Correction notice (v2). Two implementation issues affect these experiments. All LoRA training ran under DeepSpeed, which replaced the optimizer passed to the Trainer with AdamW at a constant learning rate, so the Muon and Adam arms used the same optimizer. The cross-entropy term was computed without the next-token shift, so the preference for alpha = 1 reflects that objective rather than the value of the teacher. Each comparison also uses a single GPTQ quantization, and repeated quantizations differ by up to several points. The findings on Muon's quantization robustness, the distillation weight and accuracy relative to GPTQ alone should not be relied on. See the notice on page 1. Large Language Models (LLMs) enable advanced natural language processing but face deployment challenges on resource-constrained edge devices due to high computational, memory, and energy demands. Optimizing these models requires addressing three key challenges: acquiring task-specific data, fine-tuning for performance, and compressing models to accelerate inference while reducing resource demands. We propose an integrated framework combining GPTQ-based quantization, low-rank adaptation (LoRA), and a specialized data distillation process to significantly reduce model size and complexity while preserving or enhancing task-specific performance. By leveraging data distillation, knowledge distillation via Kullback-Leibler divergence, Bayesian hyperparameter optimization, and the Muon optimizer, our pipeline achieves up to 2x memory compression (e.g., reducing a 6GB model to 3GB) and enables efficient inference for specialized tasks. Empirical results demonstrate superior performance on standard LLM benchmarks compared to GPTQ quantization alone, with the Muon optimizer notably enhancing fine-tuned models' resistance to accuracy decay during quantization.
We propose Spectral Complex Autoencoder Pruning (SCAP), a reconstruction-based criterion that measures functional redundancy at the level of individual output channels. For each convolutional layer, we construct a complex interaction field by pairing the full multi-channel input activation as the real part with a single output-channel activation (spatially aligned and broadcast across input channels) as the imaginary part. We transform this complex field to the frequency domain and train a low-capacity autoencoder to reconstruct normalized spectra. Channels whose spectra are reconstructed with high fidelity are interpreted as lying close to a low-dimensional manifold captured by the autoencoder and are therefore more compressible; conversely, channels with low fidelity are retained as they encode information that cannot be compactly represented by the learned manifold. This yields an importance score (optionally fused with the filter L1 norm) that supports simple threshold-based pruning and produces a structurally consistent pruned network. On VGG16 trained on CIFAR-10, at a fixed threshold of 0.6, we obtain 90.11% FLOP reduction and 96.30% parameter reduction with an absolute Top-1 accuracy drop of 1.67% from a 93.44% baseline after fine-tuning, demonstrating that spectral reconstruction fidelity of complex interaction fields is an effective proxy for channel-level redundancy under aggressive compression.
Singular learning theory characterizes Bayesian learning as an evolving tradeoff between accuracy and complexity, with transitions between qualitatively different solutions as sample size increases. We extend this theory to reinforcement learning, proving that the concentration of a generalized posterior over policies is governed by the local learning coefficient (LLC), an invariant of the geometry of the regret function. This theory predicts that deep reinforcement learning with SGD should proceed from simple policies with high regret to complex policies with low regret. We verify this prediction empirically in a gridworld environment exhibiting stagewise policy development: phase transitions over training manifest as "opposing staircases" where regret decreases sharply while the LLC increases.
Large language models (LLMs) often hallucinate, yet most existing fact-checking methods treat factuality evaluation as a binary classification problem, offering limited interpretability and failing to capture fine-grained error types. In this paper, we introduce InFi-Check, a framework for interpretable and fine-grained fact-checking of LLM outputs. Specifically, we first propose a controlled data synthesis pipeline that generates high-quality data featuring explicit evidence, fine-grained error type labels, justifications, and corrections. Based on this, we further construct large-scale training data and a manually verified benchmark InFi-Check-FG for fine-grained fact-checking of LLM outputs. Building on these high-quality training data, we further propose InFi-Checker, which can jointly provide supporting evidence, classify fine-grained error types, and produce justifications along with corrections. Experiments show that InFi-Checker achieves state-of-the-art performance on InFi-Check-FG and strong generalization across various downstream tasks, significantly improving the utility and trustworthiness of factuality evaluation.
Diffusion-based large language models (dLLMs) have emerged as a promising alternative to autoregressive models, leveraging simultaneous denoising to enable global planning and iterative refinement. These properties make dLLMs attractive for long-context generation. However, deploying dLLMs faces a prohibitive memory barrier, as existing inference systems are inefficient for the diffusion paradigm. We observe that current inference systems are misaligned with dLLMs. Unlike autoregressive models, whose memory footprint is dominated by the KV-Cache, dLLMs are bottlenecked by transient activations rematerialized per step. Moreover, generic memory reuse mechanisms lack the global visibility to handle dynamic memory peaks of dLLMs, which alternate between logits and feed-forward networks. To address these challenges, we present Mosaic, a memory-efficient inference system that shifts dLLM execution from local, static management to a global, dynamic paradigm. Mosaic integrates (i) a mask-only logits kernel eliminating redundant activation materialization, (ii) a lazy chunking optimizer using online heuristics to tame dynamic memory peaks, and (iii) a global memory manager leveraging virtual addressing to mitigate memory fragmentation. Evaluations show that Mosaic reduces the memory peak-to-average ratio by 2.71$\times$ on average and increases the maximum inference sequence length on identical hardware by 15.30-32.34$\times$. Crucially, Mosaic is training-free and preserves exact model outputs, while reducing end-to-end latency by 2.5%-55.4%. Our code is publicly available at https://github.com/flashserve/Mosaic.
Large language model (LLM) routing aims to exploit the specialized strengths of different LLMs for diverse tasks. However, existing approaches typically focus only on selecting LLM architectures, treating candidate models as fixed while overlooking parameter adaptation, which can substantially affect task performance. In this paper, we introduce HAPS, a hierarchical LLM routing framework that jointly searches over model architectures and parameters. Specifically, a high-level router selects among candidate LLM architectures, while a low-level router generates input-conditioned LoRA parameters for the selected architecture, expanding each candidate from a single fixed behavior into a region of reachable behaviors. The low-level router is built on the backbone of the high-level router, so that architecture selection and parameter generation share a common representation of the prompt. We further optimize the whole framework with a reinforcement learning objective. Extensive experiments show that HAPS consistently outperforms strong routing baselines across reasoning- and knowledge-intensive benchmarks, with analyses of its components, design choices, scalability, cost, and mixed open- and closed-source deployment further demonstrating the robustness of these gains. Our code is available at https://github.com/zihangtian/HAPS.
Geometric and Topological Deep Learning enhance machine learning by exploiting geometric and topological structures in data. In this context, Group Equivariant Non-Expansive Operators (GENEOs) provide a principled framework for encoding symmetries and designing efficient, interpretable neural architectures. Originally introduced in Topological Data Analysis and later adopted in Deep Learning, GENEOs unify geometric and topological approaches and include, as a special case, the operator computing persistence diagrams. Their theoretical foundations rely on group actions, equivariance, and compactness properties of operator spaces. GENEOs are defined between data spaces endowed with transformation groups, referred to as perception pairs. While previous representation results characterized linear GENEOs acting on identical perception pairs, many applications require operators between heterogeneous ones. In this work, we introduce and prove a new algebraic representation theorem for linear GENEOs acting between different perception pairs. Under mild assumptions on data domains and group actions, this result provides a complete characterization of such operators and implicitly yields a computational method to generate all linear GENEOs between two perception pairs. The proof combines tools from the theory of stochastic matrices, group actions, and invariant measures. In our paper, we also show that the space of linear GENEOs is compact and convex, making easier their use for learning and optimization. Our new theorem enlarges the applicability of GENEOs, and allows for their composition with a broader class of current architectures. We show this with an application in image reconstruction.
Large audio-language models have made rapid progress in recognizing what is present in an audio clip, but spatial audio-language understanding still lacks a clear task interface. A model must also decide where sound events occur, which semantic and spatial attributes belong to the same auditory object, how multiple objects are arranged, and whether a scene-level answer is physically plausible. We formalize this capability as audio scene analysis (ASA), a three-level problem spanning atomic perception, relational integration, and cognitive reasoning. We propose The World is Not Mono (TWNM), a framework that equips audio-language models with explicit spatial evidence. TWNM uses physically grounded First-Order Ambisonics (FOA) simulation for controllable supervision, learns slot-regularized spatial representations from multichannel audio, fuses them with semantic audio features, and trains with a progressive curriculum ending in preference optimization over metadata-derived correct answers and auxiliary format/evidence rewards. To operationalize ASA, we build a controlled benchmark from scene metadata, covering localization, attribute binding, spatial comparison, scene abduction, and counterfactual reasoning. On this benchmark, TWNM achieves 70.8% overall accuracy, 66.4% on spatial-family tasks, and 79.76% on mixed $\mathcal{L}_3$ scene-level QA under exact multiple-choice question answering (MCQA) scoring. We also audit monaural and binaural reference systems as diagnostic references with explicit audit labels, since they differ in spatial input, training interface, and output format. The supported claim is that a clearly defined ASA hierarchy, FOA-conditioned spatial representations, and metadata-grounded training enable controlled, auditable spatial audio-language reasoning, with STARSS23 providing a limited real-recording diagnostic.
Current Large Language Model reasoning systems process queries independently, discarding valuable cross-instance signals such as shared reasoning patterns and consistency constraints. We introduce Batch-of-Thought (BoT), a training-free method that processes related queries jointly to enable cross-instance learning. By performing comparative analysis across queries, BoT identifies high-quality reasoning templates, detects errors through consistency checks, and amortizes computational costs. We instantiate BoT within a multi-agent reflection architecture (BoT-R), where a Reflector performs joint evaluation to unlock mutual information gain unavailable in isolated processing. Experiments across three model families and six benchmarks demonstrate that BoT-R consistently improves accuracy and confidence calibration while reducing inference costs by up to 61%. Our theoretical and experimental analysis reveals when and why batch-aware reasoning benefits LLM systems. Our code is available at https://github.com/xuanyang19/BoT.
Recent advances in large language models (LLMs) have demonstrated transformative potential across diverse fields. However, in computer-aided synthesis planning (CASP), current LLM methodologies are often restricted to single-molecule representations, limiting their application to isolated, single-task scenarios such as precursor prediction. Addressing this gap, we present ChemBART, a BART-based language model that adopts a reaction-centric pre-training strategy. By leveraging a mask-filling pre-training task on holistic reaction expressions (Reactant > Reagent > Product), ChemBART effectively solves a variety of chemical problems, including precursor/reagent generation, temperature-yield regression, and molecular property classification. The reaction-centric pre-training further enables the integration of ChemBART with Monte Carlo tree search (MCTS) for multi-step synthesis route design, where the model serves to optimize the policy and value functions within a reinforcement learning framework. Beyond single-molecule pre-trained LLMs that are constrained to specific applications, ChemBART unifies diverse chemical tasks to facilitate synthesis planning with comprehensive implementation information. Most significantly, the proposed multi-step synthesis routes and reaction conditions were validated in the wet lab, confirming the discovery of shorter synthetic pathways with a >20% yield improvement over established literature benchmarks. Our work highlights the potential of reaction-focused pre-training and showcases the broad utility of ChemBART in closing the loop between in silico prediction and wet-lab synthesis.
A common approach to out-of-distribution prediction restricts models to causal or invariant covariates to avoid spurious associations that may change across environments. Despite its theoretical appeal, this strategy can underperform empirical risk minimization when only a subset of the causal parents of the outcome is observed. In such settings, non-causal covariates can serve as proxies for unobserved causal parents and improve prediction when the proxy relationship is stable, but they can hurt when shifts disrupt that relationship. Thus, the optimal covariate set can depend on the specific shift encountered. Because different shifts can leave distinct signatures in the covariate distribution, we propose an environment-adaptive covariate selection algorithm that chooses which covariates to use in each environment based on summaries of its unlabeled covariates. The summaries may be hand-crafted or learned from multi-environment data, and prior causal knowledge can be incorporated as constraints. We give sufficient conditions under which such summaries are informative in linear causal models, and explain when adapting only the covariate set is preferable to letting every coefficient vary with the environment. In simulations and two applications, adapting the covariate set improves prediction over static baselines, including causal and invariant covariate selection.
Denoising and score estimation are classically linked through Tweedie's formula, which relates the posterior mean under Gaussian noise to the Stein score of the noisy marginal. In this work, we extend this perspective beyond Gaussian noise to a broad class of Gibbs (energy-based) noise distributions, with the generalized Gaussian family as an example. We derive the Energy-Tweedie identity: when the denoising posterior is viewed through the lens of scoring rules, the path derivative of a kernel scoring rule defined by the noise potential recovers the Stein score of the noisy marginal. Thus, the familiar correspondence between Gaussian noise, posterior means, squared loss, and Tweedie's formula is lifted to a distributional correspondence between Gibbs noise distributions, full posterior laws, kernel scoring rules, and the Energy-Tweedie identity, which gives a Tweedie-style relation for each noise potential. Among its consequences, this identity gives a posterior-samples-to-score route to score estimation, yields a principled criterion for estimating unknown noise parameters, and enables diffusion-style sampling along user-chosen paths through the noise-parameter space, supplying the score-based perspective on recent generative methods trained with scoring rules.
Language agents increasingly require persistent worlds in which they can act, remember, and learn. Existing approaches sit at two extremes: conventional web frameworks provide reliable but fixed contexts backed by databases, while fully generative world models aim for unlimited environments, but the world is constructed primarily through generation, making it harder to maintain a fixed, deterministic global framework and reducing controllability. In this work, we introduce the Web World Model (WWM), a middle ground where world state and ``physics'' are implemented in ordinary web code to ensure logical consistency, while large language models generate context, narratives, and high-level decisions on top of this structured latent state. We build a suite of WWMs on a realistic web stack, including an infinite travel atlas grounded in real geography, fictional galaxy explorers, web-scale encyclopedic and narrative worlds, and simulation- and game-like environments. Across these systems, we identify practical design principles for WWMs: separating code-defined rules from model-driven imagination, representing latent state as typed web interfaces, and utilizing deterministic generation to achieve unlimited but structured exploration. Our results suggest that web stacks themselves can serve as a scalable substrate for world models, enabling controllable yet open-ended environments.
Long-term conversational memory poses a fundamental system challenge for LLM agents: reasoning over all past interactions improves coverage but incurs prohibitive token costs and noise, while retrieval-based methods are efficient yet often fail on multi-hop and temporal questions. Existing multi-step retrievers partially address this gap, but typically operate over an ever-growing textual history, causing context expansion and noise accumulation across iterations. We propose MemR$^3$, a backend-agnostic closed-loop controller that reformulates conversational memory retrieval as explicit stateful decision-making. At each iteration, MemR$^3$ maintains an evidence-gap state consisting of grounded information (evidence) and unresolved information requirements (gaps), and uses this state to route among three actions: retrieve, reflect, and answer. Newly retrieved snippets are incorporated into the state and then masked from subsequent prompts, so the model conditions on a compact summary of progress rather than the full retrieval history. This design turns multi-step memory retrieval into a bounded, inspectable control process whose query-time context scales with the state instead of raw accumulated text. Experiments on LongMemEval$_s$ show that MemR$^3$ surpasses implicit multi-step retrieval baselines and often approaches or exceeds full-context prompting while retrieving only 1%-5% of the full conversation tokens on long conversations. On LoCoMo, MemR$^3$ consistently improves over its underlying RAG- and Zep-based memory backbones. These results suggest that explicit evidence-gap tracking is an effective abstraction for token-efficient conversational memory.
We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$, NMD seeks matrices $W \in \mathbb{R}^{m \times r}$ and $H \in \mathbb{R}^{r \times n}$ such that $X \approx f(WH)$, where $f$ is an element-wise nonlinear function. We evaluate our method on several representative nonlinear models: the rectified linear unit activation $f(x) = \max(0, x)$, suitable for nonnegative sparse data approximation, the component-wise square $f(x) = x^2$, applicable to probabilistic circuit representation, and the MinMax transform $f(x) = \min(b, \max(a, x))$, relevant for recommender systems. The proposed framework flexibly supports diverse loss functions, including least squares, $\ell_1$ norm, and the Kullback-Leibler divergence, and can be readily extended to other nonlinearities and metrics. We illustrate the applicability, efficiency, and adaptability of the approach on real-world datasets, highlighting its potential for a broad range of applications.
Dynamic prediction of locomotor capacity after stroke could enable more individualized rehabilitation, yet current assessments largely provide static impairment scores and do not indicate whether patients can perform specific tasks such as slope walking or stair climbing. Here, we present a wearable-informed data-physics hybrid generative framework that reconstructs a stroke survivor's locomotor control from wearable inertial sensing and predicts task-conditioned post-stroke locomotion in new environments. From a single 20 m level-ground walking trial recorded by five IMUs, the framework personalizes a physics-based digital avatar using a healthy-motion prior and hybrid imitation learning, generating dynamically feasible, patient-specific movements for inclined walking and stair negotiation. Across 11 stroke inpatients, predicted postures achieved approximately 95% of the practically attainable accuracy for slope ascent and 80% for stair climbing, respectively, demonstrating reliable task-specific gait prediction. In a multicenter randomized pilot feasibility study (n = 21; 28 days), access to scenario-specific locomotion predictions to support task selection and difficulty titration was associated with larger gains in Fugl-Meyer lower-extremity scores than the control group (mean change 6.0 vs 3.7 points; p < 0.05). These results suggest that wearable-informed generative digital avatars may augment individualized gait rehabilitation planning and provide a pathway toward dynamically personalized post-stroke motor recovery strategies.
Bayesian Optimization (BO) is a key methodology for accelerating molecular discovery by estimating the mapping from molecules to their properties while seeking the optimal candidate. Typically, BO iteratively updates a probabilistic surrogate model of this mapping and optimizes acquisition functions derived from the model to guide molecule selection. However, its performance is limited in low-data regimes with insufficient prior knowledge and vast candidate spaces. Large language models (LLMs) and chemistry foundation models offer rich priors to enhance BO, but high-dimensional features, costly in-context learning, and the computational burden of deep Bayesian surrogates hinder their full utilization. To address these challenges, we propose a likelihood-free BO method that bypasses explicit surrogate modeling and directly leverages priors from general LLMs and chemistry-specific foundation models to inform acquisition functions. Our method also learns a tree-structured partition of the molecular search space with local acquisition functions, enabling efficient candidate selection via Monte Carlo Tree Search. By further incorporating coarse-grained LLM-based clustering, it substantially improves scalability to large candidate sets by restricting acquisition function evaluations to clusters with statistically higher property values. We show through extensive experiments and ablations that the proposed method substantially improves scalability, robustness, and sample efficiency in LLM-guided BO for molecular discovery.
Seismic phase picking is fundamental for microseismic monitoring and subsurface imaging. Manual processing is impractical for real-time applications and large sensor arrays, motivating the use of deep learning-based pickers trained on extensive earthquake catalogs. On a broader scale, these models are generally tuned to perform optimally in high signal-to-noise and long-duration networks and often fail to perform satisfactorily when applied to campaign-based microseismic datasets, which are characterized by low signal-to-noise ratios, sparse geometries, and limited labeled data. In this study, we present a microseismic adaptation of a network-wide earthquake phase picker, Phase Neural Operator (PhaseNO), using transfer learning and parameter-efficient fine-tuning. Starting from a model pre-trained on more than 57,000 three-component earthquake and noise records, we fine-tune it using only 200 labeled and noisy microseismic recordings from hydraulic fracturing settings. We present a parameter-efficient adaptation of PhaseNO that fine-tunes a small fraction of its parameters (only 3.6%) while retaining its global spatiotemporal representations learned from a large dataset of earthquake recordings. We then evaluate our adapted model on three independent microseismic datasets and compare its performance against the original pre-trained PhaseNO, a STA/LTA-based workflow, and two state-of-the-art deep learning models, PhaseNet and EQTransformer. We demonstrate that our adapted model significantly outperforms the original PhaseNO in F1 and accuracy metrics, achieving up to 30% absolute improvements in all test sets and consistently performing better than STA/LTA and state-of-the-art models. With our adaptation being based on a small calibration set, our proposed workflow is a practical and efficient tool to deploy network-wide models in data-limited microseismic applications.
Answering questions over long, visually rich documents demands both cross-page structural reasoning and fine-grained visual understanding. Existing approaches sacrifice one for the other: retrieval-augmented methods fragment documents and lose inter-page structure; monolithic vision-language models preserve structure but scale poorly beyond a few pages. This impasse stems from a false premise: that the macroscopic task of evidence retrieval and the microscopic task of detailed reasoning must either be split into separate systems or be processed identically. By decoupling their perceptual resolutions rather than their architectures, a single model can achieve the structural holism of monolithic processing alongside the efficiency of targeted retrieval. UniDoc realizes this through two resolution-adaptive stages: a Fast Reading stage processes all pages at low resolution to structurally identify evidence pages, and a Focused Thinking stage re-processes only those pages at high resolution for multimodal inference. To train this pipeline, we construct 30K multi-hop reasoning instances with stage-level supervision. On MMLongBench-Doc, UniDoc yields relative accuracy gains of 55.7% on Qwen2.5-VL-7B and 16.9% on Qwen3-VL-8B, while significantly reducing token cost relative to uniform high-resolution processing. Error analysis identifies page retrieval and fine-grained visual reasoning as the remaining bottlenecks, delineating concrete targets for future work.
Knowledge Graphs (KGs) are a rich source of structured data, and graph neural networks (GNNs) are the dominant tool for learning over them. However, existing message-passing GNNs struggle to scale to large KGs because they rely on the iterative message passing process to learn graph structure. This process is inefficient, especially under mini-batch training, where a node sees only a partial view of its neighborhood. In this paper, we address this problem and present gHAWK, a novel and scalable GNN training framework for large KGs. The key idea is to precompute structural features for each node that capture its local and global structure before GNN training even begins. Specifically, gHAWK introduces a preprocessing step that computes: (a)~Bloom filters to compactly encode local neighborhood structure, and (b)~TransE embeddings to represent each node's global position in the graph. These features are then fused with any domain-specific features (e.g., text embeddings), producing a node feature vector that can be used with any GNN backbone. Equipped with these structural priors, the GNN no longer needs to rediscover graph structure, significantly improving convergence and model accuracy with little memory overhead. Extensive experiments on large datasets from the Open Graph Benchmark demonstrate that gHAWK improves accuracy on both node property prediction and link prediction tasks. Remarkably, gHAWK enables simple GNNs to match or exceed more complex relation-aware ones, suggesting that careful preprocessing can substitute for architectural complexity in KG learning.