ICLR 2026 Papers

Radiance fields have emerged as a predominant representation for modeling 3D scene appearance. Neural formulations such as Neural Radiance Fields provide high expressivity but require costly ray marching for rendering, whereas primitive-based methods such as 3D Gaussian Splatting offer real-time efficiency through splatting, yet at the expense of representational power. Inspired by advances in both these directions, we introduce splattable neural primitives, a new volumetric representation that reconciles the expressivity of neural models with the efficiency of primitive-based splatting. Each primitive encodes a bounded neural density field parameterized by a shallow neural network. Our formulation admits an exact analytical solution for line integrals, enabling efficient computation of perspectively accurate splatting kernels. As a result, our representation supports integration along view rays without the need for costly ray marching. The primitives flexibly adapt to scene geometry and, being larger than prior analytic primitives, reduce the number required per scene. On novel-view synthesis benchmarks, our approach matches the quality and speed of 3D Gaussian Splatting while using 10x fewer primitives and 6x fewer parameters. These advantages arise directly from the representation itself, without reliance on complex control or adaptation frameworks.

Verifiers provide important reward signals for reinforcement learning of large language models (LLMs). However, it is challenging to develop or create reliable verifiers, especially for code generation tasks. A well-disguised wrong solution program may only be detected by carefully human-written edge cases that are difficult to synthesize automatically. To address this issue, we propose HardTestsGen, an approach to synthesize high-quality test cases for algorithmic coding problems. We curate a comprehensive algorithmic programming dataset HardTests with 26.6k problems and high-quality synthetic tests. Compared with existing tests, HardTestsGen tests demonstrate significantly higher accuracy in verifying LLM-generated code (+11.22 percentage points in precision, the percentage of actually correct code within the predicted correct ones). We also show that downstream post-training — including rejection sampling and reinforcement learning (RL) — using HardTests verifier results in improved performance of LLM code generation.

We propose a method for inferring an egocentric dense depth map from an RGB image and a sparse point cloud. The crux of our method lies in modeling the 3D scene implicitly within the latent space and learning an inductive bias in an unsupervised manner through principles of Structure-from-Motion. To force the learning of this inductive bias, we propose to optimize for an ill-posed objective: predicting latent features that are not observed in the input view, but exists in the 3D scene. This is facilitated by means of rigid warping of latent features from the input view to a nearby or adjacent (co-visible) view of the same 3D scene. "Empty" regions in the latent space that correspond to regions occluded from the input view are completed by a Contextual eXtrapolation mechanism based on features visible in input view. Once learned, the inductive bias can be transferred to modulate the features of the input view to improve fidelity. We term our method "Occluded Region Completion as Supervision" or ORCaS. We evaluate ORCaS on VOID1500 and NYUv2 benchmark datasets, where we improve over the best existing method by 8.91% across all metrics. ORCaS also improves generalization from VOID1500 to ScanNet and NYUv2 by 15.7% and robustness to low density inputs by 31.2%. Code will be released.

The message passing–readout framework has become the de facto standard of graph neural networks (GNNs) for material property prediction. However, most existing readout functions are built on an atom-decomposable inductive bias, i.e. the material-level property or feature can be reasonably assigned to contributions of individual atoms. This is a strong bias and may not hold for all properties, limiting the application scenarios (e.g. gas adsorption or separation of Metal Organic Frameworks, MOFs). In this work, we propose a region-based decomposition perspective, reformulating material properties as integrals over space and pooling contributions from spatial regions rather than atoms. Specifically, we propose a novel readout function named SpatialRead. SpatialRead introduces additional spatial nodes to represent a voxelized space, transforming the atomic isomorphic graph into a heterogeneous atom–space graph with unidirectional message flow from atoms to spatial nodes. To combine the two types of inductive bias, multimodal methods can be used to fuse the features of atoms the spatial nodes. Such a region-based readout function is especially suited for spatial properties such as gas adsorption capacity, separation ratio. Extensive experiments demonstrate that a simple PaiNN–Transformer-based SpatialRead trained from scratch outperforms state-of-the-art pre-trained foundation models on these special tasks. Our results highlight the importance of designing physically grounded readout functions tailored to the target property. The code and dataset can be found in github https://github.com/nankusa/SpatialRead.

Parameter-efficient fine-tuning (PEFT) aims to adapt large pretrained speech models using fewer trainable parameters while maintaining performance. Low-Rank Adaptation (LoRA) achieves this by decomposing weight updates into two low-rank matrices, $A$ and $B$, such that $W'=W_0+BA$. Previous studies showed that freezing $A$ and only updating $B$ can reduce trainable parameters and achieve performance close to standard LoRA, where $A$ is initialized using the principal singular vectors of $W_0$ obtained via singular value decomposition (SVD). However, because $A$ is typically initialized with only the leading singular vectors, its representation capacity is confined to a narrow subspace of the model’s knowledge. To overcome this limitation, we propose SumRA, which initializes each row of $A$ as a sum of multiple singular vectors chosen from beyond the leading components, thereby enabling $A$ to influence a larger portion of the model’s knowledge space. Experiments on multilingual automatic speech recognition (ASR) tasks show that by adapting Whisper to five new languages from Common Voice with only 10 hours of data each, our method improves word error rate from 14.42\% to 12.41\% over LoRA baselines while using 50\% less trainable parameters.

Language models often default to a narrow set of high-probability outputs, leaving their generation paths homogeneous and prone to mode collapse. Sampling-based strategies inject randomness but still struggle to guarantee diversity across multiple concurrent generation runs. We address this limitation by introducing STARS (**ST**iefel-based **A**ctivation Steering for Diverse **R**ea**S**oning), a training-free, inference-time intervention method that transforms activation steering into an exploration engine. At each token, STARS collects the hidden activations of concurrent generation runs and optimizes multiple additive steering directions jointly on the Stiefel manifold. STARS maximizes the geometric volume of the steered activations, while the Stiefel manifold induces orthogonality of the steering interventions. This formulation explicitly promotes divergent activation vectors of concurrent generation runs, and implicitly promotes divergent generation trajectories. This manifold optimization formulation can be solved using a Riemannian gradient descent algorithm with convergence guarantees, but this algorithm is too time-consuming for real-time inference. To guarantee low latency, we further design a lightweight one-step update with an aggressive, closed-form stepsize. For test case generation and scientific discovery benchmarks, STARS consistently outperforms standard sampling methods, achieving greater diversity without sacrificing qualitative performance.

Many computer vision tasks share substantial overlapping information, yet conventional codecs tend to ignore this, leading to redundant and inefficient representations. The Gray-Wyner network, a classical concept from information theory, offers a principled framework for separating common and task-specific information. Inspired by this idea, we develop a learnable three-channel codec that disentangles shared information from task-specific details across multiple vision tasks. We characterize the limits of this approach through the notion of lossy common information, and propose an optimization objective that balances inherent tradeoffs in learning such representations. Through comparisons of three codec architectures on two-task scenarios spanning six vision benchmarks, we demonstrate that our approach substantially reduces redundancy and consistently outperforms independent coding. These results highlight the practical value of revisiting Gray-Wyner theory in modern machine learning contexts, bridging classic information theory with task-driven representation learning.

The limited capacity for fine-grained visual perception presents a critical bottleneck for Vision-Language Models (VLMs) in real-world applications. Addressing this is challenging due to the scarcity of high-quality data and the limitations of existing methods: supervised fine-tuning (SFT) often compromises general capabilities, while reinforcement fine-tuning (RFT) prioritizes textual reasoning over visual perception. To bridge this gap, we propose a novel two-stage task that structures visual perception learning as a coarse-to-fine progressive process. Based on this task formulation, we develop ViPER, a self-bootstrapping framework specifically designed to enable iterative evolution through self-critiquing and self-prediction. By synergistically integrating image-level and instance-level reconstruction with a two-stage reinforcement learning strategy, ViPER establishes a closed-loop training paradigm, where internally synthesized data directly fuel the enhancement of perceptual ability. Applied to the Qwen2.5-VL family, ViPER produces the Qwen-Viper series. With an average gain of 1.7\% on seven comprehensive benchmarks spanning various tasks and up to 6.0\% on fine-grained perception, Qwen-Viper consistently demonstrates superior performance across different vision-language scenarios while maintaining generalizability. Beyond enabling self-improvement in perceptual capabilities, ViPER provides concrete evidence for the reciprocal relationship between generation and understanding, a breakthrough to developing more autonomous and capable VLMs.

Stochastic Human Motion Prediction (HMP) has become an essential task for the realm of computer vision, for its capacity to anticipate accurate and diverse future human trajectories. Current diffusion-based techniques typically enforce skeletal consistency by encoding structural priors into network architectures. Although effective in promoting plausible kinematics, this approach provides only indirect control over the generative process and often fails to guarantee strict physical constraint satisfaction. In this work, we propose a structure-aligned and joint-aware diffusion framework that enforces physical constraints by embedding skeletal topology and joint-specific dynamics directly into the diffusion process. Specifically, our framework consists of two key modules, the Joint-Adaptive Noise Generator and the Structure-Aligned Constraint Enforcer. The former component, Joint-Adaptive Noise Generator, infers joint-specific dynamics and injects heterogeneous, instance-aware noise per joint and sample to capture spatial variability and enhance motion diversity. The latter component, Structure-Aligned Constraint Enforcer, encodes skeletal topology by modeling joint connectivity and bone lengths from historical motions, and it constrains each denoising step to preserve anatomical consistency. Through their synergistic operation, these modules grant KinemaDiff direct control over physical realism and motion diversity, addressing the common limitations of indirect structural priors and uniform noise application. Extensive experiments on multiple benchmarks demonstrate the effectiveness of our method, attributable to tailoring the diffusion process through structural alignment and joint-adaptive noise modeling.

Chain-of-thought (CoT) prompting is a de-facto standard technique to elicit reasoning-like responses from large language models (LLMs), allowing them to spell out individual steps before giving a final answer. While the resemblance to human-like reasoning is undeniable, the driving forces underpinning the success of CoT reasoning still remain largely unclear. In this work, we perform an in-depth analysis of CoT traces originating from competition-level mathematics questions, with the aim of better understanding how, and which parts of CoT actually contribute to the final answer. To this end, we introduce the notion of a \textit{potential}, quantifying how much a given part of CoT increases the likelihood of a correct completion. Upon examination of reasoning traces through the lens of the potential, we identify surprising patterns including (1) its often strong non-monotonicity (due to reasoning tangents), (2) very sharp but sometimes tough to interpret spikes (reasoning insights and jumps) as well as (3) at times lucky guesses, where the model arrives at the correct answer without providing any relevant justifications before. While some of the behaviours of the potential are readily interpretable and align with human intuition (such as insights and tangents), others remain difficult to understand from a human perspective. To further quantify the reliance of LLMs on reasoning insights, we investigate the notion of CoT transferability, where we measure the potential of a weaker model under the partial CoT from another, stronger model. Indeed aligning with our previous results, we find that as little as 20% of partial CoT can ``unlock'' the performance of the weaker model on problems that were previously unsolvable for it, highlighting that a large part of the mechanics underpinning CoT are transferable.

Training large language models with FP8 formats offers significant efficiency gains. However, the reduced numerical precision of FP8 poses challenges for stable and accurate training. Current frameworks preserve training performance using mixed-granularity quantization, i.e., applying per-group quantization for activations and per-tensor/block quantization for weights. While effective, per-group quantization requires scaling along the inner dimension of matrix multiplication, introducing additional dequantization overhead. Moreover, these frameworks often rely on just-in-time scaling to dynamically adjust scaling factors based on the current data distribution. However, this online quantization is inefficient for FP8 training, as it involves multiple memory reads and writes that negate the performance benefits of FP8. To overcome these limitations, we propose MOSS, a novel FP8 training framework that ensures both efficiency and numerical stability. MOSS introduces two key innovations: (1) a two-level microscaling strategy for quantizing sensitive activations, which balances precision and dequantization cost by combining a high-precision global scale with compact, power-of-two local scales; and (2) automatic scaling for weights in linear layers, which eliminates the need for costly max-reduction operations by predicting and adjusting scaling factors during training. Leveraging these techniques, MOSS enables efficient FP8 training of a 7B parameter model, achieving performance comparable to the BF16 baseline while achieving up to 34\% higher training throughput. Our code is available at: https://anonymous.4open.science/r/MOSS-1CAF.

Safe and feasible trajectory planning is critical for real-world autonomous driving systems. However, existing learning-based planners rely heavily on expert demonstrations, which not only lack explicit safety awareness but also risk inheriting undesirable behaviors such as speeding from suboptimal human driving data. Inspired by the success of large language models, we propose Plan-R1, a two-stage trajectory planning framework that decouples principle alignment from behavior learning. In the first stage, a general trajectory predictor is pre-trained on expert data to capture diverse, human-like driving behaviors. In the second stage, the model is fine-tuned with rule-based rewards using Group Relative Policy Optimization (GRPO), explicitly aligning ego planning with principles such as safety, comfort, and traffic rule compliance. This two-stage paradigm retains human-like behaviors while enhancing safety awareness and discarding undesirable patterns from demonstrations. Furthermore, we identify a key limitation of directly applying GRPO to planning: group-wise normalization erases cross-group scale differences, causing rare, high-variance safety-violation groups to have similar advantages as abundant low-variance safe groups, thereby suppressing optimization for safety-critical objectives. To address this, we propose Variance-Decoupled GRPO (VD-GRPO), which replaces normalization with centering and fixed scaling to preserve absolute reward magnitudes, ensuring that safety-critical objectives remain dominant throughout training. Experiments on the nuPlan benchmark demonstrate that Plan-R1 significantly improves planning safety and feasibility, achieving state-of-the-art performance, particularly in realistic reactive settings.

Finding the right initialisation for neural networks is crucial to ensure smooth training and good performance. In transformers, the wrong initialisation can lead to one of two failure modes of self-attention layers: rank collapse, where all tokens collapse into similar representations, and entropy collapse, where highly concentrated attention scores lead to training instability. While previous work has studied different scaling regimes for transformers, an asymptotically exact, down-to-the constant prescription for how to initialise transformers has so far been lacking. Here, we provide an analytical theory of signal propagation through deep transformers with self-attention, layer normalisation, skip connections and MLP. Our theory yields a simple algorithm to compute trainability diagrams that identify the correct choice of initialisation hyper-parameters for a given architecture. We overcome the key challenge, an exact treatment of the self-attention layer, by establishing a formal parallel with the Random Energy Model from statistical physics. We also analyse gradients in the backward path and determine the regime where gradients vanish at initialisation. We demonstrate the versatility of our framework through three case studies. Our theoretical framework gives a unified perspective on the two failure modes of self-attention and gives quantitative predictions on the scale of both weights and residual connections that guarantee smooth training.

The ability to learn from large batches of autonomously collected data for policy improvement---a paradigm we refer to as batch online reinforcement learning---holds the promise of enabling truly scalable robot learning by significantly reducing the need for human effort of data collection while getting benefits from self-improvement. Yet, despite the promise of this paradigm, it remains challenging to achieve due to algorithms not being able to learn effectively from the autonomous data. For example, prior works have applied imitation learning and filtered imitation learning methods to the batch online RL problem, but these algorithms often fail to efficiently improve from the autonomously collected data or converge quickly to a suboptimal point. This raises the question of what matters for effective batch online reinforcement learning in robotics. Motivated by this question, we perform a systematic empirical study of three axes---(i) algorithm class, (ii) policy extraction methods, and (iii) policy expressivity---and analyze how these axes affect performance and scaling with the amount of autonomously collected data. Through our analysis, we make several observations. First, we observe that the use of Q-functions to guide batch online RL significantly improves performance over imitation-based methods. Building on this, we show that an implicit method of policy extraction---via choosing the best action in the distribution of the policy---is necessary over traditional explicit policy extraction methods from offline RL. Next, we show that an expressive policy class is preferred over less expressive policy classes. Based on this analysis, we propose a general recipe for effective batch online RL. We then show a simple addition to the recipe, namely using temporally-correlated noise to obtain more diversity, results in further performance gains. Our recipe obtains significantly better performance and scaling compared to prior methods.

Multimodal large language models built on the Mamba architecture offer efficiency advantages, yet remain hampered by redundant visual tokens that inflate inference cost, with the prefill stage accounting for the majority of total inference time. We introduce Delta-guided Two stage Pruning (DTP), a method that progressively reduces token redundancy through selective pruning at early layer and complete pruning at late layer. Unlike Transformer-oriented pruning methods, our approach derives token importance directly from Mamba’s internal parameters. The statistical distribution of these importance scores, combined with implicit attention patterns, then provides the basis for determining both the pruning layers and the tokens to be removed. Extensive evaluation across diverse benchmarks shows that DTP cuts computation by nearly 50\%, maintains higher task performance than existing pruning methods, and further achieves over a 35\% reduction in prefill latency. Beyond efficiency, our analysis reveals previously underexplored behaviors of visual tokens within Mamba layers, suggesting a principled perspective for designing future pruning techniques in Mamba-based Multimodal Large Language Models.

Instruction Tuning (IT) has been proven to be an effective approach to unlock the powerful capabilities of large language models (LLMs). Recent studies indicate that excessive IT data can degrade LLMs performance, while carefully selecting a small subset of high-quality IT data can significantly enhance their capabilities. Therefore, identifying the most efficient subset data from the IT dataset to effectively develop either specific or general abilities in LLMs has become a critical challenge. To address this, we propose a novel and efficient framework called Nait. Nait evaluates the impact of IT data on LLMs performance by analyzing the similarity of neuron activation patterns between the IT dataset and the target domain capability. Specifically, Nait captures neuron activation patterns from in-domain datasets of target domain capabilities to construct reusable and transferable neuron activation features. It then evaluates and selects optimal samples based on the similarity between candidate samples and the expected activation features of the target capabilities. Experimental results show that training on the 10\% Alpaca-GPT4 IT data subset selected by Nait consistently outperforms methods that rely on external advanced models or uncertainty-based features across various tasks. Our findings also reveal the transferability of neuron activation features across different capabilities of LLMs. In particular, IT data with more logical reasoning and programmatic features possesses strong general transferability, enabling models to develop stronger capabilities across multiple tasks, while a stable core subset of data is sufficient to consistently activate fundamental model capabilities and universally improve performance across diverse tasks.

Boolean functions constitute a fundamental object of study in machine learning and, more broadly, in theoretical computer science. Among their various complexity measures, Fourier sparsity, defined as the number of nonzero Fourier coefficients in a Boolean function’s Fourier expansion, serves as a key indicator of structural simplicity. For over three decades, learning Boolean functions with sparse Fourier representations has been a central focus of computational learning theory. A notable achievement in this line of work is the development of learning algorithms whose complexity primarily depends on the Fourier sparsity parameter. However, these approaches generally assume prior knowledge of this parameter. In this work, we address this gap in the literature on learning Fourier-sparse Boolean functions. Specifically, we study the problem of Fourier sparsity testing: given query access to a Boolean function $f : \mathbb{F}_2^n \to \{-1, +1\}$, decide whether it is $s$-Fourier sparse or far (under Hamming distance) from every such function. Our contributions are twofold. On the algorithmic side, we design a new tester with query complexity $\widetilde{O}(s^4)$, independent of the ambient dimension. On the lower bound side, we prove that any tester requires at least $\Omega(s)$ queries. Both bounds improve upon the best known results of Gopalan et al.\ (SICOMP 2011), who presented a tester with query complexity $\widetilde{O}(s^{14})$ and a lower bound of $\Omega(\sqrt{s})$. For our upper bound, we introduce a refined notion of a sampler from the junta testing framework of Chakraborty et al.\ (ICALP 2011) and combine it with $\ell_1$-minimization-based compressed sensing techniques to construct our tester. In the process, we develop a novel method for sampling the leaves of parity decision trees associated with Fourier-sparse Boolean functions. The lower bound is obtained via a reduction from communication complexity, crucially leveraging structural properties of the Fourier coefficients of a specific class of cryptographically hard functions.

Hand motion plays a central role in human interaction, yet modeling realistic 4D hand motion (*i.e.*, 3D hand pose sequences over time) remains challenging. Research in this area is typically divided into two tasks: (1) Estimation approaches reconstruct precise motion from visual observations, but often fail under hand occlusion or absence; (2) Generation approaches focus on synthesizing hand poses by exploiting generative priors under multi-modal structured inputs and infilling motion from incomplete sequences. However, this separation not only limits the effective use of heterogeneous condition signals that frequently arise in practice, but also prevents knowledge transfer between the two tasks. We present **UniHand**, a unified diffusion-based framework that formulates both estimation and generation as conditional motion synthesis. UniHand integrates heterogeneous inputs by embedding structured signals into a shared latent space through a joint variational autoencoder, which aligns conditions such as MANO parameters and 2D skeletons. Visual observations are encoded with a frozen vision backbone, while a dedicated hand perceptron extracts hand-specific cues directly from image features, removing the need for complex detection and cropping pipelines. A latent diffusion model then synthesizes consistent motion sequences from these diverse conditions. Extensive experiments across multiple benchmarks demonstrate that UniHand delivers robust and accurate hand motion modeling, maintaining performance under severe occlusions and temporally incomplete inputs.

When compressing continuous data, some loss of information is inevitable, and this incurred a distortion when reconstruction the data. The Rate–Distortion (RD) function characterizes the minimum achievable rate for a code whose decoding permits a specified amount of distortion. We exploit the connection between rate-distortion theory and entropic optimal transport to propose a novel stochastic-control formulation for the former, and use a classic result dating back to Schrodinger to show that the tradeoff between rate and mean squared error distortion is equivalent to a tradeoff between control energy and the differential entropy of the terminal state, whose probability law defines the reconstruction distribution. For a special class of sources, we show that the optimal control law and the corresponding trajectory in the space of probability measures are obtained by solving a backward heat equation. In more general settings, our approach yields a numerical method that estimates the RD function using diffusion processes with a constant diffusion coefficient. We demonstrate the effectiveness of our method through several examples.