General intelligence requires systems that acquire new skills efficiently and generalize beyond their training distributions. Although program synthesis approaches have strong generalization power, they face scaling issues due to the large combinatorial spaces that quickly render them impractical, requiring human-generated DSLs or pre-trained priors to narrow this search space. On the other hand, deep learning methods have had high successes, but they lack structured test-time adaptation and rely on heavy stochastic sampling or expensive gradient updates for fine-tuning. In this work, we propose the Latent Program Network (LPN), a novel architecture that builds in test-time search directly into neural models. LPN learns a latent space of implicit programs--neurally mapping inputs to outputs--through which it can search using gradients at test time.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA's effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.1

Mixed-Integer Linear Programming (MILP) is a powerful framework used to address a wide range of NP-hard combinatorial optimization problems, often solved by Branch and bound (B&B). A key factor influencing the performance of B&B solvers is the variable selection heuristic governing branching decisions. Recent contributions have sought to adapt reinforcement learning (RL) algorithms to the B&B setting to learn optimal branching policies, through Markov Decision Processes (MDP) inspired formulations, and ad hoc convergence theorems and algorithms. In this work, we introduce BBMDP, a principled vanilla MDP formulation for variable selection in B&B, allowing to leverage a broad range of RL algorithms for the purpose of learning optimal B&B heuristics. Computational experiments validate our model empirically, as our branching agent outperforms prior state-of-the-art RL agents on four standard MILP benchmarks.

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operations. Although we discover that the corresponding problems are NP-complete in general, we provide a comprehensive parameterized-complexity analysis with the aim of determining those properties of the problems that explain the hardness and those that make the problems tractable. For instance, we show that the problems remain hard for a small number d of features or small domain size D but the combination of both yields fixed-parameter tractability. That is, the problems are solvable in (D+1)2d |I|O(1) time, where |I|is the size of the input. We also provide a proof-of-concept implementation of this algorithm and report on empirical results.

Human ability estimation is essential for educational assessment, career advancement, and professional certification. Adaptive Testing systems can improve estimation efficiency by selecting fewer, targeted questions, and are widely used in exams, e.g., GRE, GMAT, and Duolingo English Test. However, selecting an optimal subset of questions remains a challenging nested optimization problem. Existing methods rely on costly approximations or data-intensive training, making them unsuitable for today's large-scale and complex testing environments. Thus, we propose a Closed-Form solution for question subset selection in Adaptive Testing. It directly minimizes ability estimation error by reducing ability parameter's gradient bias while maintaining Hessian stability, which enables a simple greedy algorithm for question selection. Moreover, it can quantify the impact of human behavioral perturbations on ability estimation. Extensive experiments on large-scale educational datasets demonstrate that it reduces the number of required questions by 10% compared to SOTA methods, while maintaining the same estimation accuracy.

While Multimodal Large Language Models (MLLMs) offer strong perception and reasoning capabilities for image-text input, Visual Question Answering (VQA) focusing on small image details still remains a challenge. Although visual cropping techniques seem promising, recent approaches have several limitations: the need for task-specific fine-tuning, low efficiency due to uninformed exhaustive search, or incompatibility with efficient attention implementations. We address these shortcomings by proposing a training-free visual cropping method, dubbed FOCUS, that leverages MLLM-internal representations to guide the search for the most relevant image region. This is accomplished in four steps: first, we identify the target object(s) in the VQA prompt; second, we compute an object relevance map using the key-value (KV) cache; third, we propose and rank relevant image regions based on the map; and finally, we perform the fine-grained VQA task using the topranked region.

Multi-Task Learning (MTL) in Neural Combinatorial Optimization (NCO) is a promising approach for training a unified model capable of solving multiple Vehicle Routing Problem (VRP) variants. However, existing Reinforcement Learning (RL)-based multi-task methods can only train light decoder models on small-scale problems, exhibiting limited generalization ability when solving large-scale problems. To overcome this limitation, this work introduces a novel multi-task learning method driven by knowledge distillation (MTL-KD), which enables efficient training of heavy decoder models with strong generalization ability. The proposed MTL-KD method transfers policy knowledge from multiple distinct RL-based single-task models to a single heavy decoder model, facilitating label-free training and effectively improving the model's generalization ability across diverse tasks. In addition, we introduce a flexible inference strategy termed Random Reordering Re-Construction (R3C), which is specifically adapted for diverse VRP tasks and further boosts the performance of the multi-task model. Experimental results on 6 seen and 10 unseen VRP variants with up to 1,000 nodes indicate that our proposed method consistently achieves superior performance on both uniform and real-world benchmarks, demonstrating robust generalization abilities.

Neural Architecture Search (NAS) aims to identify high-performance networks within a defined search space. Training-free metrics have been proposed to estimate network performance without actual training, reducing NAS deployment costs. However, individual training-free metrics often capture only partial architectural features, and their estimation capabilities are different in various tasks. Combining multiple training-free metrics has been explored to enhance scalability across tasks. Yet, these methods typically optimize global metric combinations over the entire search space, overlooking the varying sensitivities of different architectures to specific metrics, which may limit the final architectures' performance. To address these challenges, we propose the Per-Architecture Training-Free Metric Optimization NAS (PO-NAS) algorithm.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity--that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1% over Beam Search and 3.6% over Best-of-N, while reducing FLOPs by over 52%. Our code is avaiblae at github.com/hmarkc/VG-Search.

Prompt engineering is crucial for leveraging the full potential of large language models (LLMs). While automatic prompt optimization offers a scalable alternative to costly manual design, generating effective prompts remains challenging. Existing methods often struggle to stably generate improved prompts, leading to low efficiency, and overlook that prompt optimization easily gets trapped in local optima. Addressing this, we propose GRACE, a framework that integrates two synergistic strategies: Gated Refinement and Adaptive Compression, achieving Efficient prompt optimization. The gated refinement strategy introduces a feedback regulation gate and an update rejection gate, which refine update signals to produce stable and effective prompt improvements.