NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence

Diankun Wu, Fangfu Liu, Yi-Hsin Hung, Yueqi Duan

展开摘要

Recent advancements in Multimodal Large Language Models (MLLMs) have significantly enhanced performance on 2D visual tasks. However, improving their spatial intelligence remains a challenge. Existing 3D MLLMs always rely on additional 3D or 2.5D data to incorporate spatial awareness, restricting their utility in scenarios with only 2D inputs, such as images or videos. In this paper, we present Spatial-MLLM, a novel framework for visual-based spatial reasoning from purely 2D observations. Unlike conventional video MLLMs which rely on CLIP-based visual encoders optimized for semantic understanding, our key insight is to unleash the strong structure prior from the feed-forward visual geometry foundation model. Specifically, we propose a dual-encoder architecture: a pretrained 2D visual encoder to extract semantic features, and a 3D spatial encoder—initialized from the backbone of the visual geometry model—to extract 3D structure features. A connector then integrates both features into unified visual tokens for enhanced spatial understanding. Furthermore, we propose a space-aware frame sampling strategy at inference time, which selects the spatially informative frames of a video sequence, ensuring that even under limited token length, the model focuses on frames critical for spatial reasoning. Beyond architecture improvements, we construct a training dataset from multiple sources and train the model on it using supervised fine-tuning and GRPO. Extensive experiments on various real-world datasets demonstrate that Spatial-MLLM achieves state-of-the-art performance in a wide range of visual-based spatial understanding and reasoning tasks.

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MoBA: Mixture of Block Attention for Long-Context LLMs

Enzhe Lu, Zhejun Jiang, Jingyuan Liu, Yulun Du, Tao Jiang, Chao Hong, Shaowei Liu, Weiran He, Enming Yuan, Yuzhi Wang, Zhiqi Huang, Huan Yuan, Suting Xu, Xinran Xu, Guokun Lai, Yanru Chen, Huabin Zheng, Junjie Yan, Jianlin Su, Yuxin Wu, Yutao Zhang, Zhilin Yang, Xinyu Zhou, Mingxing Zhang, Jiezhong Qiu

展开摘要

Scaling the effective context length is essential for advancing large language models (LLMs) toward artificial general intelligence (AGI). However, the quadratic increase in computational complexity inherent in traditional attention mechanisms presents a prohibitive overhead. Existing approaches either impose strongly biased structures, such as sink or window attention which are task-specific, or radically modify the attention mechanism into linear approximations, whose performance in complex reasoning tasks remains inadequately explored. In this work, we propose a solution that adheres to the ``less structure'' principle, allowing the model to determine where to attend autonomously, rather than introducing predefined biases. We introduce Mixture of Block Attention (MoBA), an innovative approach that applies the principles of Mixture of Experts (MoE) to the attention mechanism. This novel architecture demonstrates superior performance on long-context tasks while offering a key advantage: the ability to seamlessly transition between full and sparse attention, enhancing efficiency without the risk of compromising performance. MoBA has already been deployed to handle actual production workloads with long-context requirements, demonstrating significant advancements in efficient attention computation for LLMs. Our code is available at https://github.com/MoonshotAI/MoBA.

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Learning Interestingness in Automated Mathematical Theory Formation

George Tsoukalas, Rahul Saha, Amitayush Thakur, Sabrina Reguyal, Swarat Chaudhuri

展开摘要

We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce Fermat, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through Fermat: automatically scoring the interestingness of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines. We open-source the \fermat environment at github.com/trishullab/Fermat.

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Private Set Union with Multiple Contributions

Travis Dick, Haim Kaplan, Alex Kulesza, Uri Stemmer, Ziteng Sun, Ananda Theertha Suresh

展开摘要

In the private set union problem each user owns a bag of at most $k$ items (from some large universe of items), and we are interested in computing the union of the items in the bags of all of the users. This is trivial without privacy, but a differentially private algorithm must be careful about reporting items contained in only a small number of bags. We consider differentially private algorithms that always report a subset of the union, and define the utility of an algorithm to be the expected size of the subset that it reports. Because the achievable utility varies significantly with the dataset, we introduce the *utility ratio*, which normalizes utility by a dataset-specific upper bound and characterizes a mechanism by its lowest normalized utility across all datasets. We then develop algorithms with guaranteed utility ratios and complement them with bounds on the best possible utility ratio. Prior work has shown that a single algorithm can be simultaneously optimal for all datasets when $k=1$, but we show that instance-optimal algorithms do not exist when $k>1$, and characterize how performance degrades as $k$ grows. At the same time, we design a private algorithm that achieves the maximum possible utility, regardless of $k$, when the item histogram matches a prior prediction (for instance, from a previous data release) and degrades gracefully with the $L_\infty$ distance between the prediction and the actual histogram when the prediction is imperfect.

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CausalPFN: Amortized Causal Effect Estimation via In-Context Learning

Vahid Balazadeh, Hamidreza Kamkari, Valentin Thomas, Junwei Ma, Bingru Li, Jesse C. Cresswell, Rahul Krishnan

展开摘要

Causal effect estimation from observational data is fundamental across various applications. However, selecting an appropriate estimator from dozens of specialized methods demands substantial manual effort and domain expertise. We present CausalPFN, a single transformer that *amortizes* this workflow: trained once on a large library of simulated data-generating processes that satisfy ignorability, it infers causal effects for new observational datasets out of the box. CausalPFN combines ideas from Bayesian causal inference with the large-scale training protocol of prior-fitted networks (PFNs), learning to map raw observations directly to causal effects without any task-specific adjustment. Our approach achieves superior average performance on heterogeneous and average treatment effect estimation benchmarks (IHDP, Lalonde, ACIC). Moreover, it shows competitive performance for real-world policy making on uplift modeling tasks. CausalPFN provides calibrated uncertainty estimates to support reliable decision-making based on Bayesian principles. This ready-to-use model requires no further training or tuning and takes a step toward automated causal inference (https://github.com/vdblm/CausalPFN/).

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Enhancing LLM Watermark Resilience Against Both Scrubbing and Spoofing Attacks

Huanming Shen, Baizhou Huang, Xiaojun Wan

展开摘要

Watermarking is a promising defense against the misuse of large language models (LLMs), yet it remains vulnerable to scrubbing and spoofing attacks. This vulnerability stems from an inherent trade-off governed by watermark window size: smaller windows resist scrubbing better but are easier to reverse-engineer, enabling low-cost statistics-based spoofing attacks. This work expands the trade-off boundary by introducing a novel mechanism, equivalent texture keys, where multiple tokens within a watermark window can independently support the detection. Based on the redundancy, we propose a watermark scheme with **S**ub-vocabulary decomposed **E**quivalent t**E**xture **K**ey (**SEEK**). It achieves a Pareto improvement, increasing the resilience against scrubbing attacks without compromising robustness to spoofing. Our code will be available at [https://github.com/Hearum/SeekWM](https://github.com/Hearum/SeekWM).

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FUDOKI: Discrete Flow-based Unified Understanding and Generation via Kinetic-Optimal Velocities

Jin Wang, Yao Lai, Aoxue Li, Shifeng Zhang, Jiacheng Sun, Ning Kang, Chengyue Wu, Zhenguo Li, Ping Luo

展开摘要

The rapid progress of large language models (LLMs) has catalyzed the emergence of multimodal large language models (MLLMs) that unify visual understanding and image generation within a single framework. However, most existing MLLMs rely on autoregressive (AR) architectures, which impose inherent limitations on future development, such as the raster-scan order in image generation and restricted reasoning abilities in causal context modeling. In this work, we challenge the dominance of AR-based approaches by introducing FUDOKI, a unified multimodal model purely based on discrete flow matching, as an alternative to conventional AR paradigms. By leveraging metric-induced probability paths with kinetic optimal velocities, our framework goes beyond the previous masking-based corruption process, enabling iterative refinement with self-correction capability and richer bidirectional context integration during generation. To mitigate the high cost of training from scratch, we initialize FUDOKI from pre-trained AR-based MLLMs and adaptively transition to the discrete flow matching paradigm. Experimental results show that FUDOKI achieves performance comparable to state-of-the-art AR-based MLLMs across both visual understanding and image generation tasks, highlighting its potential as a foundation for next-generation unified multimodal models. Furthermore, we show that applying test-time scaling techniques to FUDOKI yields significant performance gains, further underscoring its promise for future enhancement through reinforcement learning.

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Online Functional Tensor Decomposition via Continual Learning for Streaming Data Completion

Xi Zhang, Yanyi Li, Yisi Luo, Qi Xie, Deyu Meng

展开摘要

Online tensor decompositions are powerful and proven techniques that address the challenges in processing high-velocity streaming tensor data, such as traffic flow and weather system. The main aim of this work is to propose a novel online functional tensor decomposition (OFTD) framework, which represents a spatial-temporal continuous function using the CP tensor decomposition parameterized by coordinate-based implicit neural representations (INRs). The INRs allow for natural characterization of continually expanded streaming data by simply adding new coordinates into the network. Particularly, our method transforms the classical online tensor decomposition algorithm into a more dynamic continual learning paradigm of updating the INR weights to fit the new data without forgetting the previous tensor knowledge. To this end, we introduce a long-tail memory replay method that adapts to the local continuity property of INR. Extensive experiments for streaming tensor completion using traffic, weather, user-item, and video data verify the effectiveness of the OFTD approach for streaming data analysis. This endeavor serves as a pivotal inspiration for future research to connect classical online tensor tools with continual learning paradigms to better explore knowledge underlying streaming tensor data.

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Checklists Are Better Than Reward Models For Aligning Language Models

Vijay Viswanathan, Yanchao Sun, Xiang Kong, Meng Cao, Graham Neubig, Tongshuang Wu

展开摘要

Language models must be adapted to understand and follow user instructions. Reinforcement learning is widely used to facilitate this —typically using fixed criteria such as "helpfulness" and "harmfulness". In our work, we instead propose using flexible, instruction-specific criteria as a means of broadening the impact that reinforcement learning can have in eliciting instruction following. We propose "Reinforcement Learning from Checklist Feedback" (RLCF). From instructions, we extract checklists and evaluate how well responses satisfy each item—using both AI judges and specialized verifier programs—then combine these scores to compute rewards for RL. We compare RLCF with other alignment methods on top of a strong instruction following model (Qwen2.5-7B-Instruct) on five widely-studied benchmarks — RLCF is the only method to help on every benchmark, including a 4-point boost in hard satisfaction rate on FollowBench, a 6-point increase on InFoBench, and a 3-point rise in win rate on Arena-Hard. We show that RLCF can also be used off-policy to improve Llama 3.1 8B Instruct and OLMo 2 7B Instruct. These results establish rubrics as a key tool for improving language models' support of queries that express a multitude of needs. We release our our dataset of rubrics (WildChecklists), models, and code to the public.

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Generalizable Insights for Graph Transformers in Theory and Practice

Timo Stoll, Luis Müller, Christopher Morris

展开摘要

Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to specific design choices and lack comprehensive empirical validation on large-scale data. This leaves a gap between theory and practice, preventing generalizable insights that exceed particular application domains. Here, we propose the Generalized-Distance Transformer (GDT), a GT architecture using standard attention that incorporates many advancements for GTs from recent years, and develop a fine-grained understanding of the GDT's representation power in terms of attention and PEs. Through extensive experiments, we identify design choices that consistently perform well across various applications, tasks, and model scales, demonstrating strong performance in a few-shot transfer setting without fine-tuning. Our evaluation covers over eight million graphs with roughly 270M tokens across diverse domains, including image-based object detection, molecular property prediction, code summarization, and out-of-distribution algorithmic reasoning. We distill our theoretical and practical findings into several generalizable insights about effective GT design, training, and inference.

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Brain-Inspired fMRI-to-Text Decoding via Incremental and Wrap-Up Language Modeling

Wentao Lu, Dong Nie, Pengcheng Xue, Zheng Cui, Piji Li, Daoqiang Zhang, Xuyun Wen

展开摘要

Decoding natural language text from non-invasive brain signals, such as functional magnetic resonance imaging (fMRI), remains a central challenge in brain-computer interface research. While recent advances in large language models (LLMs) have enabled open-vocabulary fMRI-to-text decoding, existing frameworks typically process the entire fMRI sequence in a single step, leading to performance degradation when handling long input sequences due to memory overload and semantic drift. To address this limitation, we propose a brain-inspired sequential fMRI-to-text decoding framework that mimics the human cognitive strategy of segmented and inductive language processing. Specifically, we divide long fMRI time series into consecutive segments aligned with optimal language comprehension length. Each segment is decoded incrementally, followed by a wrap-up mechanism that summarizes the semantic content and incorporates it as prior knowledge into subsequent decoding steps. This sequence-wise approach alleviates memory burden and ensures semantic continuity across segments. In addition, we introduce a text-guided masking strategy integrated with a masked autoencoder (MAE) framework for fMRI representation learning. This method leverages attention distributions over key semantic tokens to selectively mask the corresponding fMRI time points, and employs MAE to guide the model toward focusing on neural activity at semantically salient moments, thereby enhancing the capability of fMRI embeddings to represent textual information. Experimental results on the two datasets demonstrate that our method significantly outperforms state-of-the-art approaches, with performance gains increasing as decoding length grows.

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Measuring and Guiding Monosemanticity

Ruben Härle, Felix Friedrich, Manuel Brack, Björn Deiseroth, Stephan Waeldchen, Patrick Schramowski, Kristian Kersting

展开摘要

There is growing interest in leveraging mechanistic interpretability and controllability to better understand and influence the internal dynamics of large language models (LLMs). However, current methods face fundamental challenges in reliably localizing and manipulating feature representations. Sparse Autoencoders (SAEs) have recently emerged as a promising direction for feature extraction at scale, yet they, too, are limited by incomplete feature isolation and unreliable monosemanticity. To systematically quantify these limitations, we introduce Feature Monosemanticity Score (FMS), a novel metric to quantify feature monosemanticity in latent representation. Building on these insights, we propose Guided Sparse Autoencoders (G-SAE), a method that conditions latent representations on labeled concepts during training. We demonstrate that reliable localization and disentanglement of target concepts within the latent space improve interpretability, detection of behavior, and control. Specifically, our evaluations on toxicity detection, writing style identification, and privacy attribute recognition show that G-SAE not only enhances monosemanticity but also enables more effective and fine-grained steering with less quality degradation. Our findings provide actionable guidelines for measuring and advancing mechanistic interpretability and control of LLMs.

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Benchmarking Egocentric Multimodal Goal Inference for Assistive Wearable Agents

Vijay Veerabadran, Fanyi Xiao, Nitin Kamra, Pedro Matias, Joy Chen, Caley Drooff, Brett D Roads, Riley Williams, Ethan Henderson, Xuanyi Zhao, Kevin Carlberg, Joseph Tighe, Karl Ridgeway

展开摘要

There has recently been a surge of interest in Wearable Assistant Agents: agents embodied in a wearable form factor such as smart glasses, who can take actions toward a user’s stated goal — a high-level language-expressed command such as “where did I leave my keys?”, “Text Alice I will be late”, or “What’s the weather in Cancun?”. In this work, we consider the complementary problem of eliminating the effort required to interact with such an agent by proactively inferring the user’s goal from multimodal contextual observations. As vision-language models (VLMs) hold strong potential to ultimately solve this problem, our work focuses on creating a strong benchmark to measure progress toward this end. Given the limited prior work in this area, establishing the benchmark required collecting a novel multimodal goal-inference dataset; our dataset comprises ~30 hours of data from 363 participants across 3,482 recordings, featuring ground-truth reference goals alongside accompanying visual, audio, digital, and longitudinal contextual observations. We ran a human predictability study, where we found that humans set a strong baseline that comprises a de facto upper bound on model performance: they show multiple choice question (MCQ) accuracy of 93%, with the best VLM achieving about 84% accuracy. However, MCQ assesses discrimination, not the model’s ultimate task of generating the goal through open-ended text generation. Through a meta-evaluation, we find that a VLM judging the generated goals is as good as a human judge if it has access to a human-authored script of the video or a correct reference goal. Finally, we evaluate several families of modern vision-language models on the benchmark, showing that larger models have a significant performance advantage, but are still far from being practically useful, as they produce relevant goals only ~57% of the time. The best-performing smaller models—whose size makes them better suited to wearable applications—perform significantly worse than their counterparts, generating ~49% accuracy on the benchmark. Through a modality ablation, we show that models benefit from extra information in relevant modalities with minimal performance degradation from irrelevant modalities, but don’t gain as much when noisy modalities are included (e.g., in the case of digital context when most of the app state is irrelevant).

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Personalized Decision Modeling: Utility Optimization or Textualized-Symbolic Reasoning

Yibo Zhao, Yang Zhao, Hongru Du, Hao Frank Yang

展开摘要

Decision-making models for individuals, particularly in high-stakes scenarios like vaccine uptake, often diverge from population optimal predictions. This gap arises from the uniqueness of the individual decision-making process, shaped by numerical attributes (e.g., cost, time) and linguistic influences (e.g., personal preferences and constraints). Developing upon Utility Theory and leveraging the textual-reasoning capabilities of Large Language Models (LLMs), this paper proposes an Adaptive Textual-symbolic Human-centric Reasoning framework (ATHENA) to address the optimal information integration. ATHENA uniquely integrates two stages: First, it discovers robust, group-level symbolic utility functions via LLM-augmented symbolic discovery; Second, it implements individual-level semantic adaptation, creating personalized semantic templates guided by the optimal utility to model personalized choices. Validated on real-world travel mode and vaccine choice tasks, ATHENA consistently outperforms utility-based, machine learning, and other LLM-based models, lifting F1 score by at least 6.5\% over the strongest cutting-edge models. Further, ablation studies confirm that both stages of ATHENA are critical and complementary, as removing either clearly degrades overall predictive performance. By organically integrating symbolic utility modeling and semantic adaptation, ATHENA provides a new scheme for modeling human-centric decisions. The project page can be found at https://yibozh.github.io/Athena.

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Structured Sparse Transition Matrices to Enable State Tracking in State-Space Models

Aleksandar Terzic, Nicolas Menet, Michael Hersche, Thomas Hofmann, Abbas Rahimi

展开摘要

Modern state-space models (SSMs) often utilize structured transition matrices which enable efficient computation but pose restrictions on the model’s expressivity, as measured in terms of the ability to emulate finite-state automata (FSA). While unstructured transition matrices are optimal in terms of expressivity, they come at a prohibitively high compute and memory cost, even for moderate state sizes. We propose a structured sparse parametrization of transition matrices in SSMs that enables FSA state tracking with provably optimal state size and depth, while keeping the computational cost of the recurrence comparable to that of diagonal SSMs. Our method, \emph{PD-SSM}, parametrizes the transition matrix as the product of a column one-hot matrix ($P$) and a complex-valued diagonal matrix ($D$). As a result, the computational cost of parallel scans scales linearly with the state size. Theoretically, the model is BIBO-stable and can emulate any $N$-state FSA with one layer of dimension $N$ and a linear readout of size $N ×N$, significantly improving on all current structured SSM guarantees. Experimentally, the model significantly outperforms a wide collection of modern SSM variants on various FSA state tracking tasks. On multivariate time-series classification, it outperforms neural controlled differential equations, a paradigm explicitly built for time-series analysis. Finally, we integrate PD-SSM into a hybrid Transformer-SSM architecture and demonstrate that the model can effectively track the states of a complex FSA in which transitions are encoded into sets of variable-length English sentences. The code is available at https://github.com/IBM/expressive-sparse-state-space-model.

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Beyond Expectations: Quantile-Guided Alignment for Risk-Calibrated Language Models

Xinran Wang, Jin Du, Azal Ahmad Khan, Qi Le, Enmao Diao, Jiawei Zhou, Jie Ding, Ali Anwar

展开摘要

Large language models can generate rare but catastrophic outputs, such as harmful conversations or insecure code. Existing Reinforcement Learning from Human Feedback (RLHF) typically maximizes average reward, leaving high-risk tail events insufficiently controlled. We introduce Quantile‑Guided Alignment (QA), a framework that allows users to specify desired improvements at any quantile—individually or across multiple reward dimensions—thus shifting the distribution of outputs with finer control toward safer, more desirable outcomes. The method extends standard RLHF via an augmented reward formulation that enforces quantile constraints. Experiments on conversation and code‐generation tasks show that quantile alignment significantly enhances quality at targeted tails while maintaining overall performance. The results position QA as a principled route to risk‑calibrated language models with tail‑focused alignment.

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CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulations

Guangyi Chen, Yunlong Deng, Peiyuan Zhu, Yan Li, Yifan Shen, Zijian Li, Kun Zhang

展开摘要

Causal Representation Learning (CRL) aims to uncover the data-generating process and identify the underlying causal variables and relations, whose evaluation remains inherently challenging due to the requirement of known ground-truth causal variables and causal structure. Existing evaluations often rely on either simplistic synthetic datasets or downstream performance on real-world tasks, generally suffering a dilemma between realism and evaluative precision. In this paper, we introduce a new benchmark for CRL using high-fidelity simulated visual data that retains both realistic visual complexity and, more importantly, access to ground-truth causal generating processes. The dataset comprises around 200 thousand images and 3 million video frames across 24 sub-scenes in four domains: static image generation, dynamic physical simulations, robotic manipulations, and traffic situation analysis. These scenarios range from static to dynamic settings, simple to complex structures, and single to multi-agent interactions, offering a comprehensive testbed that hopefully bridges the gap between rigorous evaluation and real-world applicability. In addition, we provide flexible access to the underlying causal structures, allowing users to modify or configure them to align with the required assumptions in CRL, such as available domain labels, temporal dependencies, or intervention histories. Leveraging this benchmark, we evaluated representative CRL methods across diverse paradigms and offered empirical insights to assist practitioners and newcomers in choosing or extending appropriate CRL frameworks to properly address specific types of real problems that can benefit from the CRL perspective. Welcome to visit our: Project page: https://causal-verse.github.io/ , Dataset: https://huggingface.co/CausalVerse

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Less is More: Improving LLM Alignment via Preference Data Selection

Xun Deng, Han Zhong, Rui Ai, Fuli Feng, Zheng Wang, Xiangnan He

展开摘要

Direct Preference Optimization (DPO) has emerged as a promising approach for aligning large language models with human preferences. While prior work mainly extends DPO from the aspect of the objective function, we instead improve DPO from the largely overlooked but critical aspect of data selection. Specifically, we address the issue of parameter shrinkage caused by noisy data by proposing a novel margin-maximization principle for dataset curation in DPO training. To further mitigate the noise in different reward models, we propose a Bayesian Aggregation approach that unifies multiple margin sources (external and implicit) into a single preference probability. Extensive experiments in diverse settings demonstrate the consistently high data efficiency of our approach. Remarkably, by using just 10\% of the Ultrafeedback dataset, our approach achieves 3\% to 8\% improvements across various Llama, Mistral, and Qwen models on the AlpacaEval2 benchmark. Furthermore, our approach seamlessly extends to iterative DPO, yielding a roughly 3\% improvement with 25\% online data, revealing the high redundancy in this presumed high-quality data construction manner. These results highlight the potential of data selection strategies for advancing preference optimization.

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Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning

Jaehun Jung, Seungju Han, Ximing Lu, Skyler Hallinan, David Acuna, Shrimai Prabhumoye, Mostofa Patwary, Mohammad Shoeybi, Bryan Catanzaro, Yejin Choi

展开摘要

Data diversity is crucial for training a strong language model. Yet metrics of diversity often diverge from this goal, measuring variations in heuristic features—like n-grams or embeddings—that are detached from how the model actually performs on a target task. This motivates us to ask: *Can we redefine data diversity—beyond measuring variations in heuristic features—in a way that better predicts model generalization?* Through large-scale empirical analyses spanning over 300 training runs, carefully controlled for data scale and quality, we show that data diversity can be a strong predictor of generalization in LLM reasoning—as measured by average model performance on unseen out-of-distribution benchmarks. We introduce **G-Vendi**, a metric that quantifies diversity via the entropy of model-induced loss gradients. G-Vendi scales to million-sample datasets and yet consistently outperforms heuristic alternatives, achieving strong correlation ($\text{Spearman's } \rho \approx 0.9$) with out-of-distribution (OOD) performance across both natural language inference (NLI) and math reasoning tasks. Building on this insight, we present **Prismatic Synthesis**, a framework for generating diverse synthetic data by targeting underrepresented regions in gradient space. Experimental results show that Prismatic Synthesis consistently improves model performance as we scale synthetic data—not just on in-distribution test but across unseen, out-of-distribution benchmarks—significantly outperforming state-of-the-art models in both domains. For example, PrismMath-7B, our model distilled from a 32B LLM without human verification, outperforms R1-Distill-Qwen-7B—trained on proprietary data generated by 671B R1—on 6 out of 7 challenging math benchmarks.

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Measuring and Controlling Solution Degeneracy across Task-Trained Recurrent Neural Networks

Ann Huang, Satpreet Harcharan Singh, Flavio Martinelli, Kanaka Rajan

展开摘要

Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers individual trained networks. However, different RNNs trained on the same task and achieving similar performance can exhibit strikingly different internal solutions, a phenomenon known as solution degeneracy. Here, we develop a unified framework to systematically quantify and control solution degeneracy across three levels: behavior, neural dynamics, and weight space. We apply this framework to 3,400 RNNs trained on four neuroscience-relevant tasks—flip-flop memory, sine wave generation, delayed discrimination, and path integration—while systematically varying task complexity, learning regime, network size, and regularization. We find that increased task complexity and stronger feature learning reduce degeneracy in neural dynamics but increase it in weight space, with mixed effects on behavior. In contrast, larger networks and structural regularization reduce degeneracy at all three levels. These findings empirically validate the Contravariance Principle and provide practical guidance for researchers seeking to tune the variability of RNN solutions, either to uncover shared neural mechanisms or to model the individual variability observed in biological systems. This work provides a principled framework for quantifying and controlling solution degeneracy in task-trained RNNs, offering new tools for building more interpretable and biologically grounded models of neural computation.

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