NeurIPS 2026 Papers

Conference on Neural Information Processing Systems

Decision breakdown

6,437papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    991.5%
  • Spotlight
    2403.7%
  • Poster
    6,09894.7%

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Embedded-Arena: Building Hardware-in-the-Loop Coding Agents to Run AI on Microcontrollers

Zhihan Zhang, Alexander Le Metzger, Jiuyang Lyu, Chun-Cheng Chang, Jiayi Shao, Yujia Liu, Emmanuel A Mensah, Edward Wang, Kurtis Heimerl, Gregory D Abowd, Natasha Jaques, Shwetak Patel, Vikram Iyer

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Embedded devices from wildlife monitoring stations to clinical wearables require local AI inference due to latency, communication, or privacy constraints. Optimizing models for heterogeneous microcontrollers (MCUs) requires simultaneously satisfying hard physical constraints on memory, power, and temperature while preserving accuracy, a multidimensional optimization that is today performed manually by experts. We ask whether an LLM agent can autonomously navigate this complex, multi-turn pipeline guided by real hardware feedback, and introduce a hardware-in-the-loop agent arena in which the agent iteratively refines both model and firmware---compiling, flashing, and measuring on real hardware---to enable iterative optimization. Frontier models, including Claude Opus 4.7 and Gemini 3.1 Pro, fail entirely without hardware feedback (0\% deployment success), whereas our closed-loop formulation achieves the first successful deployment within three iterations and can surpass human expert results within seven. This agentic co-optimization achieves 250× compression for vision models with <3.3\% accuracy loss and 400× for audio with <6\% Feature Error Rate loss, enabling battery-free operation on a commercial MCU via solar harvesting. We demonstrate practical impact in two real-world systems: an elk-detection camera trap (96.7\% accuracy) and a phonetic-transcription wearable (8.44\% FER) for child development research.

Spotlight
EVALUATION CARDS: An Interpretive Layer for AI Evaluation Reporting

Avijit Ghosh, Anka Reuel-Lamparth, Wm. Matthew Kennedy, Jenny Chim, Yilin Huang, Srishti Yadav, Anastassia Kornilova, Damian Stachura, Kevin Klyman, Jennifer Mickel, Felix Friedrich, Max Lamparth, Jan Batzner, Anoop Mishra, Jeba Sania, Eliya Habba, Nathan Heath, Shalaleh Rismani, Usman Gohar, Andrea Loehr, David Manheim, Ruchira Dhar, Sree Harsha Nelaturu, Aarush Sinha, Leshem Choshen, Yixiong Hao, Yanan Long, Andrew Tran, Drishti Sharma, Ishan Khire, Amit Saha, Subramanyam Sahoo, Michael Hardy, Michael A. Riegler, Kabir Manghnani, Michelle Lin, Nancy Jiang, Asaf Yehudai, Nuno Moniz, Yacine Jernite, Zeerak Talat, Stella Biderman, Mubashara Akhtar, Jessica Ji, Aris Hofmann, Mykel J Kochenderfer, Sanmi Koyejo, Irene Solaiman

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AI evaluation results are produced at scale but reported inconsistently across leaderboards, model cards, benchmark papers, and company blogs. This fragmentation is borne at the level of interpretation: readers cannot reliably compare results across sources, identify what is missing from a given report, or trace an aggregate claim to the evidence behind it. Recent efforts address isolated components of this problem but leave three gaps unresolved: They cover only narrow slices of the evaluation lifecycle and do not compose into a single interpretable record. They specify static representations that do not differentiate between the questions technical and policy readers bring to the same evidence. And they remain proposals on paper, without the extraction infrastructure required for adoption at scale. We present EVALUATION CARDS, an operational reporting layer that composes benchmark metadata, evaluation run data, and model metadata into a unified record. We (1) derive a reporting schema from a structured literature review of 52 papers and 10 stakeholder interviews, (2) implement four interpretive signals (reproducibility, documentation completeness, provenance and risk, and score comparability), rendered through reader modes calibrated to research and policy audiences, and (3) provide a deployed monitoring tool that applies EVALUATION CARDS across 5,498 models, 635 benchmarks, and 101,843 results, surfacing systematic gaps in current reporting practice.

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ECHO: Terminal Agents Learn World Models for Free

Vaishnavi Shrivastava, Ahmed Awadallah, Dimitris Papailiopoulos

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CLI agents are the closest thing language models have to an embodied setting: the model emits commands, the terminal executes them, and the returned stream---stdout, errors, file contents---records the consequences of its actions. We argue that this stream is a supervision signal, but standard agent RL largely discards it: GRPO-style training updates action tokens while ignoring environment responses, even though rollouts already contain them. We introduce ECHO (Environment Cross-entropy Hybrid Objective), an auxiliary loss that trains the policy to predict observation tokens alongside the policy gradient. ECHO reuses the same forward pass, requires no additional rollouts, and turns terminal feedback into a dense signal that remains informative even on failed trajectories. This objective shapes the policy toward a world model of terminal dynamics, plausibly improving its priors over which actions are likely to succeed. On TerminalBench 2, ECHO nearly doubles pass@1: Qwen3-8B improves from 2.70% to 5.17%, and Qwen3-14B from 5.17% to 10.79%. From base Qwen3-8B, ECHO+GRPO matches expert-SFT-then-GRPO on held-out terminal tasks without the expert demonstrations required for SFT, and closes roughly half this gap on TerminalBench 2. Without verifier rewards, ECHO can lead to self-improvement through exploration alone, suggesting environment observations are not merely context for actions but supervision for the policy itself.

Spotlight
Dynamic Tokenization via Reinforcement Patching: End-to-end Training and Zero-shot Transfer

Yulun Wu, Sravan Kumar Ankireddy, Samuel Sharpe, Nikita Seleznev, Dehao Yuan, Hyeji Kim, Nam Nguyen

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Efficiently aggregating spatial or temporal horizons to acquire compact representations has become a unifying principle in modern deep learning models, yet learning data-adaptive representations for long-horizon sequence data, especially continuous sequences like time series, remains an open challenge. While fixed-size patching has improved scalability and performance, discovering variable-sized, data-driven patches end-to-end often forces models to rely on soft discretization, specific backbones, or heuristic rules. In this work, we propose Reinforcement Patching (ReinPatch), a novel framework that jointly optimizes a sequence patching policy and its downstream sequence backbone model with reinforcement learning. By formulating patch boundary placement as a discrete decision process optimized via Group Relative Policy Gradient (GRPG), ReinPatch bypasses the need for continuous relaxations and performs dynamic patching policy optimization in a natural manner. Moreover, our method allows strict enforcement of a desired compression rate, freeing the downstream backbone to scale efficiently, and natively supports multi-level hierarchical modeling. We evaluate ReinPatch on time-series forecasting datasets, where it demonstrates compelling performance compared to state-of-the-art data-driven patching strategies. Furthermore, our detached design allows the patching module to be extracted as a standalone foundation patcher, providing the community with visual and empirical insights into the segmentation behaviors preferred by a purely performance-driven neural patching strategy.

Spotlight
Doomed to Re-Annotate, Forever: The ImageNet Story

Illia Volkov, Nikita Kisel, Tetiana Mishkina, Klara Janouskova, Jiri Matas

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Top-1 accuracy on ImageNet-1k remains the most universally reported metric in visual recognition, despite its well-documented label quality issues. In the paper, we describe the effort to obtain accurate and complete ImageNet-1k validation set annotations. The result -- ReImageNet -- is a from-scratch reannotation, which includes multilabel correction, object localisation, revised class definitions, and semantic attributes---text-recognition, rendition, reflection, crowd, and dominant. The reannotation reveals that $\approx13$\% of the original ImageNet-1k labels are incorrect, $32.7$\% of images are multilabel and $4.7$\% contain no object from an ImageNet-1k class. With the new labels, top-1 accuracy increases by $0.7$--$1.4$\% for supervised models and by $6$--$8$\% for MLLMs. We show that annotation errors in ImageNet-1k propagate into its derivative test sets, indicating that the problem is structural rather than specific to any single benchmark. We observed that LLMs outperform unaided crowd annotators, and that human and LLM collaboration with appropriate tooling represents the current quality ceiling for annotation at this scale. All [annotations](https://huggingface.co/datasets/c1rcuslegend/ReImageNet), [class definitions](https://gonikisgo.github.io/imagenet-annotation-preview/), [guidelines](https://gonikisgo.github.io/imagenet-annotation-preview/), and [analysis code](https://github.com/klarajanouskova/ImageNet) have been publicly released.

Spotlight
Do Thinking Tokens Help with Safety?

Narutatsu Ri, Abhishek Panigrahi, Sanjeev Arora

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Today's reasoning models use thinking tokens to attain stronger performance on benchmarks than their instruction-tuned counterparts. It is also generally believed that this more "deliberative" mode should improve alignment and safety, by providing the model a safe space to consider whether its planned answer to the request violates its safety principles. We present evidence that this intuition is not always correct. Across frontier open-weight reasoning models spanning GPT-OSS, Phi, OLMo, and Qwen model families, we find that the model's decision is already strongly encoded at the beginning of thinking, with a probe on the first token's hidden representation predicting refusal/compliance with $\ge0.85$ AUROC and $\sim90$\% balanced accuracy. We also find little evidence that current models can use their thinking trace to deliberate about safety, as additional thinking after the first 20\% of the trace rarely moves the final decision. While sentence-level inspection of thinking traces may show signs of oscillation between refusal- and compliance-leaning rationales, we find that in $\geq 85$\% of thinking traces, such oscillations exert limited to no influence on the final response. We also examine the effect of existing inference-time and training-based safety interventions and find that they largely alter thinking behavior by shifting models toward more refusal-leaning reasoning while substantially reducing helpfulness on benign prompts. Our results suggest that safety behavior in current reasoning models is much less deliberative than commonly assumed, highlighting the need for training methods that more effectively utilize thinking traces for safety-critical decision making.

Spotlight
Distributionally Robust Domain Randomization with Learned Risk-Sensitive Dynamics Samplers

Sukchul Jeong, Insoon Yang

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Domain randomization (DR) improves sim-to-real transfer by training policies over randomized simulator dynamics, but standard DR optimizes average performance under a fixed sampler and can miss rare failure-prone domains. We propose Risk-Sensitive Domain Randomization (RSDR), a distributionally robust formulation of episodic DR that evaluates each policy against the worst-case distribution over dynamics parameters within a KL neighborhood of a reference sampler. The resulting soft adversary has an exponential-tilting form, yielding a single temperature-controlled sampler family: negative temperatures emphasize low-return domains for robustness, zero recovers uniform DR, and positive temperatures give an optimistic sampler closely related to curriculum-style DR. Because this target changes with the policy and returns are observed only through rollouts, RSDR learns an amortized dynamics sampler by reverse-KL variational inference while reusing on-policy PPO trajectories. Across six domain-randomized MuJoCo Playground tasks, robust RSDR improves CVaR and minimum-return metrics over uniform and adaptive DR baselines, and outperforms best-tuned EPOpt.

Spotlight
Diagonalizing the Softmax: Hadamard Initialization for Tractable Cross-Entropy Dynamics

Connall Garrod, Jonathan Keating, Christos Thrampoulidis

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Cross-entropy (CE) loss is central to deep learning, but existing theory often relies on simplifications—such as squared loss or convex models—that miss key aspects of CE optimization. In this work, we study multi-class CE dynamics using a two-layer linear network with orthogonal inputs, the simplest non-convex setting where the CE implicit bias remains unresolved. This coincides with the unconstrained features model used to study neural collapse (NC). Our analysis is based on a key observation: Hadamard initialization diagonalizes the softmax operator. This allows us to extend the spectral initialization framework that Saxe et al. (2013, 2019) developed for squared loss. We prove convergence to NC under spectral CE training and give the first finite-time analysis in this setting via an explicit Lyapunov function that decreases monotonically to NC despite spurious critical points. We further identify CE-specific phenomena absent under squared loss—coupling, non-monotonic convergence, qualitative dependence on the number of classes, and exponential slowdowns. We also characterize the role of network width and show empirically that spectral dynamics qualitatively model small random initialization.

Spotlight
DeltaPrompts: Escaping the Zero-Delta Trap in Multimodal Distillation

Jaehun Jung, Hyunwoo Kim, Brandon Cui, Ximing Lu, David Acuna, Prithviraj Ammanabrolu, Yejin Choi

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Distillation enables compact Vision-Language Models (VLMs) to obtain strong reasoning capabilities, yet the prompts driving this process are typically chosen via simple heuristics or aggregated from off-the-shelf datasets. We reveal a critical inefficiency in this approach: up to 69\% of the prompts in standard chart / document reasoning datasets are effectively $\textit{zero-delta}$, meaning the teacher and student already induce the exact same answer distribution. Training on these prompts provides minimal learning signal, causing student improvement to rapidly saturate regardless of data scale. To escape the zero-delta trap, we return to first principles: distillation fundamentally minimizes distributional divergence, and thus a prompt is valuable only if it exposes a functional capability gap between the teacher and student. We quantify this gap through $\textit{answer divergence}$ ($\Delta$), demonstrating that non-zero divergence is critical for effective scaling. Building on this insight, we propose a staged synthesis pipeline that repurposes existing datasets as seeds, actively targeting student failure modes to produce better prompts. The result is $\textbf{DeltaPrompts}$, a diverse dataset of 200k synthetic, high-divergence reasoning problems. We evaluate $\text{DeltaPrompts}$ across three distinct settings: on-policy distillation with the target teacher-student pair, transfer to a novel model family without regenerating the data, and off-policy fine-tuning of a non-reasoning model. Across all scenarios, $\text{DeltaPrompts}$ drives substantial gains, yielding up to 15\% relative improvement even on top of a highly-optimized reasoning model ($\textit{e.g.,}$ Qwen3-VL-8B-Thinking)---averaged over 10 benchmarks spanning chart, document and perception-centric reasoning.

Spotlight
Deformable 2D Gaussian Splatting

Huibin Li, Chul Min Yeum

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Building upon the real-time rendering capability of 3D Gaussian Splatting (3DGS), 2D Gaussian Splatting (2DGS) achieves improved surface reconstruction and geometric fidelity for novel view synthesis through explicit planar Gaussian primitives. However, the smooth falloff inherent to Gaussian kernels fundamentally limits the reconstruction of high-frequency shape signals, causing over-smoothed edges and loss of fine geometric detail. Prior works have explored alternative kernel functions to address this limitation, yet through systematic evaluation across signal fitting tasks, we find that all existing kernels suffer from the Gibbs phenomenon — producing oscillatory artifacts near sharp discontinuities. This observation motivates a fundamentally different strategy: rather than replacing the kernel, we make it deformable. This study presents *Deformable 2D Gaussian Splatting*, which augments each Gaussian surfel with a learnable, monotonic coordinate remapping in its local tangent plane. With only a single free control point per axis (two extra parameters), the remapping enables asymmetric radial profiles, allowing each primitive to reliably capture sharp edges and irregular structures that symmetric kernels inherently cannot represent. The deformation operates on the 2D tangent plane of 2DGS, preserving the differentiable rasterization pipeline with negligible overhead, and is optimized end-to-end through rendering loss alone. Experiments on MipNeRF 360 and Tanks&Temples demonstrate that our method effectively suppresses Gibbs artifacts at sharp boundaries and achieves state-of-the-art performance among 2DGS-based approaches in PSNR, SSIM, and LPIPS.

Spotlight
Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes

Ethan Baron, Alan Amin, Andrew Wilson

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Phylogenetic inference plays a central role in understanding evolutionary relationships, with applications ranging from tracking pathogen spread to reconstructing the history of life. Conventionally, practitioners obtain posteriors over the phylogenetic tree of species using MCMC methods. However, such likelihood-based methods are only tractable for simple evolutionary models with restrictive assumptions. For more complex and realistic evolutionary models, conventional methods are prohibitively expensive, inaccurate, or even impossible. We instead advocate for a simulation-based inference approach, by using simulated data from an evolutionary model to train a neural network that predicts tree topologies conditioned on sequences. To accurately represent the complex posterior distributions over tree topologies that can arise, we present flexible models that iteratively generate trees using three natural paradigms: top-down, middle-out, and bottom-up. We use a discrete diffusion framework to train these models efficiently on large-scale simulated datasets of phylogenetic trees. For all three generative paradigms, our models fit the data substantially better than the previous state-of-the-art simulation-based method, Phyloformer 2, and obtain more accurate posteriors on real datasets. Finally, our models outperform misspecified conventional methods on data following complex evolutionary processes.

Spotlight
Deep Barycentric Regression for Optimal Transport Map Estimation and its Statistical Optimality

Kunwoong Kim, Insung Kong, Yongdai Kim

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The optimal transport (OT) map provides a geometric transformation for aligning probability distributions and has become a useful tool in machine learning. However, existing estimators of the OT map still exhibit a gap between sharp statistical guarantees and practical parametric estimation based on stable training objectives. Theoretical estimators achieve minimax optimal convergence rates, but they are typically nonparametric and can incur demanding implementation design or inference costs. Practical estimators are parametric and scalable, but their statistical guarantees remain underexplored, and their min-max, adversarial-like training objectives can be sensitive to optimization algorithms. We propose BROT (Barycentric Regression for OT), a simple two-step method that first computes the unregularized OT plan and then fits a deep neural network (DNN) to the induced barycentric targets by least-squares regression. Under standard regularity conditions, we prove that the DNN estimator of BROT attains the minimax convergence rate, when the ground-truth OT map is Lipschitz. Numerical studies on synthetic datasets and an image dataset show that BROT provides accurate map estimates, strong target distribution matching, and competitive transport costs, compared to existing estimation methods. Experiments on two downstream tasks, single-cell perturbation prediction and unsupervised domain adaptation, further suggest that the accurate estimation of BROT can translate into stronger task performance.

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Decomposing and Reshaping Scaling Laws through Token Learning Times

Pingjie Wang, zechenhu, Peiru Yang, Jingtao Han, Debing Zhang

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Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that deconstructs scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11\% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

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D-PACE: Dynamic Position-Aware Cross-Entropy for Parallel Speculative Drafting

Tianyu Wu, Yu Yao, Zhenting Qi, Han Zheng, Chengxi Zhang, Zhuohan Wang, Haoran Ma, Zichun Liao, Hima Lakkaraju, Ju Li, Yilun Du

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Speculative decoding accelerates LLM inference by having a small drafter propose tokens that a larger target model verifies in parallel. Current SOTA diffusion-based parallel drafters such as dFlash predict the full $B$-token block in one forward pass, allowing deeper drafters and higher accepted length. However, across the field, from autoregressive tree drafters to parallel block drafters, training losses use fixed per-position weights that do not adapt to the drafter's current bottleneck position. We derive per-position training weights directly from the expected accepted block length, so that each position's weight reflects its actual contribution to acceptance. The resulting loss, D-PACE (Dynamic Position-Aware Cross-Entropy), automatically identifies where the block's acceptance bottleneck lies and shifts training signal there as the drafter improves. D-PACE consistently improves both wall-clock speedup and accepted length across diverse benchmarks and positions as a drop-in replacement with negligible training overhead and requires no changes to the drafter architecture or inference pipeline, making it broadly applicable to general model architectures.

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CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Models

Chengqian Zhang, Yucheng Jin, Duo Zhang, Tiejun Li, Han Wang

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Crystal generative models mainly learn what stable crystals look like, with little explicit supervision for what makes them stable. We reveal a substantial representation gap between state-of-the-art crystal generative models and pretrained universal machine learning interatomic potentials (MLIPs) via energy probing, and show this gap can be closed by a simple training-time alignment. We propose Crystal REPresentation Alignment (CrystalREPA), a plug-and-play framework that aligns the atom-wise hidden states of generative encoders with frozen MLIP representations through an element-aware contrastive objective, transferring stability-aware atomistic priors with marginal training overhead and no additional inference cost. Across three generative frameworks, ten MLIP teachers, and two benchmark datasets, CrystalREPA consistently improves the thermodynamic stability, structural validity, and structural fidelity of generated crystals. Equally important, we find that an MLIP's transfer effectiveness is poorly predicted by its accuracy on standard leaderboards (e.g., Matbench Discovery) but strongly predicted by the distinguishability of its atom-wise representation space, yielding a practical, accuracy-independent criterion for selecting MLIP teachers for generative transfer.

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Cross-order Consensus Graph Matching

Yu Xie, Yiming Zhang, Xinyan Liang, Junqi Liu, Ming Li

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Graph matching aims to establish node correspondences while preserving both unary appearance compatibility and pairwise structural consistency. Recent deep graph matching methods have achieved strong empirical performance, but many of them either compress edge information into node embeddings before matching or rely on surrogate optimization signals for quadratic objectives. These design choices can weaken structural discrimination and may lead to optimization directions that are not aligned with the relaxed quadratic assignment problem (QAP). We propose Cross-order Consensus Graph Matching (CCGM), a framework that explicitly couples first-order node assignment and second-order edge assignment. CCGM constructs line graphs to convert edge matching into a node matching problem, learns node and edge affinities in parallel, and refines them through a Cross-order Consensus Solver motivated by the exact gradient of the factorized relaxed QAP. We further introduce Cross-order Alignment Regularization to encourage agreement between node-induced edge assignments and edge-induced node support during training. Experiments on standard visual graph matching benchmarks show that CCGM consistently improves matching accuracy over competitive baselines.

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Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Models

Jinlin Lai, Charles Margossian, Daniel Sheldon

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Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing out the latent variables. For LGMs with a non-Gaussian likelihood, exact marginalization is not possible and a popular approach is to do approximate marginalization with an integrated Laplace approximation (ILA). Using ILA produces an approximate posterior which, in some settings, can differ significantly from the correct posterior, which impacts downstream applications. We propose an importance sampling scheme to correct the error introduced by ILA. By increasing the number of samples in importance sampling, the posterior with ILA converges to the correct posterior. This idea is realized with various techniques, including pseudo-marginalization, quasi-Monte Carlo and randomized quasi-Monte Carlo. We implement our methods in an automatic differentiation framework to support gradient-based algorithms when doing inference on the hyperparameters. For the latter, we specifically consider the use of Hamiltonian Monte Carlo. We demonstrate the benefits of reduced error in various applied models.

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Continuous Latent Diffusion Language Model

Hongcan Guo, Qinyu Zhao, Yian Zhao, Shen Nie, Rui Zhu, Qiushan Guo, Feng Wang, Tao Yang, Hengshuang Zhao, Guoqiang Wei, Yan Zeng

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Autoregressive language models have achieved remarkable success in text modeling, but recent work increasingly challenges the fixed left-to-right generation order. However, existing non-autoregressive alternatives such as discrete diffusion, still struggle to jointly deliver efficiency, scalable representation learning, and global semantic modeling. We propose Cola DLM, a hierarchical continuous latent diffusion language model that learns a stable Text VAE, models a global semantic prior in latent space with a block-causal DiT, and decodes text conditionally. Theoretically, under a unified Markov-path formulation, the diffusion operates latent prior transport rather than token-level observation recovery, thereby decoupling global semantic organization from local token realization. Empirically, Cola DLM exhibits strong scaling behavior for text generation across four research questions, eight benchmarks, strictly matched $\sim$2B-parameter AR and LLaDA baselines, and scaling curves up to $\sim$2000 EFLOPs. Meanwhile, we also explore encoding text in the same continuous latent space as images, providing a feasible path toward unified discrete-continuous generative modeling. Our code will be released.

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Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

Kartik Tandon, Julian Gould, Tanishq Bhatia, Francesca Dominici, Alejandro Ribeiro, Claudio Battiloro

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Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified learning theory for these settings has been lacking. To start addressing this gap, we introduce a novel convolutional learning framework for possibly infinite-dimensional signals supported on a manifold. Namely, we use the connection Laplacian associated with a Hilbert bundle as a convolutional operator, and we derive filters and neural networks, dubbed as \textit{HilbNets}. We make HilbNets and, more generally, the convolution operation, implementable via a two-stage sampling procedure. First, we show that sampling the manifold induces a Hilbert Cellular Sheaf, a generalized graph structure with Hilbert feature spaces and edge-wise coupling rules, and we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin \& Niyogi \cite{BELKIN20081289} convergence result for the graph Laplacian to the manifold Laplacian, a theoretical cornerstone of geometric learning methods. Second, we discretize the signals and prove that the discretized (implementable) HilbNets converge to the underlying continuous architectures and are transferable across different samplings of the same bundle, providing consistency for learning. Finally, we validate our framework on synthetic and real-world tasks. Overall, our results broaden the scope of geometric learning as a whole by lifting classical Laplacian-based frameworks to settings where the signal at each point lives in its own Hilbert space.

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Complexity-Aware LoRA Aggregation for Modality-Heterogeneous Federated Person Re-identification

Kunyang Lv, Wenke Huang, Wenwen He, Bin Yang, Bo Du, Mang Ye

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A unified cross-modal person re-identification targets robust cross-modal retrieval with queries from diverse modalities like visible, infrared, and text.Such framework requires multi-modal data and centralized training, raising data costs and privacy risks. Hence, we propose a modality-heterogeneous federated ReID task to learn a unified cross-modal framework from clients with different cross-modal data.However, it faces two challenges.First, varying inter-modality complexity across tasks leads to different retrieval patterns and parameter space. Second, different intra-modality complexity results in imbalanced contributions when merging LoRA modules.Existing federated learning methods use uniform merging and transmit full models, which hinders cross-modal knowledge integration and increases communication overhead. To address these issues, we adopt Low-Rank Adaptation (LoRA), a lightweight module for fine-tuning large models through low-rank updates, enabling clients to send compact parameters.On top of LoRA, we develop MIRAGE (Modality-heterogeneous Intelligent federated ReID Aggregation with Global Efficiency), adapting aggregation to inter- and intra-modality complexity.When merging visible LoRA, MIRAGE selects key ranks to protect retrieval patterns while retaining shared ranks for common ability.As for infrared and text LoRA, it reduces conflicts with an adaptive pruning method. In both strategies, task complexity is incorporated into aggregation to balance contributions. Experiments on cross-modal retrieval tasks demonstrate the superiority of MIRAGE.The code and dataset will be publicly released.

Spotlight