NeurIPS 2026 Papers

We study compression of serialized 3D point transformers for efficient point cloud segmentation. Starting from LitePT-S, we derive \textbf{TrimPT}, a compact student that reduces channel width and stage-3 attention depth while preserving the full 1024-point attention window. TrimPT uses 5.84\,M parameters and 12.95\,GFLOPs, giving $2.18\times$ fewer parameters and $1.96\times$ fewer FLOPs than LitePT-S. To improve the compressed student, we introduce \textbf{Stage-wise Relational Feature Distillation (SRFD)}, a training-only objective that matches pairwise cosine-similarity matrices between teacher and student features at the compressed attention stages. This explicitly regularizes teacher--student affinity mismatch and adds no inference-time cost because the teacher and projection heads are discarded after training. On ScanNet semantic segmentation, the resulting \textbf{TopoPT} reaches 76.6\% mIoU with a 5.84\,M parameter inference footprint, improving over TrimPT without SRFD and matching the official LitePT-S result with substantially fewer inference-time parameters and FLOPs. TopoPT also obtains 63.9\% mAP$_{50}$ on ScanNet instance segmentation, 33.0\% mAP$_{50}$ on ScanNet200, and 81.4\% mIoU on nuScenes, suggesting that stage-wise relational distillation is a useful training-time regularizer for lightweight 3D segmentation backbones. Code and models are available at: \url{https://github.com/anon-push/TopoPT}

Recent advances in 3D reconstruction have progressed from per-scene optimization to feed-forward inference, and semantic scene understanding has followed suit—yet existing methods remain confined to object-centric perception, neglecting spatial relations between objects. We introduce \emph{3D spatial relation segmentation}, a task that requires models to identify a target object satisfying a given spatial relation with respect to a subject, consistently across multiple views. To this end, we propose RelationVGGT, a novel feed-forward framework that integrates semantic features from a visual foundation model with geometry-aware representations from a 3D geometry foundation model and leverages a relation transformer for subject-conditioned, cross-view relation prediction—requiring neither per-scene optimization nor known camera poses. We additionally provide a fully automated annotation pipeline built on ScanNet++ with VLMs and LLMs, enabling scalable training data generation for this new task.

In recent years, large language models (LLMs) have demonstrated remarkable capability to generalize across diverse natural language processing tasks, inspiring the development of graph foundation models (GFMs) for large-scale pre-training. However, unlike language models with explicit token units, graphs lack a well-defined unit for generalization, making it challenging to design effective pre-training strategies. In this work, we propose REEF, a novel GFM framework that leverages relation tokens as the fundamental units. We construct a vocabulary of relation tokens to encode relational information within graphs. To accommodate diverse relations, we introduce two hypernetworks that adaptively generate the parameters of aggregators and classifiers in graph neural networks based on relation tokens. In addition, we design another hypernetwork to construct dataset-specific projectors and incorporate a dataset-level feature bias into the initial node representations, enhancing flexibility across different datasets with the same relation. Extensive experiments demonstrate that REEF consistently outperforms existing methods in both pre-training and transfer learning, highlighting its potential as a general-purpose graph foundation model. Our code is publicly available at https://anonymous.4open.science/r/REEF-16CF/.

Open-vocabulary 3D scene understanding provides an important interface for querying and interacting with reconstructed scenes through natural language. Although recent 3DGS methods have enabled text-driven object selection and open-vocabulary segmentation, they still struggle with compositional queries involving attributes, spatial relations, and part-whole relations. Most existing approaches learn per-Gaussian or per-cluster language features, construct query-conditioned referring fields, or perform spatial reasoning only at inference time, but they do not organize the scene itself into a reusable relation-aware representation. As a result, object relations are not explicitly stored as typed and confidence-aware 3D structures, limiting compositional reasoning and multi-hop querying. To address this issue, we propose RelGS, a relation-aware 3D Gaussian Splatting framework for open-vocabulary scene understanding. RelGS learns semantic and instance embeddings for Gaussians under multi-view supervision, groups them into cross-view consistent 3D semantic nodes, and enriches each node with structured attributes verified by reverse CLIP consistency. It further constructs a confidence-weighted relation graph, where 3D spatial cues propose candidate relations and an LLM verifies their semantic plausibility. At query time, RelGS combines attribute matching, CLIP retrieval, and graph traversal to localize the target object. Extensive experiments demonstrate strong performance on word-level selection, sentence-level referring segmentation, multi-hop relational queries, and point-level semantic segmentation.

We present a new class of efficient attention mechanisms applying universal 3D Relative Positional Encoding (RPE) methods given by arbitrary integrable modulation functions $f$. They lead to the new class of 3D-Transformer models, called *RelFlexformers*, flexibly integrating those RPEs, and characterized by the $O(L \log L)$ time complexity of the attention computation for the $L$-length input sequences. RelFlexformers builds on the theory of the Non-Uniform Fourier Transform (NU-FFT), naturally generalizing several existing efficient RPE-attention methods from structured settings with tokens homogeneously embedded in unweighted grids into general non-structured heterogeneous scenarios, where tokens' positions are arbitrarily distributed in the corresponding 3D spaces. As such, RelFlexformers can be applied in particular to model point clouds. Our extensive empirical evaluation on a large portfolio of 3D datasets confirms quality improvements provided by the NU-FFT-driven attention modulation techniques in the RelFlexformers.

Relational learning is a challenging problem that has motivated a wide range of approaches, including graph-based models (e.g., graph neural networks, graph transformers), tabular methods (e.g., tabular foundation models), and sequence-based approaches (e.g., large language models), each with its own advantages and limitations. We propose *RelAgent*, an LLM-based autonomous data scientist for relational learning, which operates in two phases. In the *search phase*, an LLM agent uses database, validation, and evaluation workspace tools to construct SQL feature programs and select a predictive model. In the *inference phase*, the resulting program is executed without further LLM calls. The final predictor consists of SQL queries and a classical model, enabling fast, deterministic, and intrinsically interpretable predictions: features are human-readable queries, and predictions depend only on the resulting query-defined feature map, enabling scalable deployment using standard database systems.

Inference-time methods that generate, aggregate, and prune multiple parallel reasoning traces have emerged as a powerful paradigm for steering large language models, yet we lack a principled understanding of their accuracy--cost tradeoffs. We develop such an understanding for multi-particle methods, which maintain multiple partial chains of thought and use a process reward model (PRM) to adaptively score, prune, and replicate them. We focus on Sequential Monte Carlo (SMC), the simplest and most canonical such method. Despite SMC's long history in statistics and recent adoption for steering language and diffusion models, non-asymptotic guarantees have remained elusive. We provide (1) a simple, user-friendly analysis identifying two natural criteria which suffice for non-asymptotic convergence of SMC; (2) a simple modification of SMC achieving stronger, horizon-free guarantees when the PRM is near-perfect; and (3) a fundamental limit faced by all myopic multi-particle methods in the presence of PRM approximation errors. Empirically, we find that our criteria effectively predict the sampling error of SMC though not necessarily its final accuracy, paving the way for future work incorporating theoretical perspectives beyond sampling.

Reinforcement Learning has significantly advanced the reasoning capabilities of Multimodal Large Language Models (MLLMs), yet the resulting policies remain brittle against real-world visual degradations such as blur, compression artifacts, and low-resolution scans. Prior robustness techniques from vision and deep RL rely on static data augmentation or value-based regularization, neither of which transfers cleanly to critic-free RL fine-tuning of autoregressive MLLMs. Reinforcing reasoning against such corruptions is non-trivial: naively injecting degraded views during rollout induces reward poisoning, where perceptual occlusions trigger hallucinated trajectories and destabilize optimization. We propose ROMA, an RL fine-tuning framework that modifies the optimization dynamics to reinforce reasoning against visual degradation while preserving clean-input performance. A dual-forward-pass strategy uses teacher forcing to evaluate corrupted views against clean-image trajectories, avoiding new rollouts on degraded inputs. For distributional consistency, we apply a token-level surrogate KL penalty against the worst-case augmentation; to prevent policy collapse under regularization, an auxiliary policy gradient loss anchored to clean-image advantages preserves a reliable reward signal; and to avoid systematically incorrect invariance, correctness-conditioned regularization restricts enforcement to successful trajectories. On Qwen3-VL 4B/8B across seven multimodal reasoning benchmarks, our method improves robustness by +2.4% on seen and +2.3% on unseen corruptions over GRPO while matching clean accuracy.

The success of deep learning in medical image analysis is often hindered by the long-tail distribution of disease cases, where rare or early-stage tumors are critically under-represented. While controllable synthesis offers a potential solution, existing methods suffer from a \textit{specification bottleneck}, as low-dimensional signals like text or binary masks fail to capture complex textures and morphological variations. In this paper, we propose an exemplar-driven synthesis framework that utilizes real tumor samples as high-dimensional templates to enable precise, case-specific generation. To the best of our knowledge, this is the first work to introduce reinforcement learning (RL) into the field of 3D medical image generation, called **MedGRPO**. We formulate the unpaired tumor synthesis task as a constrained trajectory optimization problem and leverage Flow-GRPO to find an optimal generation path. By designing a multi-objective reward system encompassing texture, shape, and semantic consistency, our model effectively balances pathological fidelity with anatomical coherence without requiring paired supervision. Rigorous evaluations across four major tumor types and the external AbdomenAtlas 2.0 dataset demonstrate that our method produces high-fidelity synthetic data that significantly enhances the performance of downstream diagnostic models.

Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has begun to frame PDE solving as a code-generation task for large language models (LLMs), yet existing approaches operate primarily at inference time: relying on prompting, debugging, self-refinement, and test-time scaling rather than adapting the model itself. In parallel, reinforcement learning with verifiable rewards has emerged as a powerful post-training paradigm for code and math reasoning, but its verifiers are typically binary: a compiler runs, or a test passes. Such signals discard the graded structure of scientific correctness, where two solvers may both execute and yet differ in solution accuracy by orders of magnitude. In this work, we introduce RLVP: Reinforcement Learning with Verifiable Physics, an RL post-training framework for multi-PDE solver code generation.RLVP addresses this verifiability gap with a hybrid verifier: hard program-validity checks ensure executability, while continuous physics rewards score function-space accuracy and PDE-residual consistency. A single policy is post-trained across diverse PDE families spanning hyperbolic, parabolic, elliptic, and incompressible-flow systems. RLVP improves over both pre-trained and supervised-only baselines on PDE benchmarks, and shows zero-shot improvement transfer to held-out PDEs. We show that a smaller LLM post-trained with RLVP can outperform prompting a frontier model on in-distribution PDE solver generation. The trained policy shows evidence of compositionality in numerical motifs: it recombines stencils, time-stepping schemes, and boundary-handling primitives learned from the PDEs used in training into generated solvers for unseen PDE problems.

We study tabular reinforcement learning problems with multiple steps of lookahead information. Before acting, the learner observes $\ell$ steps of future transition and reward realizations: the exact state the agent would reach and the rewards it would collect under any possible course of action. While it has been shown that such information can drastically boost the value, finding the optimal policy is NP-hard, and it is common to apply one of two tractable heuristics: processing the lookahead in chunks of predefined sizes ('fixed batching policies'), and model predictive control. We first illustrate the problems with these two approaches and propose utilizing the lookahead in adaptive (state-dependent) batches; we refer to such policies as adaptive batching policies (ABPs). We derive the optimal Bellman equations for these strategies and design an optimistic regret-minimizing algorithm that enables learning the optimal ABP when interacting with unknown environments. Our regret bounds are order-optimal up to a potential factor of the lookahead horizon $\ell$, which can usually be considered a small constant.

3D Gaussian Splatting enables real-time novel view synthesis with high fidelity, yet its sparse and unorganized Gaussian anchors make compression challenging without harming structure and cross-view consistency. A key challenge is that effective compression depends not only on reducing parameter redundancy, but also on identifying where the compressed model is most fragile and how limited representation capacity should be allocated accordingly. We present an RL-guided distillation framework for 3DGS compression (RLGS). RLGS first uses a lightweight reinforcement learning policy to predict informative viewpoint offsets for adaptive distillation. It then distills a compact student 3DGS from a high-quality teacher under multi-view rendering supervision. Finally, it introduces an Unbalanced Optimal Transport based structural selection module to align teacher-student anchor distributions in voxelized space, thereby retaining the most informative anchors during pruning and allocation. Under the same bitrate constraints, our method consistently outperforms strong 3DGS compression baselines in rendering quality. At matched rendering quality, it further reduces model size while preserving structural fidelity, achieving up to about 15% additional size reduction at comparable rendering quality over prior methods.

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in Porteus [1975], we derive two Q-value-style extensions and show that the associated operators are contractions in the $L_\infty$ and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

Reinforcement learning (RL) has been effective for post-training autoregressive (AR) language models, but extending these methods to diffusion language models (DLMs) is challenging due to intractable sequence-level likelihoods. Existing approaches therefore rely on surrogate likelihoods or heuristic approximations, which can introduce bias and obscure the sequential structure of denoising. We formulate diffusion-based sequence generation as a finite-horizon Markov decision process over the denoising trajectory and derive the policy gradient that decomposes over denoising steps in terms of stepwise advantages, without requiring explicit evaluation of the sequence likelihood. Grounded in this theorem, we develop tractable approximations for large-scale training: (i) denoising steps are selected for policy updates via an entropy-guided approximation bound, and (ii) stepwise advantages are estimated using a one-step denoising completion naturally provided by the diffusion model, avoiding costly multi-step rollouts or auxiliary value networks. Experiments demonstrate state-of-the-art results on nearly all benchmarks spanning coding, logical reasoning, and mathematical reasoning, outperforming existing RL post-training approaches for DLMs.

RL for code correctness is now established: have the model generate a program, run it against hidden test cases, and reward solutions that pass. Extending this to code optimization seems straightforward: just add execution time to the reward. But in practice, once timing drives the reward, small problems in measurement noise, reward sparsity, or GRPO instability overwhelm the signal and make RL fail: generated solutions are barely faster, and more of them can fail. We make execution time learnable through three stages: (1) how code is tested, by building DMC-Optim with large optimization tests and a calibrated sandbox; (2) how speed is turned into reward, by composing correctness and speed in the RL environment and using an offline simulator to predict the most promising configurations; and (3) how the model learns from that reward, by adapting GRPO and evaluation to the sparser, noisier timed-execution setting. On DMC-Optim, the strongest optimization-aware configurations improve strict top-decile pass@1 from 18.1% to 27.7% on Qwen 2.5 7B and from 28.7% to 42.4% on CWM 32B, while preserving most of the pure-correctness score. When the timing sandbox is degraded, robust optimization RL reaches up to roughly 130% improvement over standard RLVR. On LCB, CWM 32B wins up to 70.3% of best-sample speed comparisons against standard RLVR; relative to the fastest correct human submissions per problem, it reaches about half the human rate of complexity-class improvements (14% vs. 28%).

To date, the field of reinforcement learning (RL) has primarily focused on developing discounted methods, which are designed to optimize the short-term or transient performance of RL agents. Conversely, the field has been reluctant to explore and invest in methods that are designed to optimize the long-term or steady-state performance of RL agents. In this position paper, we challenge this reluctance under the framing that RL agents should be viewed as competitive swimmers. That is, we argue that, like competitive swimmers, RL agents cannot hope to win all races, or solve all tasks, based on transient performance alone. To this end, we first motivate the need for RL agents that can adequately optimize both the transient and steady-state performance. Then, we summarize recent works which show that discounted methods have deficiencies when it comes to optimizing the steady-state performance. Finally, we argue in favor of more attention and investment from the community towards average-reward methods, which are designed to optimize the steady-state performance. Namely, we challenge common misconceptions associated with average-reward methods, and highlight recent advancements which suggest that such methods present a viable and potentially superior alternative.

Fast weight architectures offer a promising alternative to standard transformers for long-context modeling by replacing the KV-cache with a recurrently updated fixed-size memory. Despite this architectural shift, they are typically trained with the same next-token prediction (NTP) objective as standard transformers. This creates a mismatch: fast weight models rely on an evolving memory state to support future predictions, while NTP provides only token-level supervision for the immediate next token. We address this mismatch with next-sequence prediction (NSP), a sequence-level extension of NTP that trains models to produce coherent multi-token continuations from their recurrent memory state. To optimize this sequence-level objective, we propose ReFINE ($\textbf{Re}$inforced $\textbf{F}$ast we$\textbf{I}$ghts via $\textbf{N}$ext s$\textbf{E}$quence prediction). ReFINE selects informative token positions based on prediction entropy, generates multi-token rollouts, assigns sequence-level rewards, and optimizes the model with Group Relative Policy Optimization (GRPO). ReFINE is applicable throughout the training lifecycle of pre-trained language models: mid-training, post-training, and test-time training. Experiments on LaCT-760M and DeltaNet-1.3B show that ReFINE consistently outperforms NTP-based supervised fine-tuning in needle-in-a-haystack retrieval, long-context question answering, and diverse tasks in LongBench. ReFINE provides an effective and versatile framework for improving long-context modeling in fast weight architectures.

Diffusion and flow-matching models scale because pretraining simply regresses against a closed-form target built by analytically noising clean data samples. In many settings, only a reward function is available, scoring how desirable a generation is, so training must proceed online from a pretrained model. Existing methods either rely on costly SDE rollouts, sometimes with reward gradients, or adopt heuristic reward-dependent variants of the pretraining objective. Under a stochastic optimal control formulation of KL-regularized reward maximization, the optimal generative process tilts only the clean-endpoint distribution and leaves the conditional noising law unchanged. Combining this path-space characterization with the adjoint-matching optimality condition and a REINFORCE estimator to avoid reward gradients, we derive Reinforce Adjoint Matching (RAM). At each step, we draw a clean endpoint from the current model with any off-the-shelf sampler, evaluate its reward, noise it to several training states, and regress against a closed-form, reward-weighted target. Like the pretraining objective, RAM is simple and scales. On Stable Diffusion 3.5M, RAM achieves the highest reward on composability, text rendering, and human preference. It is much more training efficient, reaching Flow-GRPO's peak GenEval accuracy in~$50\times$ fewer training steps.

Federated Incremental Learning (FIL) aims to learn sequential tasks across distributed clients under strict privacy constraints while mitigating catastrophic forgetting. However, existing methods often rely on storing, transmitting, or generating previous data to retrain the model, which not only introduces potential privacy risks but also incurs additional memory, communication, and computational costs, thereby limiting their deployment on resource-constrained edge devices. To tackle this challenge, we propose \textit{SPR-FIL}, a novel rehearsal-free and lightweight \underline{S}tatistical \underline{P}rototype \underline{R}egularization framework for \underline{F}ederated \underline{I}ncremental \underline{L}earning that leverages Gaussian statistics and preserves previous knowledge through aligned prototypes and subspace-constrained encoder updates. More specifically, the server aggregates client-side statistics into global prototypes and dynamically aligns historical prototypes with the evolving feature space through anchor-based moment matching. Locally, clients utilize these aligned prototypes to induce virtual posteriors which serve as soft supervision for distillation while encoder updates are further regularized by projecting gradients onto the orthogonal complement of covariance-induced historical knowledge subspaces. Extensive experiments demonstrate that SPR-FIL is model-agnostic, communication-efficient, and consistently outperforms state-of-the-art methods across various FIL settings, achieving improvements of up to 9.73\%.