Numerical Analysis
Papers
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Tuesday 29 September
Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the training distribution and ask: under what assumptions on the target function or operator is stable extrapolation possible, and how far beyond the training domain can one extrapolate? Existing theory controls the test error through additive penalties measuring the discrepancy between the training and test distributions. Such guarantees show robustness to small distribution shifts, but can be very pessimistic in comparison to OOD performance observed empirically. We identify classes of holomorphic functions and operators for which the OOD generalization error converges at algebraic rates even in the presence of large distribution shifts. This phenomenon stems from the increasing smoothness of higher-index coordinates, leading to what we term a `blessing of high dimensionality'. For learning with either polynomials, deep neural networks or deep neural operators, we derive explicit rates for arbitrary test measures supported on suitable domains and quantify how the admissible domain depends on the underlying regularity of the function or operator. Our extrapolation guarantees are independent of the test distribution, depending only on its support. We also present a series of numerical experiments across a range of functions and operators that support the main theoretical findings.
Computation and Language
LAURA: Knowledge Distillation for Interpretable Ambiguous Clause Identification in Legal Contracts
Legal contracts contain ambiguities that expose enterprises to financial and legal risks. Some ambiguities allow flexible interpretation without triggering disputes, while others lead to significant legal conflicts. This makes identification alone insufficient, and interpretable rationale analysis essential. We propose LAURA, a post-training framework for interpretable ambiguous clause identification. LAURA leverages knowledge distillation with an IRAC-Unlearning prompting technique to transfer knowledge from a teacher LLM to an open-weight student model (<=1B parameters), which is then trained using a joint objective combining classification and rationale generation losses. The framework supports both legal and non-legal stakeholders in making informed decisions about which ambiguities require further attention. Extensive experiments across 7 baselines and 7 open-weight models demonstrate that LAURA with Flan-T5 (250M) delivers state-of-the-art interpretability over all interpretable baselines while matching the identification performance of the best-performing opaque baseline.
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Artificial Intelligence
JudgeProfile: Understanding and Steering Subjectivity in LLM Judges
LLM judges are inherently subjective, often favoring different responses in pairwise comparison when neither option is objectively wrong. To study this subjectivity, we introduce JudgeProfile, a framework that dissects LLM evaluation into perception (how a judge compares two responses across specific attributes like clarity, correctness, and detail) and prioritization (how much each attribute influences the final choice). We curate SubjectiveSet, a dataset of 50,013 response pairs from 17 public data sources, evaluated by 21 LLM judges across 87 attributes. We find a hidden consensus in perception: judges frequently agree on attribute judgments even when their overall choices diverge. Building on this separation, we first characterize each judge's prioritization using attribute weights estimated from its own overall choices. These weights differ across judges even when estimated from the same attribute judgments. We then learn new weights from reference labels to adapt their decisions to a target evaluation standard. Reweighting perceived attributes improves average held-out agreement with reference labels from 66.48% to 71.97%, outperforming fine-tuning and rubric prompting. Our findings show that understanding and steering the subjectivity of LLM judges requires attention not only to what they perceive, but also to how they prioritize it.
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Machine Learning
When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation
Modern learning systems often acquire supervision at multiple resolutions, trading annotation cost against information content. We study cost-aware two-resolution learning, where expensive fine labels reveal a vector response and cheaper coarse labels reveal a scalar aggregate formed with unknown weights, while the target remains the full response. The challenge is that unknown aggregation changes which directions coarse data can identify, so the value of coarse supervision depends jointly on cost, noise, and identification. We characterize this information geometry and develop an estimate-and-track policy that learns the aggregation rule and tracks the optimal resolution mix. We derive a closed-form break-even condition for coarse supervision and prove that the online policy attains the optimal leading cumulative-risk coefficient, with a matching local asymptotic minimax lower bound. Synthetic experiments support the predicted all-fine/mixed transition, show the online learner approaching the oracle-share benchmark, and demonstrate a finite-budget gain over all-fine acquisition when coarse supervision is sufficiently favorable. Our results provide a principled way to balance information and annotation cost across supervision resolutions.
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Computer Vision · Cross-listed from quant-ph
Quantum Fidelity Landscape-Guided Prior Calibration for Single-Circuit QGAN Image Generation
Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate this theoretical insight, we propose BasicQGAN, a QGAN framework incorporating quantum prior calibration. Before adversarial optimization, BasicQGAN aligns the prior-induced QFL with the data-induced QFL. Experimental results on small-scale grayscale image datasets show that BasicQGAN achieves stable and effective end-to-end pixel-level image generation while requiring fewer qubits and trainable parameters than representative patch-based quantum generators. Furthermore, experiments with different initial quantum-state ensembles show that QFL-calibrated ensembles achieve better generative performance.
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Computational Engineering
Interpolating Neural Operator (INO): A Data-Free and Efficient Approach for Learning PDE Solution Operators
Neural operators have become a popular approach to approximate the solution operators of parametric partial differential equations (PDEs). However, existing neural operators either require a large amount of simulation data or a long physics-informed training on GPUs, and they cannot tell how accurate an individual prediction is. In this paper, we propose the Interpolating Neural Operator (INO), a data-free interpolating neural network that is trained directly on the weak form of the PDE. In INO, the Karhunen-Loève coordinates of the input field are treated as additional inputs together with the spatial coordinates, and each input is approximated by a C-HiDeNN sub-network whose trainable parameters are nodal values. Since the network is multilinear in its parameters, training reduces to a sequence of one-dimensional linear solves by greedy alternating least squares. As a result, INO trains on one CPU core and predicts a new solution in microseconds. For coercive problems, the total error of every prediction is bounded by a computable residual bound that requires no reference solution, and the same bound applies to the predictions of other methods that satisfy the boundary conditions exactly. Before each prediction, INO checks whether the leading coordinates of the input lie within the range on which it is trained, and inputs outside this range can be passed to a conventional solver or to an INO trained on a wider range. INO is compared with physics-informed FNO and DeepONet on different benchmarks. INO is the most accurate model on most of these problems, by 15$\times$ on two-dimensional Helmholtz at $65^2$ and 53$\times$ on the diffusion-reaction benchmark, and on the one- and two-dimensional problems its training on one CPU core takes 3-80$\times$ less time than the physics-informed baselines on one GPU.
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Computation and Language
Lost in Conversation or Lost in Translation? Diagnosing Multi-Turn Degradation in RAG
When conversing with large language models (LLMs), users often begin with a simple question and build towards a multi-hop question through follow-up turns. Retrieval-augmented generation (RAG) and its graph-based variant (GraphRAG) have become the dominant approaches for grounding LLM responses in external evidence, yet both are evaluated almost exclusively on single-turn, fully specified queries. We systematically investigate this evaluation mismatch through a large-scale simulation study. Building on prior work on multi-turn LLM evaluation, we transform questions from multi-hop question answering (QA) benchmarks into underspecified conversations and evaluate ten LLM assistants with eight retrieval systems across 1.5 million simulated conversations. Our findings reveal that multi-turn interaction causes widespread performance degradation, incurring relative performance drops of up to 21% and increasing unreliability by 47%, making RAG systems simultaneously less accurate and less reliable. We identify two distinct failure modes behind this degradation. Systems are either lost in translation, where conversational rephrasing distorts the retrieval query, or lost in conversation, where retrieval succeeds but the LLM fails to synthesize evidence distributed across turns.
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Machine Learning
Learned Queries and Keys Are All You Need: Replacing the Value Projection with Structured Transforms
To reduce the number of parameters and cache memory requirements of transformers we introduce dual-headed transformers instead of three heads. We studied Walsh-Hadamard Transform (WHT), Discrete Cosine Transform (DCT), Discrete Fourier Transform, filterbank based Shearlet Transform, and Multiplication-Avoiding (MA) operators to construct dual heads. We combine spatial patches and their orthogonal transforms (or Shearlet and MA operators) in a structure similar to the attention block. We obtained better results than triple headed transformers in ImageNet. Extensive simulation examples are presented.
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Machine Learning
Know Thyself, Teach Thyself: Internal Information Flow for Selective Self-Distillation
Self-distillation turns knowledge distillation into a closed learning loop and offers a path toward recursive self-improvement. Without an external teacher, however, the model must determine both what information can improve its supervision and which induced changes should be learned. Existing methods typically improve teacher-generated data or select training examples in isolation, leaving the information transferred between these stages unmeasured. We introduce InFlow, a retrieval-guided on-policy self-distillation framework that models this process as potential-to-realized information flow. InFlow first retrieves potentially informative sources using certainty-calibrated hidden-state trajectories, then measures their realized effect through the Jensen–Shannon divergence between the teacher's initial and retrieval-conditioned answer beliefs. Examples with larger belief shifts are selected for on-policy distillation. Our analysis formalizes the information optimized by retrieval and selection and relates the answer-level shift to the teacher–student distillation gap. Across four open-weight language models and three knowledge domains, InFlow achieves the strongest cross-model average among the compared selection methods, with ablations supporting both stages of the framework. Our code is available at https://github.com/1240148048/INFLOW.
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Computer Vision
AESplat: Advancing Pose-Free Feed-Forward 3D Gaussian Splatting via Decoupled Appearance Modeling
Pose-free feed-forward 3D Gaussian Splatting (3DGS) has demonstrated remarkable potential for generalized novel view synthesis. However, existing methods typically predict Gaussian appearance attributes represented by spherical harmonics (SH) in the same manner, overlooking the fundamental distinction between view-independent and view-dependent appearance, which results in suboptimal rendering quality. In this paper, we present AESplat, a novel and general framework for pose-free feed-forward 3DGS that introduces an effective decoupled appearance modeling strategy based on an analysis of SH, enabling higher-quality rendering. Specifically, AESplat directly derives the zeroth-order SH coefficient, which represents the base view-independent appearance component, from the input images without training. The higher-order SH coefficients are subsequently predicted by a shallow multilayer perceptron equipped with two efficient 3D-aware inductive biases to model view-dependent appearance variations. Extensive experiments across multiple datasets demonstrate that our method significantly outperforms state-of-the-art approaches, achieving a $0.8$ dB improvement in PSNR over the pose-free method NAS3R and a $1.1$ dB improvement over the pose-required method DepthSplat on the RealEstate10K dataset. Project page: https://aesplat.github.io/.
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Machine Learning
Normalize-Then-Precondition: A Hierarchical Approach to Marginal Scale and Interaction Geometry for LLM Training
Matrix optimizers have emerged as a promising direction, with Muon standing out as a prominent design. Revisiting Muon through its full-Gram representation, we observe that it jointly processes marginal-scale and interaction information. This opens an alternative way to organize geometric information hierarchically, motivating the Normalize-Then-Precondition framework. Specifically, it first uses diagonal-Gram information to construct a marginally normalized update, then applies spectral preconditioning to its directional interaction geometry. Building on this framework, we develop NormPre with NormPre-G and NormPre-L adopting global and localized spectral preconditioning, grounded in spectral-norm steepest descent and a regularized formulation followed by leading mode selection, respectively. To enable large-scale training, NormPre-G uses Newton-Schulz iterations and NormPre-L employs randomized sketching to approximate the leading interaction eigenspace. Theoretically, we establish $\mathcal{O}(T^{-1/2})$ convergence guarantees for simplified versions of NormPre. Across extensive pretraining experiments on GPT-2 Small, LLaMA and Qwen3, both variants consistently outperform AdamW, Muon and MANO under matched training budgets. Further efficiency and spectral analyses reveal the complementary strengths of two variants and characterize their performance-efficiency trade-off. We open-source our code through a GitHub repository at https://github.com/zx-gong/NormPre.
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Computation and Language
Video2Skill: From Streaming Experience to Reusable Embodied Skills
Manipulation behaviors vary widely across objects and scenes, but they share a small set of reusable skills, and planning with these skills helps embodied agents generalize to new tasks. Yet an agent can only plan with skills it knows. Recovering skills from observed experience, the inverse of planning, builds this knowledge over time and yields skill data for training future agents. Vision-Language Models (VLMs) describe individual manipulation events well, but can they organize a stream of events into reusable skills? We formulate this problem as Streaming Embodied Skill Discovery (SESD): a model watches videos in sequence and maintains a persistent skill library that shapes its later decisions. To systematically measure this ability, we introduce Video2Skill, a benchmark that covers robot tabletop manipulation and human kitchen activity and tests three core capabilities: (i) locating manipulation events in time, (ii) grouping events of the same transformation, and (iii) deciding when to reuse an existing skill or create a new one. Across 19 open-source VLMs, many models group events at near-chance level, and scale does not consistently help. Their errors depend on how perception and library updates are coupled: joint models merge distinct transformations into one skill, while models that update the library from text descriptions duplicate recurring ones. Supervised fine-tuning, including our counterfactual library-state rebalancing (CLaRe), improves grouping but exposes a deeper bottleneck: trained models consolidate familiar skills yet rarely expand the library. Their libraries stall below half the reference size, and transformations unseen in training are located in time but almost never given a new skill. Recognizing when existing skills are insufficient thus emerges as the central challenge.
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Machine Learning
CHAIN: Calibrated LLM Forecasting via Causal-Temporal Hypergraph Inference
Large language models have achieved significant progress in event forecasting, yet their probability outputs exhibit systematic calibration bias that varies heterogeneously across different domains and question types, undermining the trustworthiness of probabilistic outputs for decision-making under uncertainty. However, existing calibration methods typically correct probability outputs after prediction is complete, without modeling the structural sources of bias within the prediction process itself. To address this challenge, we decompose probabilistic prediction over causal-temporal hypergraphs into three stages, evidence weighting, evidence aggregation, and source fusion, and propose CHAIN, which designs stage-specific mechanisms to mitigate bias at each stage: (i) modulating the temporal decay function by causal topological distance, (ii) aggregating approximately independent causal chains via Noisy-OR after direction-aware deduplication, and (iii) driving adaptive fusion by causal coverage and directional balance. Experimental results on cross-domain forecasting benchmarks show CHAIN outperforms existing methods in expected calibration error, Brier score, and accuracy. Our project is available at https://github.com/QwenQKing/Chain.
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Information Retrieval
GRP v0.1 Technical Report
Industrial recommendation systems rely on multi-stage cascades whose retrieval, ranking, and serving components are difficult to replace jointly. We present GRP, a generative recommendation framework that combines retrieval, ranking, and reward modeling in a single encoder-decoder model, and evaluate a progressive path toward end-to-end recommendation. The model generates multimodal Semantic IDs and scores candidates with a jointly trained ranking module. The frozen ranking module then supplies rewards for reinforcement-learning post-training. We introduce mGRPO, which adds a reference-anchored margin to reward optimization to preserve the likelihood of logged targets. Offline experiments examine history encoding, model capacity allocation, event selection, tokenization, and reward discrimination. Serving optimizations reduce end-to-end retrieval latency by 69%. Online experiments evaluate the model as a retrieval source, with early-ranking bypass, and with replacement of weaker sources. In a retrieval-only comparison, view time increases by 0.46% and shares by 0.77% relative to production. A separate comparison combining bypass and source replacement yields increases of 0.82% in view time and 2.56% in shares, with neutral platform-level guardrails. These results support progressive deployment while identifying remaining gaps in ranking quality and performance across recommendation metrics.
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Artificial Intelligence · Cross-listed from eess.SP
MyoCodec: A Streaming Neural Codec for Electromyography
Neural codecs encode continuous signals into compact sequences of discrete tokens, providing an interface for efficient transmission, storage, and token-based sequence modeling. This paradigm has been widely adopted in modern speech and audio frameworks; however, the biosignal domain still lacks a neural codec designed specifically for low-bitrate streaming and generalization across diverse downstream tasks. We present MyoCodec, a streaming neural codec designed for electromyography (EMG). Inspired by recent neural audio codecs, MyoCodec combines causal Transformers with residual vector quantization to encode continuous EMG signals into different levels of EMG representations spanning from continuous latent features to discrete tokens operating at 50 Hz. Trained on twelve public EMG datasets, MyoCodec achieves favorable performance in both intrinsic codec quality and representative downstream tasks, including typing (emg2qwerty), hand-pose (emg2pose), speech decoding (emg2speech), and speech-to-EMG synthesis (speech2emg). Across these tasks, MyoCodec exhibits strong performance against prior models while providing a compact and causal EMG representation. During streaming inference, it requires compute time of only 0.482 ms for each 20 ms frame, enabling real-time streaming. Also, the discrete token representation provided by MyoCodec has the potential to support integration into language-model based approaches, creating a path toward LLM-based interactive systems, where tokenized EMG representations are directly processed into such language or speech models. Code and model weights are released.
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Machine Learning
Where Root Cause Analysis Fails: A Retrieval-Reranking Decomposition
Identifying the root cause of an anomaly among hundreds of sensors is critical for preventing safety incidents and costly downtime in complex monitored systems. Existing studies evaluate root cause analysis (RCA) methods using top@k accuracy. We show that this metric has a fundamental blind spot: it conflates two failure modes, retrieval failure, where the true cause is never considered, and reranking failure, where it is considered but ranked too low. In this work, we introduce a retrieval-reranking decomposition and audit four well-known benchmarks to expose this blind spot. Our experiments show that, on benchmarks with complex faults, statistical baselines mis-rank the true cause 79-100% of the time, and graph-based methods never clearly beat the best statistical baseline, whether their causal graphs are learned on short fault windows, on retrieved candidate pools guaranteed to contain the cause, or on multi-day normal-operation data. Meanwhile, on simple benchmarks where faults manifest significantly at their origin, retrieval is nearly solved (98-100%). Guided by the decomposition, we build a two-stage pipeline combining a multi-signal retriever with an LLM reranker that, as one fixed configuration, matches or exceeds the best baseline's top@1 accuracy on all six benchmark suites (by up to +12 points), with no causal graph or labeled data required. When all methods rank the same retrieved candidates with the true cause guaranteed present, adding a short system-description document lets the reranker lead the best baseline by +7 to +18 points on every benchmark. Code is available at https://github.com/cruiseresearchgroup/DecompRCA.
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Computer Vision
When Semantics Matter: Reliability-Aware Semantic-Rhythm Control for Co-Speech Gesture Generation
Co-speech gesture generation aims to synthesize natural gestures that are both temporally synchronized with speech and semantically consistent with the spoken content. Although recent methods can generate rhythmically plausible motions, they often rely heavily on acoustic prosody while underutilizing textual semantics, especially when semantic annotations are incomplete, noisy, or unavailable. Consequently, the generated gestures may follow speech rhythm while failing to express the intended semantics. To address this problem, we propose a reliability-aware semantic-rhythm control framework for co-speech gesture generation. We first learn a discrete motion prior that represents continuous gestures in a compact and structured motion-code space. We then introduce a dual-branch semantic contribution estimation mechanism consisting of a full multimodal branch and an audio-only branch. Their distributional discrepancy is formulated as conditional information gain to quantify how much textual semantics changes the predicted motion. Based on this estimate, a controllable semantic-rhythm objective selectively strengthens semantic guidance in content-relevant segments while limiting unnecessary semantic intervention in rhythm-dominant segments. Furthermore, we treat background noise as an acoustic reliability condition and introduce noise-conditioned feature modulation together with beneficial latent perturbation to improve generation robustness under realistic acoustic environments. Experiments on benchmark datasets demonstrate that the proposed framework achieves a favorable balance among semantic expressiveness, rhythmic synchronization, motion diversity, and robustness, enabling reliable and controllable co-speech gesture generation.
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Computation and Language
ProgressCompass: Embodied Progress Reward Models Are Lost Without the Right Context
Embodied agents now take on ever longer tasks. For long tasks, knowing only whether a task finally succeeds or fails says little; the steps along the way matter. Progress Reward Models (PRMs) score how far a task has come at every step, and serve as dense rewards, verifiers and monitors. Yet in long tasks the current frame alone often cannot tell how far the task has come, because progress depends on what happened before. We call this problem context-dependent progress estimation. Existing benchmarks on progress estimation mostly focus on short tasks whose progress can be read from the current observation, and whether PRMs can estimate progress when context is needed remains underexplored. We therefore build ContextProgress-Bench, with 24 manipulation tasks for 120 episodes. The benchmark covers three settings: (i) State Recall, where information needed for progress appeared earlier but is not in the current frame; (ii) Sequence Tracking, where steps follow a fixed order, so progress requires knowing which steps are done and which comes next; and (iii) Recurrence Disambiguation, where look-alike frames sit at very different progress. We then run a paired diagnosis: each PRM keeps the same input format in both runs, and in one run its instruction integrates the right context. Even PRMs that read the entire history get lost in estimating progress, yet with the right context the same five models cut their progress error by 77-82%. Embodied PRMs are thus not incapable of progress estimation, but lost without the right context. We therefore propose ProgressCompass, an autonomous agentic loop that reorients an existing PRM and uses current general-purpose VLMs to supply the context the PRM needs. Wrapped in the loop, the same frozen PRM cuts its progress error by 63% and raises its rank agreement by 76%. With such a compass, PRMs estimate progress far better on longer, more complex tasks.
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Machine Learning
MARCO: Multi-Round Agentic Reinforcement for Conditional Molecular Optimization
Molecular optimization is inherently iterative: a candidate is proposed, evaluated against several objectives, and revised while preserving a relationship to the source molecule. Most instruction-following models instead emit one edited molecule, forcing validity, property improvement, and similarity control into a single response. We introduce MARCO, an evaluator-grounded reinforcement-learning framework that trains molecular editors on bounded proposal–feedback–revision trajectories. MARCO aggregates shaped turn rewards into an undiscounted trajectory return for group-relative policy optimization. We evaluate two consequences of this training: Same-1 tests the trained policy under a one-response budget, while Same-5 tests whether the same policy can use verifier feedback when up to five responses are available. Across the three-objective MuMOInstruct benchmark, three Qwen backbones, and seen/unseen instruction splits, SFT-initialized MARCO obtains the highest product of property success rate and similarity in every reported primary setting. Same-5 further improves the observed score under the tested budget, while four-objective and public-checkpoint experiments test transfer across constraint sets and initialization regimes.
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Computer Vision
Reprogramming Vision-Language Models via Structured Prompt Reparameterization
Visual reprogramming adapts pretrained models to downstream tasks by modifying their input and output interfaces while keeping the backbone fixed. In vision-language models, existing methods mainly rely on intra-class prompt aggregation and do not explicitly model relationships among classes. However, fine-grained categories often exhibit highly overlapping attribute descriptions and strong inter-class correlation in the text embedding space, where discriminative cues lie in subtle low-variance components. We propose Reparameterized Inter-Class Visual Reprogramming (RVP), a structured framework that aggregates multiple text prompts within each class and applies residual correction across classes. We also show that CLIP-based visual reprogramming with input-independent linear output aggregation can be expressed as a linear mapping from frozen image embeddings to downstream logits, and use this view to design a structured reparameterization that models shared semantic components and class-specific differences. RVP uses only a single visual prompt and can be reparameterized at inference into a frozen backbone followed by a linear classifier, incurring nearly zero computational overhead. Across 11 few-shot classification benchmarks and four CLIP backbones, RVP consistently improves over prior visual reprogramming methods with comparable or better inference efficiency.
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Artificial Intelligence
MLToolBench: Learning Tool-Augmented Agents for Machine Learning Development
Machine learning engineering (MLE) agents have made substantial progress, but learning through ML experimentation remains costly in time and computation. Synthetic environments reduce these costs while introducing variations in data and experimental settings that require task-specific diagnosis. Access to diagnostic tools alone does not ensure that agents learn when to use them or how to act on their findings. We introduce ToolMLBench, a suite of executable tools for data inspection, code verification, and experiment diagnosis, together with an SFT and RL pipeline for learning their use. Diagnostic calls acquire evidence whose value depends on subsequent decisions, so final outcomes provide limited guidance on which calls to reinforce. We address this challenge with SPICE, which measures how privileged context changes the likelihood of a sampled tool action and uses this difference as a turn-level reward alongside the final outcome. We train on 80 synthetic tasks and evaluate on 25 in-domain and 10 out-of-domain tasks. Providing tool interfaces and descriptions alone yields inconsistent gains across unadapted models. With the same diagnostic interface, our training pipeline raises in-domain success from 24.8% to 52.4% for Qwen3-8B and from 35.6% to 69.2% for Qwen3.5-35B-A3B. The latter also improves from 31% to 48% out-of-domain, supporting learned diagnostic tool use on held-out sources and targets.
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Machine Learning
Understanding Private Evolution as Learning-Augmented Clustering
Private Evolution (PE) is a differentially private algorithm for synthetic data generation. While it can be viewed as a Wasserstein learning algorithm, it performs much better in practice than worst-case Wasserstein analyses would predict. We recast PE as generative model-augmented Wasserstein learning. We show theoretically that when we take into account the use of a generative model that is able to capture something about the true distribution, then we can obtain much better performance bounds. For example, if the generator gives samples in the same low-dimensional space as the distribution, then sample complexity depends on intrinsic, not ambient, dimension. We also show that standard variants of PE can fail to converge on simple well-clustered instances, and propose a new geometry-aware version of PE with provable convergence on such instances. Experimentally, we show that our new algorithm is competitive with standard baselines and can improve recall.
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Computer Vision
ReWorld-Track: A Recursive Event World Model for Language-Guided Multi-Camera Tracking
Language-guided multi-camera tracking must preserve a target identity across unobserved gaps, where similar candidates and uncertain returns can make early associations unreliable. A wrong match can corrupt the history used to predict later observations and propagate identity errors across subsequent camera handoffs. We propose ReWorld-Track, a recursive event world model that carries association uncertainty into future predictions. Candidate matches and continued waiting define alternative target states, whose posterior probabilities are used to update a persistent recurrent belief. This representation preserves uncertainty about alternative trajectories through successive observations. This belief predicts the next camera, arrival time, and entry region, while appearance and language evidence guide association. By training across successive handoffs, the model learns to retain uncertainty that remains useful for later predictions and identity decisions. ReWorld-Track achieves HOTA scores of 65.19 on CityFlowV2 and 45.36 on MTMMC, with improved identity continuity across repeated handoffs. On MTMMC, its structured posterior update gains 0.50 HOTA points over a similarly sized generic updater and 0.94 points over fixed-moment soft association, raising next-camera accuracy from 86.03% to 87.41% and reducing median arrival-time error from 0.78 s to 0.71 s for subsequent target returns.
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Robotics
Kinematic Nonlinear Spatio-Temporal Trajectory Warping for Contact-Rich Dexterous Manipulation Demonstrations
We present a straightforward but effective method for repurposing existing contact-rich dexterous manipulation demonstrations. Starting from inputs of hand and object trajectories, our method outputs high-quality nonlinear trajectory warps that account for intermediate waypoints, environmental barriers, temporal shifts, and varied start/end configurations. Foundational to our method is the utilization of contact distributions, which we show allows us to reliably compute complex and high-dimensional dexterous hand trajectories following a simple object-centric warp specification pipeline. We evaluate our method across 12 variations sourced from 4 demonstrations in a publicly available dataset of human hand motion data, perform baseline comparisons, and demonstrate generalization of our approach to different manipulators. Results and code will be made available on publication.
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Computation and Language
Gödel Forest: Balancing Search Depth and Breadth for Data-Centric Recursive Self-Improvement
Recursive self-improvement (RSI) aims to achieve compounding gains by having models improve themselves. While most existing RSI systems optimize external agent harnesses or prompts around a frozen base model, data-centric RSI directly updates the model's own parameters by training on agent-generated data. However, because validating data strategies requires expensive model training, existing methods face a fundamental dilemma: a single agent gets trapped in narrow directions and lacks exploration breadth, while naive parallel search or heavy trace sharing sacrifices long-horizon search depth. To address this challenge, we introduce G"odel Forest, a multi-agent framework that organizes recursive self-improvement as an ensemble of co-evolving search trees. In G"odel Forest, each agent autonomously grows a persistent tree, deepening, branching, or pruning data strategies based on model feedback to secure depth, while parallel trees explore distinct regions of the data space to expand breadth. Crucially, rather than leaving trees isolated or flooding them with heavy execution logs, a dynamically co-evolving memory connects the forest: agents continuously distill their successes and failures into compact procedural lessons anchored to a global leaderboard. Through this forest ecosystem, a dead-end in one tree instantly warns the whole forest against unpromising paths, while an empirical breakthrough quickly seeds new exploration branches in neighboring trees. Evaluated on RSIBench-Data across six diverse domains, G"odel Forest outperforms the single-agent baseline by an average of 10.70% while reducing wall-clock time on five tasks. Ablations confirm that co-evolving shared memory yields a +7.00% gain over independent parallel search, demonstrating that collective distillation is key to scalable self-improvement. The code is available at https://github.com/evolvent-ai/Godel-Forest.
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Machine Learning
Human-inspired, Task-Dimension-Guided Exploration for Efficient Learning in High Dimensions
Efficient exploration in high-dimensional decision spaces remains a central challenge for decision-making systems. Humans, in contrast, can navigate large decision spaces with remarkable efficiency. Recent behavioral studies suggest that humans reduce dimensionality in large decision spaces by probing candidate feature dimensions, identifying reward-relevant ones, and restricting the effective decision space. Inspired by this mechanism, we propose TDGE (Task-Dimension-Guided Exploration), a human-inspired, model-agnostic algorithm with an automatically constructed task-dimension–feature–item hierarchy. TDGE follows a top-down exploration strategy: it first selects task-relevant feature dimensions, then identifies informative features within those dimensions, and finally recommends concrete items based on the selected features. Experiments on MovieLens-20M, LastFM, and Amazon recommendation datasets show that TDGE substantially improves exploration efficiency and cold-start adaptation over baseline algorithms. Comparisons with other structured algorithms and ablation studies attribute these gains to TDGE's hierarchical structure and semantic feature-space exploration, with robust results across clustering methods and hierarchy depths. Recommendation-trajectory visualizations also show exploration patterns similar to human dimension-guided behavior.
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Artificial Intelligence
FairDiff: Mitigating the Self-Reinforcing Matthew Effect in Diffusion Recommender Models
While the "Matthew Effect" and filter bubbles are widely recognized outcome-level biases in recommender systems, we reveal that Diffusion Recommender Models (DRMs) uniquely compound this issue through their generative dynamics. Rather than merely inheriting data imbalances, DRMs trigger a self-reinforcing amplification of popularity bias. We identify that this phenomenon is driven by two compounding mechanisms. First, while optimization loss is universally dominated by high-frequency items across recommenders, DRMs suffer from a unique structural prior mismatch during generation. Because the forward terminal distribution of long-tailed data deviates significantly from the standard Gaussian prior, reverse sampling trajectories inherently collapse toward high-density popular items, fundamentally suppressing niche item generation. To dismantle this self-reinforcing loop, we propose FairDiff, a plug-and-play fairness-aware diffusion framework. To overcome the popularity-dominated loss, we introduce Popularity Condition Guidance (PCG). Rather than altering the training objective, PCG acts as an inference-time distributional reweighting mechanism, mathematically reshaping the score-based gradient field to penalize high-popularity regions and guide trajectories toward niche semantics. Furthermore, we design a Semantic Calibration (SC) Module to bridge the prior mismatch, aligning the forward and reverse distributions via one-step optimal transport. Comprehensive evaluations demonstrate that FairDiff achieves state-of-the-art performance while effectively mitigating the self-reinforcing Matthew Effect, highlighting its value as a general framework for DRMs.
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Artificial Intelligence
FineSID: Scalable and Efficient Semantic Identifier Learning for Generative Recommendation
A critical prerequisite of generative recommendation is designing semantic identifiers (SIDs) that are both scalable to large item sets and efficiently learnable. Existing SID learning methods fundamentally rely on Top-1 hard assignment during vector quantization. While heuristic strategies – such as clustering-based initialization or forced post-hoc collision resolution – can artificially inflate codebook coverage, they often disrupt end-to-end semantic alignment and fail to address the underlying optimization bottleneck: sparse gradient propagation. In standard Top-1 assignment, gradients concentrate on a narrow subset of frequently selected codewords, leaving the majority inherently under-trained and causing severe SID collisions. To overcome this limitation natively without relying on complex initialization priors, we propose FineSID, a unified quantization framework that moves beyond Top-1 assignment by enabling fine-grained gradient propagation across the entire codebook. Instead of updating only a single selected codeword, FineSID distributes learning signals to all codewords in a soft, differentiable manner. This design promotes globally balanced codebook optimization while strictly preserving semantic consistency, effectively alleviating SID collisions and stabilizing training in large, high-dimensional codebooks. Extensive experiments on multiple public benchmarks demonstrate that FineSID is robust to initialization configurations and consistently improves both codebook utilization and recommendation accuracy. Our work provides a principled, initialization-agnostic solution for semantic identifier learning, advancing the practicality of generative recommendation.
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Machine Learning
Stochastic Heavy Ball with Polyak Step Size and Armijo Line Search: A General Convergence Analysis
Polyak step size (PS) and Armijo line search (ALS) have received increasing attention in stochastic optimization, with encouraging empirical performance and theoretical guarantees. However, their convergence theory for stochastic heavy ball (SHB) methods remains limited. In this work, we develop a unified convergence analysis for SHB equipped with PS and ALS. To this end, we introduce a modified Armijo rule that closely parallels the Polyak step size, together with a decoupling analysis that isolates the historical dependence induced by momentum. For SHB with standard PS and ALS, we establish expected convergence for strongly convex, convex, and non-convex objectives without interpolation or restrictive conditions on the momentum parameter. Under interpolation or strong growth, we further strengthen the results to almost sure rates and last-iterate convergence. Moreover, for general settings beyond interpolation, we prove almost sure convergence to the exact optimum or to stationarity for SHB with diminishing variants of PS and ALS. These results provide a more comprehensive theoretical view of Polyak step size and Armijo line search for stochastic heavy ball methods.
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Game Theory
When One Leak Pays Forever: Context Binding and the Price of Deterring Collusion
A coalition that deviates once can profit many times when what it sells keeps working. In a threshold-encrypted mempool, a leading defense against maximal extractable value (MEV), a quorum of the decryption committee that sells its decryption capability to a front-runner exposes every later block that the capability still decrypts. We ask how large a penalty, such as slashable stake, deters this kind of collusion. In our repeated game, a single leak by any coalition in a monotone family of authorized coalitions (for example, any $k$ of the $n$ committee members) unlocks a set of future rounds, costs a one-time penalty, and ends the coalition's participation. We show that every dynamic deviation reduces to choosing a leak time, so deterrence holds if and only if each coalition's penalty covers the largest discounted value that a single leak reaches. Without discounting, over $T$ rounds of unit value full reuse needs a penalty of $T$ while binding each leak to its own round needs $1$, so no penalty that is constant in the horizon deters unbounded reuse; a reuse window of $w$ rounds costs at most $w$ times the largest per-round value. The cheapest profile of per-party stakes that deters every coalition solves a covering linear program. For blockchain design, per-epoch keys cut the required stake from the value of a key's lifetime to the value of one epoch; we calibrate the gap on Ethereum front-running data and place Ferveo and Shutter in the model. The analysis extends to sealed-bid auctions, multi-authority voting, and federated learning under a shared key.