Safety alignment in Large Language Models (LLMs) inherently presents a multi-objective optimization conflict, often accompanied by an unintended degradation of general capabilities. Existing mitigation strategies typically rely on global gradient geometry to resolve these conflicts, yet they overlook Modular Heterogeneity within Transformers, specifically that the functional sensitivity and degree of conflict vary substantially across different attention heads. Such global approaches impose uniform update rules across all parameters, often resulting in suboptimal trade-offs by indiscriminately updating utility sensitive heads that exhibit intense gradient conflicts. To address this limitation, we propose Conflict-Aware Sparse Tuning (CAST), a framework that integrates head-level diagnosis with sparse fine-tuning. CAST first constructs a pre-alignment conflict map by synthesizing Optimization Conflict and Functional Sensitivity, which then guides the selective update of parameters. Experiments reveal that alignment conflicts in LLMs are not uniformly distributed. We find that the drop in general capabilities mainly comes from updating a small group of “high-conflict” heads. By simply skipping these heads during training, we significantly reduce this loss without compromising safety, offering an interpretable and parameter-efficient approach to improving the safety-utility trade-off.
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Multilingual Retrieval-Augmented Generation (mRAG) leverages cross-lingual evidence to ground Large Language Models (LLMs) in global knowledge. However, we show that current mRAG systems suffer from a language bias during reranking, systematically favoring English and the query’s native language. By introducing an estimated oracle evidence analysis, we quantify a substantial performance gap between existing rerankers and the achievable upper bound. Further analysis reveals a critical distributional mismatch: while optimal predictions require evidence scattered across multiple languages, current systems systematically suppress such “answer-critical” documents, thereby limiting downstream generation performance. To bridge this gap, we propose Language-Agnostic Utility-driven Reranker Alignment (LAURA), Experiments across diverse languages and generation models show that LAURA effectively mitigates language bias and consistently improves mRAG performance.
While agent evaluation has shifted toward long-horizon tasks, most benchmarks still emphasize local, step-level reasoning rather than the global constrained optimization (e.g., time and financial budgets) that demands genuine planning ability. Meanwhile, existing LLM planning benchmarks underrepresent the active information gathering and fine-grained local constraints typical of real-world settings. To address this, we introduce DeepPlanning, a challenging benchmark for practical long-horizon agent planning. It features multi-day travel planning and multi-product shopping tasks that require proactive information acquisition, local constrained reasoning, and global constrained optimization. Evaluations on DeepPlanning show that even frontier agentic LLMs struggle with these problems, highlighting the importance of reliable explicit reasoning patterns and parallel tool use for achieving better effectiveness-efficiency trade-offs. Error analysis further points to promising directions for improving agentic LLMs over long planning horizons. We open-source the code and data to support future research.
Strategic planning is critical for multi-step reasoning, yet compact Language Language Models (LLMs) often lack the capacity to formulate global strategies, leading to error propagation in long-horizon tasks. Our analysis reveals that LLMs possess latent reasoning capabilities that can be unlocked when conditioned on explicit plans from a teacher model; however, runtime reliance on external guidance is often impractical due to latency and availability constraints. To bridge this gap, we propose PILOT (Planning via Internalized Latent Optimization Trajectories), a non-invasive framework designed to internalize the strategic oversight of large models into intrinsic Latent Guidance. Instead of altering backbone weights, PILOT employs a lightweight Hyper-Network to synthesize a query-conditioned Latent Guidance. This vector acts as an internal steering mechanism, guiding the model’s representations toward optimal reasoning paths. Extensive experiments on mathematical and coding benchmarks demonstrate that PILOT effectively stabilizes reasoning trajectories, consistently outperforming strong baselines (e.g., +8.9% on MATH500) with negligible inference latency. Our code is available at: https://anonymous.4open.science/r/PILOT-B266
High-stakes domains such as finance, law, and biomedicine demand both accurate results and rigorous reasoning. Current reinforcement learning paradigms primarily rely on outcome-based rewards, often overlooking latent logical fallacies in intermediate steps. Leveraging the cognitive asymmetry where falsifying local errors is more efficient than generating global correctness, we propose RADO (Reasoning Audit-Driven Optimization). RADO introduces a specialized audit model augmented with external tools to identify local logical ruptures and calibrate reward signals. By integrating Direct Preference Optimization (DPO) with Group Relative Policy Optimization (GRPO), our framework enables explicit supervision over reasoning paths. Experimental results demonstrate that RADO consistently improves final accuracy while significantly enhancing logical rigor in high-stakes domains.
As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%.
Recent advances in Large Language Models (LLMs) have demonstrated strong capabilities in tasks such as code generation and mathematical reasoning. However, their potential to internalize structured spatial knowledge remains underexplored. This study investigates whether LLMs, grounded in locally relative human observations, can construct coherent global spatial cognition by integrating fragmented relational descriptions. We focus on two core aspects of spatial cognition: spatial perception, where models infer consistent global layouts from local positional relationships, and spatial navigation, where models learn road connectivity from trajectory data and plan optimal paths between unconnected locations. Experiments conducted in a simulated urban environment demonstrate that LLMs not only generalize to unseen spatial relationships between points of interest (POIs) but also exhibit latent representations aligned with real-world spatial distributions. Furthermore, LLMs can learn road connectivity from trajectory descriptions, enabling accurate path planning and dynamic spatial awareness during navigation.
Large language models (LLMs) are shaping global values, yet they frequently exhibit a pronounced WEIRD (Western, Educated, Industrialized, Rich, Democratic) cultural bias, marginalizing diverse viewpoints and posing challenges for reconciling diverse populations with varying cultural backgrounds and value systems. In this work, we move beyond simple alignment methods to propose a new paradigm for cross-cultural fairness. We introduce a Nash Consensus Negotiation framework under the formulation of cross-cultural consensus as a Nash Equilibrium. Each LLM iteratively proposes and refines natural-language guidelines, guided by a utility function balancing self-consistency with mutual acceptance, while penalizing redundancy. The process expands the proposal space and converges to a consensus, yielding fair and interpretable consensus outcomes. We evaluate our framework against baselines using quantitative metrics, qualitative analysis, and large-scale human studies. Experiments demonstrate that our framework generates higher-quality and more balanced consensus, effectively mitigating assimilation toward WEIRD values. Furthermore, we finetune diverse LLM architectures with negotiation data via preference optimization and supervised reasoning, reducing cultural distances by up to 95.53%. Overall, our work offers a systematic path to mitigate cultural bias in LLMs by guiding them toward self-consistency, mutually-acceptable equilibria.
Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution
PDF ↗Large Language Model (LLM)-based optimization has recently shown promise for autonomous problem solving, yet most approaches still cast LLMs as passive constraint checkers rather than proactive strategy designers, limiting their effectiveness on complex Constraint Optimization Problems (COPs). To address this, we present AutoCO, an end-to-end Automated Constraint Optimization method that tightly couples operations-research principles of constraint relaxation with LLM reasoning. A core innovation is a unified triple-representation that binds relaxation strategies, algorithmic principles, and executable codes. This design enables the LLM to synthesize, justify, and instantiate relaxation strategies that are both principled and executable. To navigate fragmented solution spaces, AutoCO employs a bidirectional global–local coevolution mechanism, synergistically coupling Monte Carlo Tree Search (MCTS) for global relaxation-trajectory exploration with Evolutionary Algorithms (EAs) for local solution intensification. This continuous exchange of priors and feedback explicitly balances diversification and intensification, thus preventing premature convergence. Extensive experiments on three challenging COP benchmarks validate AutoCO’s consistent effectiveness and superior performance, especially in hard regimes where current methods degrade. Results highlight AutoCO as a principled and effective path toward proactive, verifiable LLM-driven optimization.
Automating scientific poster generation requires hierarchical document understanding and coherent content-layout planning.Existing methods often rely on flat summarization or optimize content and layout separately.As a result, they often suffer from information loss, weak logical flow, and poor visual balance.We present PosterForest, a training-free framework for scientific poster generation.Our method introduces the Poster Tree, a structured intermediate representation that captures document hierarchy and visual-textual semantics across multiple levels.Building on this representation, content and layout agents perform hierarchical reasoning and recursive refinement, progressively optimizing the poster from global organization to local composition.This joint optimization improves semantic coherence, logical flow, and visual harmony.Experiments show that PosterForest outperforms prior methods in both automatic and human evaluations, without additional training or domain-specific supervision.
General Machine Learning · Hardware and Software
Sparse sketches such as the sparse Johnson–Lindenstrauss transform are a core primitive in randomized numerical linear algebra because they leverage random sparsity to reduce the arithmetic cost of sketching, while still offering strong approximation guarantees. Their random sparsity, however, is at odds with efficient implementations on modern GPUs, since it leads to irregular memory access patterns that degrade memory bandwidth utilization. Motivated by this tension, we pursue a sketch–kernel co-design approach: we design a new family of sparse sketches, BlockPerm-SJLT, whose sparsity structure is chosen to enable FlashSketch, a corresponding optimized CUDA kernel that implements these sketches efficiently. The design of BlockPerm-SJLT introduces a tunable parameter that explicitly trades off the tension between GPU-efficiency and sketching robustness. We provide theoretical guarantees for BlockPerm-SJLT under the oblivious subspace embedding (OSE) framework, and also analyze the effect of the tunable parameter on sketching quality. We empirically evaluate FlashSketch on standard RandNLA benchmarks, as well as an end-to-end ML data attribution pipeline called GraSS. FlashSketch pushes the Pareto frontier of sketching quality versus speed, across a range of regimes and tasks, and achieves a global geomean speedup of roughly $1.7 \times$ over the prior state-of-the-art GPU sketches.
Deep Learning · Robustness
While data augmentation is essential for robust point cloud recognition, conventional spatial mixup strategies often compromise geometric integrity by generating physically unrealistic samples. To overcome this limitation, we propose PSMix, which shifts the mixing paradigm to the spectral domain via the Spherical Harmonic Transform. Instead of simple coordinate interpolation, PSMix performs a rotation-aware hierarchical mixing on spectral coefficients. This approach explicitly preserves global structural properties while diversifying local details, achieving a balance that spatial methods struggle to maintain. Complementing this, we introduce an adversarial rotation optimization strategy to enforce invariance against challenging orientations. Extensive experiments on ModelNet-C and ScanObjectNN-C demonstrate that PSMix achieves state-of-the-art robustness, while also serving as an orthogonal plug-in that further boosts the performance of existing spatial strategies.
Deep Learning · Large Language Models
Gradient signals in LLM training are highly anisotropic: recurrent linguistic structure concentrates energy into a small set of dominant spectral directions, while context-specific information resides in a long tail. We show that this spike–tail separation persists throughout training, with the spike occupying only about 1.5% of directions yet dominating optimizer statistics. This dominance suppresses tail learning by contracting tail updates through second-moment normalization and tightening the globally stable learning-rate bound. Motivated by this analysis, we propose \textit{Spectra}, a spike-aware optimizer that suppresses the dominant low-rank spike subspace without amplifying the noise-sensitive spectral tail. Spectra tracks the spike subspace via cached, warm-started power iteration and applies low-rank spectral shaping with negligible overhead and substantially reduced optimizer-state memory. On LLaMA3-8B trained on 50B tokens, Spectra reaches the same target loss 30% faster than AdamW, reduces per-step end-to-end overhead by 0.7%, cutting optimizer-state memory by 49.25%, and improves average downstream accuracy by 1.62%. Compared to Muon, Spectra is $5.1\times$ faster in optimizer processing time, achieves a lower final loss, and improves average accuracy by 0.66%. Spectra's Megatron integration is released publicly (https://tinyurl.com/29n4vv5f).
Reinforcement Learning · Everything Else
Controlling spreading processes on networks such as epidemics, information cascades, product adoption, requires policies that perform on realistic stochastic dynamics, not just tractable approximations. Yet policies trained on standard simplifications (mean-field ODEs, Markovian dynamics) suffer severe performance degradation at deployment. We trace this sim-to-real gap to three theoretical pathologies: Optimism Bias, where deterministic approximations systematically underestimate variance via Jensen's inequality; Hub Blindness, where global state aggregation obscures the super-spreaders driving scale-free networks; and the Valley of Death, where mean-value critics fail to navigate the bimodal nature (extinction vs. viral) of cascade outcomes. We resolve these challenges through two synergistic contributions. First, the Stratified Mean-Field Observer partitions nodes by influence tier, preserving hub dynamics at $O(N)$ cost while producing fixed-dimensional observations that enable zero-shot transfer across network scales and topologies. Second, we demonstrate that Distributional RL via Truncated Quantile Critics is essential for risk-aware control of bimodal cascades. Trained on a GPU-accelerated simulator supporting non-Markovian renewal dynamics, our approach achieves $59\times$ improvement over Markovian baselines and robust zero-shot transfer to real-world social networks (Facebook, Twitter, YouTube), effectively closing the simulation-to-reality gap.
Deep Learning · Large Language Models
Representation steering offers a lightweight mechanism for controlling the behavior of large language models (LLMs) by intervening on internal activations at inference time. Most existing methods rely on a single global steering direction, typically obtained via difference-in-means over contrastive datasets. This approach implicitly assumes that the target concept is homogeneously represented across the embedding space. In practice, however, LLM representations can be highly non-homogeneous, exhibiting clustered, context-dependent structure, which renders global steering directions brittle. In this work, we view representation steering through the lens of optimal transport (OT), noting that standard difference-in-means steering implicitly corresponds to the OT map between two unimodal Gaussian distributions with identical covariance, yielding a global translation. To relax this restrictive assumption, we theoretically model source and target representations as Gaussian mixture models and formulate steering as a discrete OT problem between semantic latent clusters. From the resulting transport plan, we derive an explicit, input-dependent steering map via barycentric projection, producing a smooth, kernel-weighted combination of cluster-level shifts. We term this method Concept Heterogeneity-aware Representation Steering (CHaRS). Through numerous experimental settings, we show that CHaRS yields more effective behavioral control than global steering.
Applications · Chemistry, Physics, and Earth Sciences
Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size ($N$), dataset size ($D$), and compute budget ($C$). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10× reduces validation loss by up to 3.2×. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to longer training durations yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance.\footnote{Code is available at \url{https://anonymous.4open.science/r/scaling-laws-weather-model-8560/}}
Deep Learning · Theory
Modern foundation models are evaluated through broad capabilities such as arithmetic, reasoning, safety, and robustness, yet it remains unclear in a principled sense when *finite tests* can meaningfully certify such claims. We develop a rigorous theory of capability evaluation by formalizing evaluation as inference over a task family and asking when guarantees over the full family can be inferred from a strict subset of tests. We analyze two canonical regimes. In stochastic multi-environment evaluation, we characterize when uniform certification is possible across multiple environments and show that the sample complexity is governed by a $\chi^2$-radius of the environment family, yielding near-optimal evaluation protocols with matching lower bounds under a natural overlap condition. In contrast, for worst-case, rule-like capabilities, we establish fundamental impossibility results. Even for structured model classes such as Boolean circuits of bounded size, black-box evaluation cannot, in general, certify global properties. Together, these results provide a principled framework for understanding when finite evaluation can and cannot certify capabilities.
Social Aspects · Robustness
Split Federated Learning (SFL) enables privacy-preserving collaborative training by partitioning models between clients and a server. However, under non-IID data distributions, SFL often suffers from biased optimization and unstable convergence, while existing solutions largely adapt techniques from conventional federated learning. In this work, we observe that the split architecture of SFL inherently alters how client information is represented and coordinated, opening opportunities for bias compensation beyond parameter-level aggregation. Based on this insight, we propose BESplit, an architecture-aware framework that exploits the intrinsic structure of SFL to mitigate non-IID effects. First, to prevent biased local data from dominating global updates, we introduce Evidential Aggregation (EA) to perform fine-grained reweighting of client contributions based on evidential uncertainty. Second, to further reduce distributional skew, we develop Bias-Compensated Collaboration (BCC) to align split-layer representations by pairing complementary clients. Finally, Dual-Teacher Distillation (DTD) is incorporated to synchronize knowledge between decoupled client and server models, enabling independent local inference. Extensive experiments on five benchmark datasets demonstrate that BESplit consistently outperforms state-of-the-art methods in accuracy, convergence stability, and computational efficiency under diverse non-IID settings.
Reinforcement Learning · Inverse
Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully solving an RL problem each iteration to compute dual gradients. More recent adversarial methods avoid this cost at the expense of stability and monotonic dual improvement, by directly optimizing the primal problem and using a discriminator to provide rewards. In this work, we bridge the gap between these approaches by enabling monotonic improvement of the reward function and policy without having to fully solve an RL problem at every iteration. Our key theoretical insight is that a trust-region-optimal policy for a reward function update can be globally optimal for a smaller update in the same direction. This smaller update allows us to explicitly optimize the dual objective while only relying on a local search around the current policy. In doing so, our approach avoids the training instabilities of adversarial methods, offers monotonic performance improvement, and learns a reward function in the traditional sense of IRL—one that can be globally optimized to match expert demonstrations. Our proposed algorithm, *Trust Region Inverse Reinforcement Learning (TRIRL)*, outperforms state-of-the-art imitation learning methods across multiple challenging tasks by a factor of 2.4x in terms of aggregate inter-quartile mean, while recovering reward functions that generalize to system dynamics shifts.
Optimization · Non-Convex
The Densest $k$-Subgraph (D$k$S) is a fundamental combinatorial problem known for its theoretical hardness and breadth of applications. Recently, Lu et al. (AAAI 2025) introduced a penalty-based non-convex relaxation that achieves promising empirical performance; however, a rigorous theoretical understanding of its success remains unclear. In this work, we bridge this gap by providing a comprehensive theoretical analysis. We first establish the tightness of the relaxation, ensuring that the global maximum values of the original combinatorial problem and the relaxed problem coincide. Then we reveal the benign geometry of the optimization landscape by proving a strict dichotomy of stationary points: all integral stationary points are local maximizers, whereas all non-integral stationary points are strict saddles with explicit positive curvature. We propose a saddle-escaping Frank--Wolfe algorithm and prove that it achieves exact convergence to an integral local maximizer in a finite number of steps.