search, indicating a DSL coverage limitation rather than a search-budget effect.

Multi-trajectory inference for tool-use LLM agents - generating multiple reasoning attempts and selecting among them - benefits from transferring knowledge across attempts so that later ones avoid the pitfalls of earlier ones. Existing cross-trajectory memory methods (trajectory-level reflection, atomic fact extraction, raw observation injection) are each evaluated under a single inference strategy on a single task, making it unclear whether reported gains reflect properties of the memory abstraction or of the inference method. We propose a unified framework that decomposes memory along two axes -- the scope of transfer (within an expansion vs. across trajectories) and the abstraction of the transferred content -- and evaluate four methods under three inference strategies (best-of-N, beam search, MCTS) on four tool-use benchmarks spanning SQL, knowledge-graph, and CLI environments, in a verifier-free setting that matches the deployment regime of practical agents. The experiment matrix identifies the inference method as a confound: the same memory method produces statistically distinct results under different inference strategies on the same examples. Reflection reaches significance only under MCTS (not under best-of-N); within-expansion injection (conditioning each candidate on prior siblings' outcomes) helps only diversity-starved beam search; and atomic fact extraction is accuracy-neutral but shortens trajectories by 19-26% on tasks with reusable environmental structure.

Surprisal theory posits that the processing difficulty of a word is determined by its predictability in context, offering a potential link between human sentence processing and next-word predictions from language models. While language model (LM) surprisals successfully predict reading times in naturalistic text, they systematically underpredict the magnitude of difficulty observed in controlled studies of syntactic ambiguity, particularly in garden path sentences. This mismatch might arise from differences in the computational constraints between humans and LMs. Here we test one such hypothesis, specifically, that LMs may be able to simultaneously consider a greater number of distinct sentence interpretations at once, compared to humans. Using Recurrent Neural Network Grammars (RNNGs) with word-synchronous beam search, we systematically vary the number of simultaneous parses used to compute word surprisal, and then use these surprisals to predict human reading times. Reducing the number of simultaneous active parses indeed increases the magnitude of predicted garden path effects, but not nearly enough to capture the full magnitude of the effects in humans. This suggests that differences in the number of simultaneous parses available to LMs and humans cannot reconcile LM-based surprisal with human sentence processing.

Generative retrieval offers a promising alternative by unifying the fragmented multi-stage retrieval process into a single end-to-end model. However, its practical adoption in industrial e-commerce search remains challenging, given the massive and dynamic product catalogs, strict latency requirements, and the need to align retrieval with downstream ranking goals. In this work, we propose a retrieval framework tailored for real-world recall scenarios, positioning generative retrieval as a recall-stage supplement rather than an end-to-end replacement. Our method, CQ-SID (Category-and-Query constrained Semantic ID), employs category-aware and query-item contrastive learning along with Residual Quantized VAEs to encode items into hierarchical semantic cluster identifiers, significantly reducing beam search complexity. Additionally, we develop EG-GRPO (Expert-Guided Group Relative Policy Optimization), a reinforcement learning approach that aligns generative recall with downstream ranking under sparse rewards by injecting ground-truth samples to stabilize training. Offline experiments on TmallAPP search logs show that CQ-SID achieves up to 26.76% and 11.11% relative gains in semantic and personalized click hitrate over RQ-VAE baselines, while halving beam search size. EG-GRPO further improves multi-objective performance. Online A/B tests confirm gains in GMV (+1.15%) and UCTCVR (+0.40%). The generative recall channel now contributes substantially in production, accounting for over 50.25% of exposures, 58.96% of clicks, and 72.63% of purchases, demonstrating a viable path for deploying generative retrieval in real-world e-commerce systems.

To address the issues of high interruption time and measurement report overhead under user equipment (UE) mobility especially in high speed 5G use cases the use of AI/ML techniques (AI/ML beam management and mobility procedures) have been proposed. These techniques rely heavily on data that are most often simulated for various scenarios and do not accurately reflect real deployment behavior or user traffic patterns. Therefore, there is an utmost need for realistic datasets under various conditions. This work presents a dataset collected from a commercially deployed network across various modes of mobility (pedestrian, bike, car, bus, and train) and at multiple speeds to depict real time UE mobility. When collecting the dataset, we focused primarily on handover (HO) scenarios, with the aim of reducing the HO interruption time and maintaining continuous throughput during and immediately after HO execution. To support this research, the dataset includes timing advance (TA) measurements at various signaling events such as RACH trigger, MAC CE, and PDCCH grant which are typically missing in existing works. We cover a detailed description of the creation of the dataset; experimental setup, data acquisition, and extraction. We also cover an exploratory analysis of the data, with a primary focus on mobility, beam management, and TA. We discuss multiple use cases in which the proposed dataset can facilitate understanding of the inference of the AI/ML model. One such use case is to train and evaluate various AI/ML models for TA prediction.

Multimodal large language models (MLLMs) have achieved remarkable success in general perception, yet complex multi-step visual reasoning remains a persistent challenge. Although recent agentic approaches incorporate tool use, they often neglect critical execution feedback. Consequently, they suffer from the imagination-action-observer (IAO) bias, a misalignment between prior imagination and observer feedback that undermines reasoning stability and optimality. To bridge this gap, we introduce V-ABS, an action-observer driven beam search framework that enables deliberate reasoning through thinker-actor-observer iterations. We also propose an entropy-based adaptive weighting algorithm to mitigate the IAO bias by dynamically balancing the confidence scores between the policy priors and the observational feedback. Moreover, we construct a large-scale supervised fine-tuning (SFT) dataset comprising over 80k samples to guide the model to assign higher prior confidence to correct action paths. Extensive experiments across eight diverse benchmarks show that V-ABS achieves state-of-the-art performance, delivering an average improvement of 19.7% on the Qwen3-VL-8B baseline and consistent gains across both open-source and proprietary models.

Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam search, best-of-n, majority voting) can improve upon greedy decoding, both approaches suffer from limitations: sampling generally commits to a single path, while search often expends excessive computation regardless of task complexity. To address these, we introduce Entropy-informed decoding (EDEN), a plug-and-play, model-agnostic decoding framework that adaptively allocates computation based on the model's own uncertainty, approximating higher-width beam search with fewer expansions. At each generation step, EDEN estimates the entropy of the output token distribution and adjusts the branching factor monotonically with the entropy, expanding more candidates in high-entropy regions and following a greedier path in low-entropy regions, improving token efficiency. Experiments across complex tasks, including mathematical reasoning, code generation, and scientific questions, demonstrate that EDEN consistently improves output quality over existing decoding strategies, achieving better accuracy-expansion trade-offs than fixed-width beam search. By treating next-token selection as a noisy maximisation problem, we prove that branching factors monotone in entropy are guaranteed to find better (i.e. more probable) continuations than any fixed branching factor within the same total expansion budget, and derive explicit regret rates characterising the benefit of the adaptive allocation.

Generative retrieval (GR) ranks documents by autoregressively generating document identifiers. Because many GR methods rely on trie-constrained beam search, they are vulnerable to early pruning of relevant prefixes under finite-beam decoding. Planning Ahead in Generative Retrieval (PAG) mitigates this failure mode by using simultaneous decoding to compute a document-level look-ahead prior that guides subsequent sequential decoding. We reproduce PAG at inference time and stress-test its decoding behavior. Using the authors' released checkpoint and identifier/trie artifacts under the reported decoding setup, we reproduce the main effectiveness results on MS MARCO Dev and TREC-DL 2019/2020, and corroborate the reported beam-size-latency trade-off in our hardware setting. Beyond reproduction, we introduce plan drift diagnostics that quantify how intent-preserving query variations alter the planner's top-n candidate set and highest-weight planner tokens, and how these changes affect guided decoding. We find that PAG's planning signal is brittle under lexical surface-form variation: intent-preserving typos can trigger plan collapse, where the planned candidate pool shifts enough that the look-ahead bonus provides little useful guidance, effectively reverting decoding toward weaker unguided search. We further evaluate fixed-index cross-lingual robustness using non-English mMARCO queries against an English index, and assess query-side mitigation strategies that require no re-indexing; query translation provides the strongest recovery in our setting. Overall, our results confirm PAG's reported effectiveness and the benefit of planning-guided decoding under the released inference setup, while showing that these gains depend on the stability of the planning signal under realistic query variation and query-document mismatch.

Active perception is a fundamental problem in autonomous robotics in which the robot must decide where to move and what to sense in order to obtain the most informative observations for accomplishing its mission. Existing approaches either solve a computationally expensive traveling salesman problem over heuristically selected informative nodes, or adopt a more efficient but overly constrained shortest path tree formulation. To address these limitations, we explore beam search algorithms as scalable alternatives. While the standard beam search provides scalability by preserving the top-B paths at each depth level, it is prone to local optima and exhibits parameter sensitivity. Our first contribution is a node-wise beam search (NBS) algorithm, which maintains top-B candidates per node to enable more effective exploration of the solution space. Systematic benchmarking on graphs shows that NBS consistently outperforms other baselines and maintains strong performance even at low beam widths. As a second contribution, we integrate the concept of frontiers into the path selection criterion, introducing the expected gain metric, which better balances exploration and exploitation compared to existing alternatives. Our third contribution proposes the rapidly-exploring random annulus graph (RRAG), a novel graph construction method that preserves full orientation sampling and ensures connectivity in cluttered environments through a fallback local sampling-based planner. Extensive experiments demonstrate that NBS combined with RRAG achieves the highest performance across all three representative active perception tasks, outperforming state-of-the-art algorithms by at least 20% in one or more tasks. We further validate the approach on real robotic platforms in different scenarios.

This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions' characters. The problem arises in molecular sequence comparison, where structural distance constraints between residues must be respected, and in time-series analysis where events are required to occur within specified temporal delays. We propose a search framework based on the root-based state graph representation, in which the state space comprises a generally large number of rooted state subgraphs. To cope with the resulting combinatorial explosion, an iterative beam search strategy is employed, dynamically maintaining a global pool of promising candidate root nodes, enabling effective control of diversification across iterations. To exploit the search for high-quality solutions, several known heuristics from the LCS literature are utilized into the standalone beam search procedure. To the best of our knowledge, this is the first comprehensive computational study on the VGLCS problem comprising 320 synthetic instances with up to 10 input sequences and up to 500 characters. Experimental results show robustness of the designed approach over the baseline beam search in comparable runtimes.

In LLM-based code generation, multiple code candidates are often generated in parallel from the same prompt -- for example, in best-of-N sampling or multi-candidate code completion. These requests can share KV caches through a common prefix, yet the extent to which their Mixture-of-Experts (MoE) expert routing overlaps, and how this overlap varies across layers, remains insufficiently understood. We study Qwen3.5-35B-A3B-FP8 (256 routed experts, top-8) by performing tree-search-based branching generation from a shared prefix (851 completed codes, temperature 0.7) and analyzing the results with a compiler-output-based alignment (gcc -S -O0 assembly) that controls for token-identity confounds. Our findings are threefold: (1) At positions where both sequences generated the same token, Jaccard similarity reaches 0.649 (40x random), while even at positions with different tokens it remains 0.175 (11x random). (2) A layer-wise decomposition reveals a crossing pattern: same-token routing similarity exceeds different-token similarity across all layers, but dips in the middle layers (L14-20), while different-token similarity peaks in the middle layers at 14x random. (3) In tree-search code generation, 67% of successfully compiled codes concentrate in the top three assembly-equivalent groups, and 99.6% of within-group differences consist of comments and blank lines. We show that diversity in top-P search, including beam search, poses a significant challenge. These results refine the "context-independent routing" claim of prior work through layer-wise decomposition and suggest opportunities for improving search efficiency in LLM code generation.

Recommendation system delivers substantial economic benefits by providing personalized predictions. Generative recommendation (GR) integrates LLMs to enhance the understanding of long user-item sequences. Despite employing attention-based architectures, GR's workload differs markedly from that of LLM serving. GR typically processes long prompt while producing short, fixed-length outputs, yet the computational cost of each decode phase is especially high due to the large beam width. Furthermore, since the beam search involves a vast item space, the sorting overhead becomes particularly time-consuming. We propose xGR, a GR-oriented serving system that meets strict low-latency requirements under high-concurrency scenarios. First, xGR unifies the processing of prefill and decode phases through staged computation and separated KV cache. Second, xGR enables early sorting termination and mask-based item filtering with data structure reuse. Third, xGR reconstructs the overall pipeline to exploit multi-level overlap and multi-stream parallelism. The experiments on real-world datasets demonstrate that xGR achieves at least 2.89x throughput compared to the state-of-the-art baseline under strict latency constraints.

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