NeurIPS 2026 Papers

Would experience designing faster GPU kernels also help close in on a long-standing open mathematical conjecture? Large Language Models (LLMs) integrated into evolutionary search have recently produced state-of-the-art solutions on optimization tasks, including open mathematical conjectures, GPU kernel design, scientific law discovery, and combinatorial puzzles. To achieve this, prior work applied search scaffolds to one target task at a time, so every new problem is approached from scratch and the experience accumulated during search is discarded once the model finishes its attempt. This leaves the capability of iteratively evolving a solution (\textit{e.g.}, knowing which part to mutate and how, deciding when to backtrack) entirely in the scaffold rather than in the model itself. Whether the model itself could acquire this capability and reuse it across different tasks has been largely unexamined. To address this, we introduce \textbf{\textsc{Evolution Fine-Tuning} (EFT)}, a mid-training paradigm that teaches LLMs to evolve solutions across tasks by converting evolutionary search trajectories into supervision. We construct \datasetName, a 156K-trajectory dataset spanning 10 domains and 371 optimization tasks, and fine-tune open-source LLMs from 2B to 9B parameters. Empirically, EFT confers cross-task generalization: across 22 held-out tasks, our models surpass their base counterparts by 10.22\% on average. Furthermore, when paired with test-time RL, our model match state-of-the-art performance on two circle-packing tasks and outperforms its base-model counterparts on the Erdős minimum-overlap problem. EFT thus serves as a ``practice phase'' for general-purpose discovery agents that doesn't solve new problems from scratch.

Time series foundation models (TSFMs) are increasingly used for probabilistic forecasting across diverse domains, yet the reliability of their uncertainty estimates remains poorly understood. In this work, we study uncertainty calibration in probabilistic TSFMs from a broader methodological and empirical perspective. We introduce a taxonomy of how TSFMs represent predictive uncertainty and develop a fine-grained evaluation framework for calibration in multi-horizon forecasting that distinguishes pooled, horizon-wise, and stronger conditional notions of calibration. Using this framework, we conduct a comprehensive empirical evaluation of popular TSFMs across diverse datasets and show that current models exhibit distinct and systematic patterns of miscalibration that standard metrics often obscure. We further analyze common post-hoc recalibration methods and characterize which forms of calibration they can improve and which tend to persist. Our results provide practical guidance for evaluating and improving uncertainty calibration in TSFMs and highlight important limitations of current practice.

Continual fine-tuning is essential for large language models (LLMs) to dynamically adapt to real-world environments, yet it inevitably suffers from catastrophic forgetting, particularly the performance degradation of previous tasks and LLMs' general-purpose knowledge. Although existing methods, such as orthogonal gradient projection, mitigate the forgetting across various fine-tuning tasks, they fundamentally fail to preserve pre-training LLMs' inherent general-purpose knowledge because the original data and gradients of off-the-shelf pre-training LLMs required by these methods are strictly unknown and highly diverse. To bridge this critical gap, we propose EoupCT, a novel framework designed to Estimate and Orthogonalize Unknown Pre-training gradients for Continual LLM fine-Tuning. Specifically, EoupCT estimates pre-training gradients by dynamically generating pseudo data that is most susceptible to forgetting for new tasks through a learnable soft prompt equipped with Gumbel-Softmax relaxation. Furthermore, we formulate a multi-objective optimization problem and introduce a first-order efficient Pareto optimizer that jointly optimizes LLM parameters and the soft prompt, rigorously enforcing orthogonality between new task updates and the estimated pre-training gradients. Extensive experiments across multiple LLMs demonstrate that EoupCT effectively preserves both task-specific proficiency and inherent general-purpose knowledge, successfully mitigating the catastrophic forgetting.

Gaze following requires both scene understanding and gaze reasoning to localize the gaze target of an in-scene person. Recently, vision foundation models (VFMs) have demonstrated strong performance on this task, enabling simpler architectures while outperforming prior methods. However, we observe a key limitation of VFM-based approaches: while VFMs substantially improve scene understanding, they contribute little to gaze reasoning. As a result, existing methods often rely on semantically salient objects rather than true gaze cues, leading to degraded performance when targets are not salient. To address this, we propose a novel training mechanism to enhance gaze reasoning in VFMs for gaze following. Our method includes: (1) a head-conditioned local LoRA, which enables localized adaptation to preserve scene token learning while improving head token learning for gaze reasoning; and (2) an out-of-cone penalty, which injects gaze cues into head tokens while aligning them with scene tokens. Experiments on the GazeFollow and VAT datasets demonstrate that our method achieves state-of-the-art performance, with particularly strong improvements when gaze targets are not semantically salient. Our findings offer valuable insights for advancing future gaze following research. We will release the code once the paper is accepted.

Foundation models trained on large unlabeled corpora develop emergent capabilities — tasks that go beyond the training objective. We extend this paradigm to multimodal biology with Bonbon, a foundation model for molecular interactions trained on approximately 3.2 trillion tokens of paired protein-ligand sequences. From a single self-supervised objective, Bonbon exhibits four zero-shot emergent capabilities at hierarchical levels of resolution — functional (mechanism of action), residue (binding site localization, including orthosteric/allosteric discrimination), bond (covalent versus non-covalent engagement), and atom (active moiety identification at single-bond resolution). All four capabilities generalize to out-of-distribution proteins. Bonbon was trained on protein-ligand sequences alone, without any task-specific supervision and without structural coordinates. We conducted controlled scaling experiments across four model scales from 42M to 1.6B parameters; every capability evaluated shows a sharp jump at the largest scale on continuous metrics, even as pretraining loss decreases smoothly. This demonstrates that loss-based scaling laws alone are insufficient to predict when zero-shot emergent capabilities become available. The capabilities reported here emerge after training at a 1:2,000 parameter-to-token ratio to accommodate the sparsity of paired biological interaction data. The same frozen representations achieve state-of-the-art binding and affinity predictions at five orders of magnitude greater speed than structure-based methods. In prospective wet-lab validation, Bonbon achieves a 70% hit rate on de novo compounds, discovering novel chemotypes not previously documented as inhibitors for those targets. All of the tested compounds had less than 60% structural similarity to molecules in the training corpus.

Tabular foundation models achieve strong accuracy on choice prediction tasks, but their predictions often violate the economic logic those tasks require: raising a price can increase predicted demand, implied willingness-to-pay estimates are frequently negative or implausible, and unavailable alternatives receive nonzero probability. We propose a two-stage adapter that takes a foundation model's predicted choice probabilities as a precomputed feature and embeds them inside a multinomial logit's utility. In Stage 1, we fit the multinomial logit's structural coefficients by maximum likelihood with sign constraints; in Stage 2, we freeze those coefficients and fit a small neural correction operating on the foundation model's predictions. We prove that this composition exactly preserves the multinomial logit's marginal rate of substitution, so analytically computable value-of-time becomes a mathematical guarantee rather than an empirical accident. Across three datasets and two foundation models, the adapter gains 6.4 percentage points (pp) of test accuracy on average over the multinomial logit and up to 12.8 pp, maintains 100\% cost monotonicity, and produces values of time within the published transportation-economics range on the transportation datasets. Performance degrades gracefully under foundation-model context restriction, retaining at least 6 pp of accuracy gain even at 10\% of the original foundation-model context.

Speculative decoding accelerates LLM inference but suffers from performance degradation when target models are fine-tuned for specific domains. A naive solution is to retrain draft models for every target model, which is costly and inefficient. To address this, we introduce a practical parameter- and data-efficient framework named Efficient Draft Adaptation, abbreviated as EDA, for efficiently adapting draft models. EDA introduces three innovations: (1) a decoupled architecture that utilizes shared and private components to model the shared and target-specific output distributions separately, enabling parameter-efficient adaptation by updating only the lightweight private component; (2) a data regeneration strategy that utilizes the fine-tuned target model to regenerate training data, thereby improving the alignment between training and speculative decoding, leading to higher average acceptance length; (3) a sample selection mechanism that prioritizes high-value data for efficient adaptation. Our experiments show that EDA effectively restores speculative performance on fine-tuned models, achieving superior average acceptance lengths with significantly reduced training costs compared to full retraining. Code will be released upon acceptance.

Large language model (LLM) inference serving is undergoing rapid growth and large-scale deployment, motivating us to rethink how the inference process itself can be leveraged to enable efficient task-specific LLM adaptation. In this paper, we propose a forward-only approach for efficient LLM adaptation with forward-only passes in LLM inference serving. We exploit the angle concentration of activations induced by each singular value decomposition (SVD) component to measure its contribution—_dispersed_ or _concentrated_—to the angle concentration of the hidden states. Based on this, our forward-only search then efficiently identifies the weight matrix with the highest dispersion that merits rank reduction. We then selectively remove the higher-order components and retain the lower-order components in SVD. Empirical results across diverse datasets demonstrate the competitive accuracy of our forward-only approach, while theoretical analysis shows lower peak memory and greater speedup than the gradient-based approach, and greater speedup than the exhaustive search approach. The extended experiments further present the robustness and generalization of our forward-only approach to various LLMs with up to 57B parameters. The code is included in the supplementary material.

Collaboratively fine-tuning (FT) large language models (LLMs) over heterogeneous mobile devices fosters immense potential applications of personalized intelligence. However, such a vision faces critical system challenges. Existing federated LLM fine-tuning approaches remain limited by prohibitive on-device resource overhead, straggler-prone synchronous aggregation, and the assumption of a unified pretrained backbone across heterogeneous devices. In this paper, we propose EC-MobiLLM, a novel design for efficient collaborative LLM fine-tuning across heterogeneous mobile devices and heterogeneous backbones. EC-MobiLLM adopts a server-assisted side-tuning paradigm to minimize on-device overhead and pioneers non-blocking asynchronous collaboration to accelerate training. Moreover, EC-MobiLLM introduces adaptive feature alignment to support collaboration across heterogeneous backbones, aligning with practical needs in real-world deployments. Extensive experimental results demonstrate that EC-MobiLLM can maintain robust fine-tuning performance while achieving extremely low on-device memory, with at least 95.2\% reduction in computation overhead, 93.2\% reduction in communication costs and $5.1\times$ faster convergence compared to existing methods, validating its efficacy for practical LLM adaptation over heterogeneous mobile devices.

Reinforcement learning (RL) has become a key training step for improving mathematical reasoning in large language models (LLMs), but it often has high GPU memory usage, which makes it hard to use in settings with limited resources. To reduce these issues, we propose Evolution Strategies with Sharpness-Aware Maximization (ESSAM), a full parameter fine-tuning framework that tightly combines the zeroth-order search in parameter space from Evolution Strategies (ES) with the Sharpness-Aware Maximization (SAM) to improve generalization. We conduct fine-tuning experiments on the mainstream mathematica reasoning task GSM8K. The results show that ESSAM achieves an average accuracy of 78.27\% across all models and its overall performance is comparable to RL methods. It surpasses classic RL algorithm PPO with an accuracy of 77.72\% and is comparable to GRPO with an accuracy of 78.34\%, and even surpassing them on some models. Further generalization experiments show that the models trained with ESSAM exhibit stronger generalization ability. Their average performance achieves the best results on 5 out of 6 datasets, indicating that ESSAM can effectively improve the generalization performance of fine-tuned models. In terms of GPU memory usage, ESSAM reduces the average GPU memory usage by $18\times$ compared to PPO and by $10\times$ compared to GRPO, achieving an extremely low GPU memory usage. In addition, we design an accelerated variant of ESSAM, which achieves nearly a twofold speedup while maintaining the same GPU memory usage as ESSAM, and attains an average accuracy of 78.02\% across all models, outperforming PPO. Code: https://anonymous.4open.science/r/ESSAM-3F4F/

Foundation models for EEG analysis are still in their infancy, limited by two key challenges: (1) variability across datasets caused by differences in recording devices and electrode configurations, and (2) the low signal-to-noise ratio (SNR) of EEG, where neural activity is often buried under artifacts and non-brain sources. To address these challenges, we present \textit{EEG-X}, a device-agnostic and noise-robust foundation model for EEG representation learning. EEG-X introduces a location-based channel embedding that enables robust transfer across heterogeneous EEG devices and electrode layouts. To improve robustness against noise, EEG-X employs a novel noise-aware masking-reconstruction strategy that reconstructs artifact-cleaned signals rather than raw noisy EEG and introduces a novel Dictionary-based Convolutional Transformation (DiCT) that improves reconstruction-based pretraining by comparing signals in a structured feature space instead of directly in the raw signal space. Experiments across datasets collected from diverse EEG devices show that EEG-X consistently outperforms state-of-the-art methods across multiple downstream tasks and demonstrates strong cross-domain generalization when pretraining and downstream datasets differ in electrode layouts and recording configurations paving the way towards foundation models. The models and code are available at :https://anonymous.4open.science/r/EEG-X-CEDE/README.md

Adapting Multimodal Large Language Models (MLLMs) to specialized and diverse downstream applications necessitates fine-tuning, typically through parameter-efficient methods such as *Low-Rank Adaptation* (LoRA). However, fine-tuning MLLMs severely degrades pre-trained upstream capabilities, a phenomenon known as *catastrophic forgetting*. Existing Methods primarily rely on parameter pruning to strike a balance between the downstream adaptation and upstream knowledge retention. Empirical analysis indicates that these methods are subject to *parameter space entanglement*, wherein the imposition of downstream adaptation and upstream retention within a unified parameter space results in suboptimal outcomes for both objectives. To address this, we introduce Dual-Pronged LoRA, a novel fine-tuning framework for MLLMs featuring two components. (1) *Task-Decoupled Contextual Routing* (TDCR) makes the first attempt to explicitly decouple tasks by modeling a downstream contextual support region. It adaptively activates the LoRA branch exclusively for downstream-relevant inputs and bypasses it otherwise, thereby preventing downstream adaptation from interfering with pre-trained knowledge. (2) *Downstream-Performance-Oriented Rank Sculpting* (DPO-RS) maximizes downstream adaptation performance by dynamically sculpting ranks via gradient energy. It effectively strengthens critical layers while compressing redundant ones and is theoretically grounded in the minimization of information loss. Extensive experimental results indicate that Dual-Pronged LoRA achieves near-zero forgetting while attaining new state-of-the-art downstream performance.

Zeroth-order (ZO) optimization enables memory-efficient fine-tuning of large language models (LLMs) using only forward passes, but it remains unclear how useful adaptation is distributed across layers. In this work, we reveal a surprising phenomenon: ZO fine-tuning is sharply dominated by a single decoding layer. Across multiple LLM families and downstream tasks, fine-tuning this dominant layer alone consistently matches or even exceeds full-model ZO fine-tuning. We further show that the dominant layer is task-agnostic but model-specific, and can be identified before training through a simple inference-only analysis of activation outliers. Specifically, the dominant layer consistently aligns with the first activation-outlier layer in the pre-trained model. To explain this phenomenon, we analyze how perturbation effects propagate under ZO optimization. We find that the dominant layer combines two key properties: high perturbation sensitivity and early placement in the residual stream, allowing perturbation-induced effects to propagate and accumulate through remaining subsequent decoding layers. As a result, this layer produces disproportionately strong and stable optimization signals under forward-only updates. Extensive experiments on LLaMA2-7B and Qwen3-8B across nine benchmarks show that dominant-layer ZO fine-tuning improves average performance over full-model MeZO and LoRA-based ZO fine-tuning while achieving up to 4.52$\times$ training speedup.

Vision foundation models trained on discretely sampled images achieve strong performance on classification benchmarks, yet whether their representations encode the continuous processes underlying their training data remains unclear. This question is especially pertinent in computational pathology, where we posit that models whose latent representations implicitly capture continuous disease progression may better reflect underlying biology, support more robust generalization, and enable quantitative analyses of features associated with disease transitions. Using diffusion pseudotime, a method developed to infer developmental trajectories from single-cell transcriptomics, we probe whether foundation models organize disease states along coherent progression directions in representation space. Across four cancer progressions and six models, we find that all pathology-specific models recover trajectory orderings significantly exceeding null baselines, with vision-only models achieving the highest fidelities ($\tau > 0.78$ on CRC-Serrated). Model rankings by trajectory fidelity on reference diseases strongly predict few-shot classification performance on held-out diseases ($\rho = 0.92$), and exploratory analysis shows cell-type composition varies smoothly along inferred trajectories in patterns consistent with known stromal remodeling. Together, these results demonstrate that vision foundation models can implicitly learn to represent continuous processes from independent static observations, and that trajectory fidelity provides a complementary measure of representation quality beyond downstream performance. While demonstrated in pathology, this framework could be applied to other domains where continuous processes are observed through static snapshots.

Foundation models for time-dependent partial differential equations (PDEs) are trained on large and diverse collections of physical systems and can generalize effectively to new downstream tasks. After fine-tuning on only a few trajectories from a target domain, they often achieve strong accuracy in low-data regimes. However, these models are typically large and computationally intensive, limiting their usefulness as fast surrogates for numerical solvers. We propose Teacher Rollout Extension (TREX), a knowledge distillation framework that transfers the predictive capability of a pretrained foundation model into a compact and efficient student. Starting from a fine-tuned teacher, TREX augments limited downstream data by generating long synthetic trajectories through teacher rollouts with periodic noise injection. This procedure samples from the teacher-induced rollout distribution without requiring explicit knowledge of the initial-condition distribution, while exposing the student to long-horizon states and local recovery behavior around states encountered during autoregressive prediction. The student can further incorporate task-specific inductive biases, such as equivariance, that the teacher does not necessarily enforce. We evaluate TREX on multiple PDE benchmarks. The resulting students match or even surpass the teacher’s accuracy while reducing the number of parameters by several orders of magnitude and achieving more than an order-of-magnitude speedup in inference.

Graph Foundation Models (GFMs) have attracted growing attention for their ability to model multi-domain graphs universally and generalize to unseen downstream tasks. However, existing GFMs typically rely on a single domain-invariant representation space, which inevitably blurs two fundamental connectivity patterns, \emph{homophily} and \emph{heterophily}, that govern how nodes relate across domains. Additionally, hard-partitioning the graph into disjoint subgraphs discards edges that are essential for self-supervised pre-training. In this work, we introduce $\underline{\text{HHGFM}}$, a $\underline{\text{H}}$omophilic and $\underline{\text{H}}$eterophilic Pattern-Disentangled $\underline{\text{G}}$raph $\underline{\text{F}}$oundation $\underline{\text{M}}$odel that encodes homophily and heterophily separately while keeping the original edge structure intact. Specifically, we propose a node-level soft disentanglement mechanism that estimates each neighbor's homophilic and heterophilic contributions and uses them as edge weights, thereby preserving the original graph structure. Low-pass and high-pass filters then serve as dual backbones to align homophilic and heterophilic patterns separately, supported by our generalization analysis. Extensive experiments on a range of graph datasets validate the effectiveness of our method.

Video diffusion alignment has been heavily reliant on scalar rewards. These rewards are typically derived from learned reward models in human preference datasets, requiring additional training and extensive collection. Moreover, scalar rewards provide coarse, global supervision, offering limited prompt-generation mismatch credit assignment and making models prone to reward exploitation and unstable optimization. We propose \textbf{Diffusion-DRF}, a free, rich, and differentiable reward framework for video diffusion fine-tuning. Diffusion-DRF employs a frozen, off-the-shelf Vision-Language Model (VLM) as the critic, eliminating the need for reward model training. Instead of relying on a single scalar reward, it decomposes each user prompt into multi-dimensional questions with freeform dense VQA explanation queries, yielding information-rich feedback. By direct differentiable optimization over this rich feedback, Diffusion-DRF achieves stable reward-based tuning without preference datasets collection. Diffusion-DRF achieves significant gains both quantitatively and qualitatively, outperforming state-of-the-art Flow-GRPO by 4.74 points in overall performance on unseen VBench-2.0.

Distillation and Reinforcement Learning (RL) fine-tuning are the primary pillars of diffusion post-training. While traditionally studied in isolation, the interaction between these phases remains poorly understood, and in particular how fine-tuning impacts the generative quality of distilled models. We introduce Rewarded Moment Matching Distillation (RMMD), a novel framework that simultaneously distills diffusion models and maximizes a reward function. RMMD preserves the high-fidelity "naturalness" characteristic of advanced distillation (e.g., 8-step Moment Matching) by adapting the sampling loop for on-policy training and repurposing the distillation loss as a proxy for integral KL regularization. By evaluating the FID-Reward Pareto fronts on ImageNet, we demonstrate that RMMD achieves superior trade-offs compared to single-step baselines (DI++) and multi-step competitors (DRaFT, HyperNoise). Finally, we apply RMMD to GenCast, a state-of-the-art weather forecasting model, to distill it while optimizing the Continuous Ranked Probability Score (CRPS) metric. The resulting distilled model achieves a 7.5x speedup while outperforming the teacher model on 93% of target weather variables, and being better calibrated. This proves that RMMD scales to complex, high-dimensional scientific domains.

Diffusion-based foundation models for crystal generation have become competent priors over the manifold of plausible materials, but turning that prior into generation of promising candidates requires targeting stability while balancing several conflicting properties at once. Fine-tuning is expensive and produces a new model for every new objective, while differentiable guidance is not applicable to many real-world rewards. We instead adapt these models at \emph{inference time} using Diffusion Tree Search (DTS), a Monte Carlo tree search procedure over the denoising trajectory. We make two technical contributions on top of DTS that are particularly relevant for AI-for-science applications. First, we show how to use existing property-conditional foundation models (e.g., classifier-free guidance variants of MatterGen) as guided proposals inside DTS, with importance-corrected backups and selection that keep the unconditional base model as the target distribution. Second, we extend DTS to multi-objective sampling by maintaining per-objective soft value estimates and selecting expansions through a sampled scalarization, so a single search produces samples spanning a Pareto front while sharing computation across preferences. We instantiate both adaptations on de novo crystal generation: single-objective stability search with different underlying models, conditional generation of crystals belonging to rare space groups, and a multi-objective tasks using a pretrained conditional model. Across these, DTS-based inference-time adaptation improves stability rates and Pareto-front quality without modifying the base models.