ICLR 2026 Papers

Self-supervised models exhibit a surprising stability in their internal representations. Whereas most prior work treats this stability as a single property, we formalize it as two distinct concepts: **statistical identifiability** (consistency of representations across runs) and **structural identifiability** (alignment of representations with some unobserved ground truth). Recognizing that perfect pointwise identifiability is generally unrealistic for modern representation learning models, we propose new model-agnostic definitions of statistical and structural near-identifiability of representations up to some error tolerance $\epsilon$. Leveraging these definitions, we prove a statistical $\epsilon$-**near-identifiability** result for the representations of models with nonlinear decoders, generalizing existing identifiability theory beyond last-layer representations in e.g. generative pre-trained transformers (GPTs) to near-identifiability of the intermediate representations of a broad class of models including (masked) autoencoders (MAEs) and supervised learners. Although these weaker assumptions confer weaker identifiability, we show that independent components analysis (ICA) can resolve much of the remaining linear ambiguity for this class of models, and validate and measure our near-identifiability claims empirically. With additional assumptions on the data-generating process, statistical identifiability extends to structural identifiability, yielding a simple and practical recipe for disentanglement: ICA post-processing of latent representations. On synthetic benchmarks, this approach achieves state-of-the-art disentanglement using a vanilla autoencoder. With a foundation model-scale MAE for cell microscopy, it disentangles biological variation from technical batch effects, substantially improving downstream generalization.

The releases of powerful open-weight large language models (LLMs) are often not accompanied by access to their full training data. Existing interpretability methods, particularly those based on activations, often require or assume distributionally similar data. This is a significant limitation when detecting and defending against novel potential threats like backdoors, which are by definition out-of-distribution. In this work, we introduce a new method for understanding, monitoring and controlling fine-tuned LLMs that interprets weights, rather than activations, thereby sidestepping the need for data that is distributionally similar to the unknown training data. We demonstrate that the top singular vectors of the weight difference between a fine-tuned model and its base model correspond to newly acquired behaviors. By monitoring the cosine similarity of activations along these directions, we can detect salient behaviors introduced during fine-tuning with high precision. For backdoored models that bypass safety mechanisms when a secret trigger is present, our method stops up to 100% of attacks with a false positive rate below 1.2%. For models that have undergone unlearning, we detect inference on erased topics with accuracy up to 95.42% and can even steer the model to recover "unlearned" information. Besides monitoring, our method also shows potential for pre-deployment model auditing: by analyzing commercial instruction-tuned models (OLMo, Llama, Qwen), we are able to uncover model-specific fine-tuning focus including mathematical problem solving, emoji usage, and Midjourney prompt generation.

Slot Attention (SA) with pretrained diffusion models has recently shown promise for object-centric learning (OCL), but suffers from slot entanglement and weak alignment between object slots and image content. We propose Contrastive Object-centric Diffusion Alignment (CODA), a simple extension that (i) employs register slots to absorb residual attention and reduce interference between object slots, and (ii) applies a contrastive alignment loss to explicitly encourage slot–image correspondence. The resulting training objective serves as a tractable surrogate for maximizing mutual information (MI) between slots and inputs, strengthening slot representation quality. On both synthetic (MOVi-C/E) and real-world datasets (VOC, COCO), CODA improves object discovery (e.g., +6.1% FG-ARI on COCO), property prediction, and compositional image generation over strong baselines. Register slots add negligible overhead, keeping CODA efficient and scalable. These results indicate potential applications of CODA as an effective framework for robust OCL in complex, real-world scenes. Code and pretrained models are available at https://github.com/sony/coda.

The process through which humans perceive and learn visual representations in dynamic environments is highly complex. From a structural perspective, the human eye decouples the functions of cone and rod cells: cones are primarily responsible for color perception, while rods are specialized in detecting motion, particularly variations in light intensity. These two distinct modalities of visual information are integrated and processed within the visual cortex, thereby enhancing the robustness of the human visual system. Inspired by this biological mechanism, modern hardware systems have evolved to include not only color-sensitive RGB cameras but also motion-sensitive Dynamic Visual Systems, such as spike cameras. Building upon these advancements, this study seeks to emulate the human visual system by integrating decomposed multi-modal visual inputs with modern latent-space generative frameworks. We named it ***SpikeGen***. We evaluate its performance across various spike-RGB tasks, including conditional image and video deblurring, dense frame reconstruction from spike streams, and high-speed scene novel-view synthesis. Supported by extensive experiments, we demonstrate that leveraging the latent space manipulation capabilities of generative models enables an effective synergistic enhancement of different visual modalities, addressing spatial sparsity in spike inputs and temporal sparsity in RGB inputs.

Heuristic functions are central to the performance of search algorithms such as A*, where \emph{admissibility}—the property of never overestimating the true shortest-path cost—guarantees solution optimality. Recent deep learning approaches often disregard full admissibility and provide limited guarantees on generalization beyond the training data. We address both of these limitations. First, we pose heuristic learning as a constrained optimization problem and introduce \emph{Cross-Entropy Admissibility (CEA)}, a loss function that enforces admissibility during training. When evaluated on the Rubik’s Cube domain, our method yields heuristics with near-perfect admissibility and significantly stronger guidance than compressed pattern database (PDB) heuristics. On the theoretical side, we derive a new upper bound on the expected suboptimality of A*. By leveraging PDB abstractions and the structural properties of graphs such as the Rubik’s Cube, we tighten the bound on the number of training samples needed for A* to generalize to unseen states. Replacing a general hypothesis class with a ReLU neural network gives bounds that depend primarily on the network’s width and depth, rather than on graph size. Using the same network, we also provide the first generalization guarantees for \emph{goal-dependent} heuristics.

Despite its recent successes, Deep Reinforcement Learning (DRL) is notoriously sample-inefficient. We argue that this inefficiency stems from the standard practice of optimizing policies directly in the high-dimensional and highly redundant parameter space $\\Theta$. This challenge is greatly compounded in multi-task settings. In this work, we develop a novel, unsupervised approach that compresses the policy parameter space $\\Theta$ into a low-dimensional latent space $\\mathcal Z$. We train a generative model $g:\\mathcal Z\\to\\Theta$ by optimizing a behavioral reconstruction loss, which ensures that the latent space is organized by functional similarity rather than proximity in parameterization. We conjecture that the inherent dimensionality of this manifold is a function of the environment's complexity, rather than the size of the policy network. We validate our approach in continuous control domains, showing that the parameterization of standard policy networks can be compressed up to five orders of magnitude while retaining most of its expressivity. As a byproduct, we show that the learned manifold enables task-specific adaptation via Policy Gradient operating in the latent space $\\mathcal{Z}$.

Unsupervised Reinforcement Learning with Verifiable Rewards (URLVR) offers a pathway for Large Language Models (LLMs) to improve without human supervision. Particularly, many works use model intrinsic information as rewards for URLVR, showing promising improvements, yet their potential and limitations remain unclear. In this work, we revisit URLVR through the lens of intrinsic rewards. We present a unified theoretical framework showing that intrinsic reward methods share a core mechanism: they trade uncertainty for performance by leveraging the model’s prior knowledge to sharpen output distributions. Empirical analysis confirms this tradeoff, revealing distinct failure modes and showing that collapse is not inevitable in small, domain-specific regimes such as test-time training. Beyond these findings, early intrinsic reward dynamics also provide a lightweight indicator of model-task priors, complementing $pass@k$ in assessing RL trainability. These insights highlight both the promise and pitfalls of URLVR, motivating future directions such as external rewards and hybrid supervision strategies.

Recent advances in Large Language Model (LLM) compression, such as quantization and pruning, have achieved notable success. However, as these techniques gradually approach their limits, relying on a single method for further compression has become increasingly challenging. In this work, we explore an alternative solution by combining quantization and sparsity. This joint approach, though promising, introduces new difficulties due to the inherently conflicting requirements on weight distributions: quantization favors compact ranges, while pruning benefits from high variance. To attack this problem, we propose Optimal Brain Restoration (OBR), a general and training-free framework that aligns pruning and quantization by error compensation between both. OBR minimizes performance degradation on downstream tasks by building on a second-order Hessian objective, which is then reformulated into a tractable problem through surrogate approximation and ultimately reaches a closed-form solution via group error compensation. Experiments show that OBR incurs only a 1.4 perplexity degradation on Llama2-7B to enable aggressive W4A4KV4 quantization with 50% sparsity, delivering up to 4.72x speedup and 6.4x memory reduction compared to the FP16-dense baseline.

An important aspect subtending language understanding and production is the ability to independently encode positional and symbolic information of the words within a sentence. In Transformers, positional information is typically encoded using Positional Encodings (PEs). One such popular PE, namely Rotary PE (RoPE), has been widely used due to its empirical success. Recently, it has been argued that part of RoPE's success emerges from its ability to encode robust positional and semantic information using large and small frequencies, respectively. In this work, we perform a deeper dive into the positional versus symbolic dichotomy of attention heads behavior, both at the theoretical and empirical level. We provide general definitions of what it means for a head to behave positionally or symbolically, prove that these are two mutually exclusive behaviors and develop a metric to quantify them. We apply our framework to analyze Transformer-based LLMs using RoPE and find that all heads exhibit a strong correspondence between behavior and frequency use. Finally, we introduce canonical tasks designed to be either purely positional or symbolic, and demonstrate that the Transformer performance causally relates to the ability of attention heads to leverage the appropriate frequencies. In particular, we show that we can control the Transformer performance by controlling which frequencies the attention heads can access. Altogether, our work provides a detailed understanding of RoPE, and how its properties relate to model behavior.

We introduce k-NLPmeans and k-LLMmeans, text-clustering variants of k-means that periodically replace numeric centroids with textual summaries. The key idea—summary-as-centroid—retains k-means assignments in embedding space while producing human-readable, auditable cluster prototypes. The method is LLM-optional: k-NLPmeans uses lightweight, deterministic summarizers, enabling offline, low-cost, and stable operation; k-LLMmeans is a drop-in upgrade that uses an LLM for summaries under a fixed per-iteration budget whose cost does not grow with dataset size. We also present a mini-batch extension for real-time clustering of streaming text. Across diverse datasets, embedding models, and summarization strategies, our approach consistently outperforms classical baselines and approaches the accuracy of recent LLM-based clustering without extensive LLM calls. Finally, we provide a case study on sequential text streams and release a StackExchange-derived benchmark for evaluating streaming text clustering.

Unsupervised pre-training can equip reinforcement learning agents with prior knowledge and accelerate learning in downstream tasks. A promising direction, grounded in human development, investigates agents that learn by setting and pursuing their own goals. The core challenge lies in how to effectively generate, select, and learn from such goals. Our focus is on broad distributions of downstream tasks where solving every task zero-shot is infeasible. Such settings naturally arise when the target tasks lie outside of the pre-training distribution or when their identities are unknown to the agent. In this work, we (i) optimize for efficient multi-episode exploration and adaptation within a meta-learning framework, and (ii) guide the training curriculum with evolving estimates of the agent’s post-adaptation performance. We present ULEE, an unsupervised meta-learning method that combines an in-context learner with an adversarial goal-generation strategy that maintains training at the frontier of the agent’s capabilities. On XLand-MiniGrid benchmarks, ULEE pre-training yields improved exploration and adaptation abilities that generalize to novel objectives, environment dynamics, and map structures. The resulting policy attains improved zero-shot and few-shot performance, and provides a strong initialization for longer fine-tuning processes. It outperforms learning from scratch, DIAYN pre-training, and alternative curricula.

Fourier neural operator (FNO) has demonstrated substantial potential in learning mappings between function spaces, such as numerical partial differential equations (PDEs). However, FNO may suffer from inefficiencies when applied to large-scale, high-dimensional function spaces due to the computational overhead associated with high-dimensional Fourier and convolution operators. In this work, we introduce the Tucker-FNO, an efficient neural operator that decomposes the high-dimensional FNO into a series of 1-dimensional FNOs through Tucker decomposition, thereby significantly reducing computational complexity while maintaining expressiveness. Especially, by using the theoretical tools of functional decomposition in Sobolev space, we rigorously establish the universal approximation theorem of Tucker-FNO. Experiments on high-dimensional numerical PDEs such as Navier-Stokes, Plasticity, and Burger's equations show that Tucker-FNO achieves substantial improvement in execution time and performance over FNO. Moreover, by virtue of the compact Tucker decomposition, Tucker-FNO generalizes seamlessly to high-dimensional visual signals by learning mappings from the positional encoding space to the signal's implicit neural representations (INRs). Under this operator INR framework, Tucker-FNO gains consistent improvements on continuous signal restoration over traditional INR methods in terms of efficiency and accuracy.

The explosive growth of large language models (LLMs) has created a vast but opaque landscape: millions of models exist, yet their evolutionary relationships through fine-tuning, distillation, or adaptation are often undocumented or unclear, complicating LLM management. Existing methods are limited by task specificity, fixed model sets, or strict assumptions about tokenizers or architectures. Inspired by biological DNA, we address these limitations by mathematically defining *LLM DNA* as a low-dimensional, bi-Lipschitz representation of functional behavior. We prove that LLM DNA satisfies *inheritance* and *genetic determinism* and establish its existence. Building on this theory, we derive a general, scalable, training-free pipeline for DNA extraction. In experiments across 305 LLMs, DNA aligns with prior studies on limited subsets and achieves superior or competitive performance on various tasks. Beyond these tasks, DNA comparisons uncover previously undocumented relationships among LLMs. We further construct the evolutionary tree of LLMs using phylogenetic algorithms, which align with shifts from encoder-decoder to decoder-only architectures, reflect temporal progression, and reveal distinct evolutionary speeds across LLM families.

Skill-based reinforcement learning (SBRL) enables rapid adaptation in environments with sparse rewards by pretraining a skill-conditioned policy. Effective skill learning requires jointly maximizing both exploration and skill diversity. However, existing methods often face challenges in simultaneously optimizing for these two conflicting objectives. In this work, we propose a new method, Adaptive Multi-objective Projection for balancing Exploration and skill Diversification (AMPED), which explicitly addresses both: during pre-training, a gradient-surgery projection balances the exploration and diversity gradients, and during fine-tuning, a skill selector exploits the learned diversity by choosing skills suited to downstream tasks. Our approach achieves performance that surpasses SBRL baselines across various benchmarks. Through an extensive ablation study, we identify the role of each component and demonstrate that each element in AMPED is contributing to performance. We further provide theoretical evidence that, with a greedy skill selector, greater skill diversity reduces fine-tuning sample complexity. These results highlight the importance of explicitly harmonizing exploration and diversity and demonstrate the effectiveness of AMPED in enabling robust and generalizable skill learning.

Deep clustering has recently achieved remarkable progress across various domains. However, existing clustering methods typically treat all samples equally, neglecting the inherent differences in their feature patterns and learning states. Such redundant learning often drives models to overemphasize simple feature patterns in high-density regions, weakening their ability to capture complex yet diverse ones in low-density regions. To address this issue, we propose a novel plug-in designed to mitigate overfitting to simple and redundant feature patterns while encouraging the learning of more complex yet diverse ones. Specifically, we introduce a density-aware clustering head initialization strategy that adaptively adjusts each sample's contribution to cluster prototypes according to its local density in the feature space. This strategy mitigates the bias towards high-density regions and encourages a more comprehensive attention on medium- and low-density ones. Furthermore, we design a dynamic sample selection strategy that evaluates the learning state of samples based on the feature consistency and pseudo-label stability. By removing sufficiently learned samples and prioritizing unstable ones, this strategy adaptively reallocates training resources, enabling the model to consistently focus on samples that remain under-learned throughout training. Our method can be integrated as a plug-in into a wide range of deep clustering architectures. Extensive experiments on multiple benchmark datasets demonstrate that our method improves clustering accuracy by up to $\textbf{6.1}$\% and enhances training efficiency by up to $\textbf{1.3$\times$}$. $\textbf{Code is available in the supplementary material.}$

Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different aspects organized and encoded in separate subspaces? Is it possible to find these "natural" subspaces in a purely unsupervised way? Somewhat surprisingly, we can indeed achieve this and find interpretable subspaces by a seemingly unrelated training objective. Our method, neighbor distance minimization (NDM), learns non-basis-aligned subspaces in an unsupervised manner. Qualitative analysis shows subspaces are interpretable in many cases, and encoded information in obtained subspaces tends to share the same abstract concept across different inputs, making such subspaces similar to "variables" used by the model. We also conduct quantitative experiments using known circuits in GPT-2; results show a strong connection between subspaces and circuit variables. We also provide evidence showing scalability to 2B models by finding separate subspaces mediating context and parametric knowledge routing. Viewed more broadly, our findings offer a new perspective on understanding model internals and building circuits.

Providing high-quality feedback to Large Language Models (LLMs) on a diverse training distribution can be difficult and expensive, and providing feedback only on a narrow distribution can result in unintended generalizations. To better leverage narrow training data, we propose *contrastive weight steering*, a simple post-training method that edits the model parameters using weight arithmetic. We isolate a behavior direction in weight-space by subtracting the weight deltas from two small fine-tunes---one that induces the desired behavior and another that induces its opposite---and then add or remove this direction to modify the model's weights. We apply this technique to mitigate sycophancy and induce misalignment, and find that weight steering often generalizes further than activation steering, achieving stronger out-of-distribution behavioral control before degrading general capabilities. We also show that, in the context of task-specific fine-tuning, weight steering can partially mitigate undesired behavioral drift: it can reduce sycophancy and under-refusals introduced during fine-tuning while preserving task performance gains. Finally, we provide preliminary evidence that emergent misalignment can be detected by measuring the similarity between fine-tuning updates and an "evil" weight direction, suggesting that it may be possible to monitor the evolution of weights during training and detect rare misaligned behaviors that never manifest during training or evaluations.

Unsupervised domain adaptation (UDA) is a statistical learning problem when the distribution of training (source) data is different from that of test (target) data. In this setting, one has access to labeled data only from the source domain and unlabeled data from the target domain. The central objective is to leverage the source data and the unlabeled target data to build models that generalize to the target domain. Despite its potential, existing UDA approaches often struggle in practice, particularly in scenarios where the target domain offers only limited unlabeled data or spurious correlations dominate the source domain. To address these challenges, we propose a novel distributionally robust learning framework that models uncertainty in both the covariate distribution and the conditional label distribution. Our approach is motivated by the multi-source domain adaptation setting but is also directly applicable to the single-source scenario, making it versatile in practice. We develop an efficient learning algorithm that can be seamlessly integrated with existing UDA methods. Extensive experiments under various distribution shift scenarios show that our method consistently outperforms strong baselines, especially when target data are extremely scarce.

Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman–Pearson lemma, a classical result in statistics that characterizes the optimal rejection rule as a likelihood ratio test. We show that this perspective not only unifies the behavior of several post-hoc selection baselines, but also motivates new approaches to selective classification which we propose here. A central focus of our work is the setting of covariate shift, where the input distribution at test time differs from that at training. This realistic and challenging scenario remains relatively underexplored in the context of selective classification. We evaluate our proposed methods across a range of vision and language tasks, including both supervised learning and vision-language models. Our experiments demonstrate that our Neyman-Pearson-informed methods consistently outperform existing baselines, indicating that likelihood ratio-based selection offers a robust mechanism for improving selective classification under covariate shifts.