ICLR 2026 Papers

Submodular maximization has broad applications in machine learning, network design, and data mining. However, classical algorithms often suffer from prohibitively high computational costs, which severely limit their scalability in practice. In this work, we focus on maximizing Sums of Concave over Modular functions (SCMs), an important subclass of submodular functions, under three fundamental constraints: cardinality, knapsack, and partition matroids. Our method integrates three components: continuous relaxation, Accelerated Approximate Projected Gradient Ascent (AAPGA), and randomized rounding, to efficiently compute near-optimal solutions. We establish a $(1 - \varepsilon - \eta - e^{-\Omega(\eta^2)})$ approximation guarantee for both cardinality and partition matroid constraints, with query complexity $O\left(n^{1/2}\varepsilon^{-1/2} (T_1 + T_2)\right)$. For the knapsack constraint, the approximation ratio degrades by a factor of $1/2$, with query complexity $O\left(n T_1 + n^{1/2}\varepsilon^{-1/2} T_2\right)$, where $T_1$ denotes the computational cost of evaluating the concave extension, and $T_2$ denotes the computational cost of backpropagation. By leveraging efficient convex optimization techniques, our approach substantially accelerates convergence toward high-quality solutions. In empirical evaluations, we demonstrate that AAPGA consistently outperforms standard PGA. On small-scale experiments, AAPGA achieves superior results in significantly less time, being up to $32.3\times$ faster than traditional methods. On large-scale experiments, our parallel multi-GPU implementation further enhances performance, demonstrating the scalability of our approach.

The recent advancement of Large Language Models (LLMs) has revolutionized the algorithm design patterns. A new paradigm, LLM-based Automated Algorithm Design (LLM-AAD), has emerged to generate code implementations for high-quality algorithms. Unlike the traditional expert-driven algorithm development, in the LLM-AAD paradigm, ideas behind the algorithm are often implicitly embedded within the generated code. Therefore, measuring similarity for algorithms may help identify whether a generated algorithm is innovative or merely a syntactic refinement of an existing code implementation. However, directly applying existing code similarity metrics to algorithms raises a critical limitation: they do not necessarily reflect the similarity between algorithms. To address this, we introduce a novel perspective that defines algorithm similarity through the lens of its problem-solving behavior. We represent the problem-solving trajectory of an algorithm as the sequence of intermediate solutions progressively generated by the algorithm. The behavioral similarity is calculated by the resemblance between two problem-solving trajectories. Our approach focuses on how an algorithm solves a problem, not just its code implementation or final output. We demonstrate the utility of our similarity measure in two use cases. (i) Improving LLM-AAD: Integrating our similarity measure into a search method demonstrates promising results across two AAD tasks, proving the effectiveness of maintaining behavioral diversity in the algorithm search. (ii) Algorithm analysis. Our similarity metric provides a new perspective for analyzing algorithms, revealing distinctions in their problem-solving behaviors.

Data-free continual model merging (DFCMM) aims to fuse independently fine-tuned models into a single backbone that evolves with incoming tasks without accessing task data. This paper formulate two fundamental desiderata for DFCMM: transparency, avoiding interference with earlier tasks, and fidelity, adapting faithfully to each new task. This poses a challenge that existing approaches fail to address: how to bridge data-level desiderata with parameter-space optimization to ensure transparency and fidelity in the absence of task data. To this end, we propose NUFILT (NUll-space FILTering), a data-free framework that directly links these desiderata to optimization. Our key observation is that task vectors approximately align with representation subspaces, providing structural surrogates for enforcing transparency and fidelity. Accordingly, we design a null-space projector that preserves prior responses by filtering out overlapping components of new task vectors, thereby ensuring transparency, and a lightweight LoRA adapter that injects complementary task-specific signals, enabling fidelity in adapting to new tasks. The adapter is trained with a projection-based surrogate loss to retain consistency with previous knowledge while introducing novel directions. This joint filtering–adaptation process allows the backbone to absorb new knowledge while retaining existing behaviors, and the updates are finally fused back in a layer-wise linear fashion without extra parameters or inference cost. Theoretically, we establish approximate subspace alignment guarantees that justify null-space filtering. Empirically, NUFILT achieves state-of-the-art performance with minimal forgetting on both vision and NLP benchmarks, improving average accuracy by 4–7\% over OPCM and WUDI-Merging, while narrowing the gap to fine-tuning and reducing computation overhead.

Execution-based feedback like unit testing is widely used in the development of coding agents through test-time scaling (TTS) and reinforcement learning (RL). This paradigm requires scalable and reliable collection of unit test cases to provide accurate feedback, and the resulting feedback is often sparse and cannot effectively distinguish between trajectories that are both successful or both unsuccessful. In contrast, execution-free feedback from reward models can provide more fine-grained signals without depending on unit test cases. Despite this potential, execution-free feedback for realistic software engineering (SWE) agents remains underexplored. Aiming to develop versatile reward models that are effective across TTS and RL, however, we observe that two verifiers with nearly identical TTS performance can nevertheless yield very different results in RL. Intuitively, TTS primarily reflects the model’s ability to select the best trajectory, but this ability does not necessarily generalize to RL. To address this limitation, we identify two additional aspects that are crucial for RL training: classification accuracy and calibration. We then conduct comprehensive controlled experiments to investigate how to train a robust reward model that performs well across these metrics. In particular, we analyze the impact of various factors such as training data scale, policy mixtures, and data source composition. Guided by these investigations, we introduce SWE-RM, an accurate and robust reward model adopting a mixture-of-experts architecture with 30B total parameters and 3B activated during inference. SWE-RM substantially improves SWE agents on both TTS and RL performance. For example, it increases the accuracy of Qwen3-Coder-Flash from 51.6% to 62.0%, and Qwen3-Coder-Max from 67.0% to 74.6% on SWE-Bench Verified using TTS, achieving new state-of-the-art performance among open-source models. On RL training, SWE-RM lifts the resolve rate of execution-based counterparts by 3 absolute points on SWE-Bench Verified.

Large language models (LLMs) suffer from hallucination and context forgetting. Prior studies suggest that attention drift is a primary cause of these problems, where LLMs' focus shifts towards newly generated tokens and away from the initial input context. To address this, we make use of a related, intrinsic characteristic of LLMs: attention sink – the tendency to consistently allocate high attention to the very first token (i.e., ⟨BOS⟩) of a sequence. Concretely, we propose an advanced context anchoring method, SINKTRACK, which treats ⟨BOS⟩ as an information anchor and injects key contextual features (such as those derived from the input image or instruction) into its representation. As such, LLM remains anchored to the initial input context throughout the entire generation process. SINKTRACK is training-free, plug-and-play, and introduces negligible inference overhead. Experiments demonstrate that SINKTRACK mitigates hallucination and context forgetting across both textual (e.g., +18.9% on QuAC with Llama3.1-8B-Instruct) and multi-modal (e.g., +23.0% on M3CoT with Qwen2.5-VL-7B-Instruct) tasks. Its consistent gains across different architectures and scales underscore the robustness and generalizability. We also analyze its underlying working mechanism from the perspective of information delivery. Our source code is available at anonymous GitHub.

Algorithms for solving the linear classification problem have a long history, dating back at least to 1936 with linear discriminant analysis. For linearly separable data, many algorithms can obtain the exact solution to the corresponding 0-1 loss classification problem efficiently, but for data which is not linearly separable, it has been shown that this problem, in full generality, is NP-hard. Alternative approaches all involve approximations of some kind, such as the use of surrogates for the 0-1 loss (for example, the hinge or logistic loss), none of which can be guaranteed to solve the problem exactly. Finding an efficient, rigorously proven algorithm for obtaining an exact (i.e., globally optimal) solution to the 0-1 loss linear classification problem remains an open problem. By analyzing the combinatorial and incidence relations between hyperplanes and data points, we derive a rigorous construction algorithm, incremental cell enumeration (ICE), that can solve the 0-1 loss classification problem exactly in $O\left(N^{D+1}\right)$---exponential in the data dimension $D$. To the best of our knowledge, this is the first standalone algorithm---one that does not rely on general-purpose solvers---with rigorously proven guarantees for this problem. Moreover, we further generalize ICE to address the polynomial hypersurface classification problem in $O\left(N^{G+1}\right)$ time, where $G$ is determined by both the data dimension $D$ and the polynomial degree $K$ defining the hypersurface. The correctness of our algorithm is proved by the use of tools from the theory of hyperplane arrangements and oriented matroids. We demonstrate the effectiveness of our algorithm on real-world datasets, achieving optimal training accuracy for small-scale datasets and higher test accuracy on most datasets. Furthermore, our complexity analysis shows that the ICE algorithm offers superior computational efficiency compared with state-of-the-art branch-and-bound algorithm.

We present MeanCache, a training-free caching framework for efficient Flow Matching inference. Existing caching methods reduce redundant computation but typically rely on instantaneous velocity information (e.g., feature caching), which often leads to severe trajectory deviations and error accumulation under high acceleration ratios. MeanCache introduces an average-velocity perspective: by leveraging cached Jacobian--vector products (JVP) to construct interval average velocities from instantaneous velocities, it effectively mitigates local error accumulation. To further improve cache timing and JVP reuse stability, we develop a trajectory-stability scheduling strategy as a practical tool, employing a Peak-Suppressed Shortest Path under budget constraints to determine the schedule. Experiments on FLUX.1, Qwen-Image, and HunyuanVideo demonstrate that MeanCache achieves $4.12\times$, $4.56\times$, and $3.59\times$ acceleration, respectively, while consistently outperforming state-of-the-art caching baselines in generation quality. We believe this simple yet effective approach provides a new perspective for Flow Matching inference and will inspire further exploration of stability-driven acceleration in commercial-scale generative models.

Deep neural networks often remain overconfident on Out-of-Distribution (OoD) inputs. We revisit this problem through Riemannian information geometry. We model the network's predictions as a statistical manifold and find that OoD inputs exhibit higher local Fisher-Rao sensitivity. By quantifying this sensitivity with the trace of the Fisher Information Matrix (FIM), we derive a unifying geometric connection between two common OoD signals: feature magnitude and output uncertainty. Analyzing the limitations of this multiplicative form, we extend our analysis using a product manifold construction. This provides a theoretical framework for the robust additive scores used in state-of-the-art (SOTA) detectors and motivates our final, competitive method.

RNA secondary structure forms the basis for folding and function, with non-canonical (NC) interactions indispensable for catalysis, regulation, and molecular recognition. Despite their importance, predicting NC base pairs remains challenging due to the absence of a standardized benchmark for systematic evaluation. To address this, we introduce NC-Bench, the first benchmark dedicated to NC base-pair prediction. NC-Bench provides 925 curated RNA sequences with 6,708 high-quality NC annotations, fine-grained edge and orientation classification tasks, and IsoScore-based embedding evaluation, offering a rigorous foundation for systematic assessment. Building on this, we propose NCfold, a dual-branch framework that couples sequence features with structural priors derived from RNA foundation models (RFMs) via Representative Embedding Fusion (REF) and REF-weighted self-attention. The closed-loop design iteratively refines sequence and structure representations, alleviating data sparsity and enhancing predictive accuracy. Experiments on NC-Bench show that NCfold outperforms existing methods, with zero-shot and ablation studies confirming its effectiveness and underscoring the need for NC-specific benchmarks. Together, NC-Bench and NCfold establish a systematic foundation for NC base-pair prediction, advancing our understanding of RNA structure and enabling next-generation RNA-centric applications. The datasets and codes are publicly available at https://github.com/heqin-zhu/NCBench.

Autoregressive (AR) models have emerged as powerful tools for image generation by modeling images as sequences of discrete tokens. While Classifier-Free Guidance (CFG) has been adopted to improve conditional generation, its application in AR models faces two key issues: guidance diminishing, where the conditional–unconditional gap quickly vanishes as decoding progresses, and over-guidance, where strong conditions distort visual coherence. To address these challenges, we propose SoftCFG, an uncertainty-guided inference method that distributes adaptive perturbations across all tokens in the sequence. The key idea behind SoftCFG is to let each generated token contribute certainty-weighted guidance, ensuring that the signal persists across steps while resolving conflicts between text guidance and visual context. To further stabilize long-sequence generation, we introduce Step Normalization, which bounds cumulative perturbations of SoftCFG. Our method is training-free, model-agnostic, and seamlessly integrates with existing AR pipelines. Experiments show that SoftCFG significantly improves image quality over standard CFG and achieves state-of-the-art FID on ImageNet 256 × 256 among autoregressive models.

Amortized simulator-based inference offers a powerful framework for tackling Bayesian inference in computational fields such as engineering or neuroscience, increasingly leveraging modern generative methods like diffusion models to map observed data to model parameters or future predictions. These approaches yield posterior or posterior-predictive samples for new datasets without requiring further simulator calls after training on simulated parameter-data pairs. However, their applicability is often limited by the prior distribution(s) used to generate model parameters during this training phase. To overcome this constraint, we introduce *PriorGuide*, a technique specifically designed for diffusion-based amortized inference methods. PriorGuide leverages a novel guidance approximation that enables flexible adaptation of the trained diffusion model to new priors at test time, crucially without costly retraining. This allows users to readily incorporate updated information or expert knowledge post-training, enhancing the versatility of pre-trained inference models.

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

Recent work has demonstrated that controlled pretraining experiments are a powerful tool for understanding learning, reasoning, and memorization in large language models (LLMs). However, the computational cost of pretraining presents a significant constraint. To overcome this constraint, we propose to conduct multiple pretraining experiments simultaneously during a *single* training run. We demonstrate the feasibility of this approach by conducting ten experiments during the training of a 1.5B parameter model on 210B tokens. Although we only train a single model, we can replicate the results from multiple previous works on data contamination, poisoning, and memorization. We also conduct novel investigations into knowledge acquisition, mathematical reasoning, and watermarking. For example, we dynamically update the training data until the model acquires a particular piece of knowledge. Remarkably, the influence of the ten experiments on the model's training dynamics and overall performance is minimal. However, interactions between different experiments may act as a potential confounder in our approach. We propose to test for interactions with continual pretraining experiments, finding them to be negligible in our setup. Overall, our findings suggest that performing multiple pretraining experiments in a single training run can enable rigorous scientific experimentation with large models on a compute budget.

We study gradient-based data attribution, aiming to identify which training examples most influence a given output. Existing methods for this task either treat network parameters uniformly or rely on implicit weighting derived from Hessian approximations, which do not fully model functional heterogeneity of network parameters. To address this, we propose a method to explicitly learn parameter importance weights directly from data, without requiring annotated labels. Our approach improves attribution accuracy across diverse tasks, including image classification, language modeling, and diffusion, and enables fine-grained attribution for concepts like subject and style.

Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep MLPs suffer from high inference cost, while efficient embedding-based models lack sufficient expressiveness. To resolve this, we propose the Decoupled Representation Refinement (DRR) architectural paradigm. DRR leverages a deep refiner network, alongside non-parametric transformations, in a one-time offline process to encode rich representations into a compact and efficient embedding structure. This approach decouples slow neural networks with high representational capacity from the fast inference path. We introduce DRR-Net, a simple network that validates this paradigm, and a novel data augmentation strategy, Variational Pairs (VP) for improving INRs under complex tasks like high-dimensional surrogate modeling. Experiments on several ensemble simulation datasets demonstrate that our approach achieves state-of-the-art fidelity, while being up to 27$\times$ faster at inference than high-fidelity baselines and remaining competitive with the fastest models. The DRR paradigm offers an effective strategy for building powerful and practical neural field surrogates and INRs in broader applications, with a minimal compromise between speed and quality.

Training billion-parameter Transformers is often brittle, with transient loss spikes and divergence that waste compute. Even though the recently developed Edge of Stability (EoS) theory provides a powerful tool to understand and control the stability of optimization methods via the (preconditioned) curvature, these curvature-controlling methods are not popular in large-scale Transformer training due to the complexity of curvature estimation. To this end, we first introduce a fast online estimator of the largest (preconditioned) Hessian eigenvalue (i.e., curvature) based on a warm-started variant for power iteration with Hessian–vector products. We show theoretically, and verify empirically, that the proposed method makes per-iteration curvature tracking feasible at billion-parameter scale while being more accurate. Using this tool, we find that training instabilities coincide with surges in preconditioned curvature and that curvature grows with depth. Motivated by these observations, we propose architecture warm-up: progressively growing network depth to carefully control the preconditioned Hessian and stabilize training. Experiments on large Transformers validate that our approach enables efficient curvature tracking and reduces instabilities compared to existing state-of-the-art stabilization techniques without slowing down convergence.

Distributed learning has achieved remarkable success in training deep neural networks (DNNs) on large datasets, but the communication bottleneck limits its scalability. Various compression techniques have been proposed to alleviate this limitation; however, they either use fixed parameters throughout training or rely on complex and computationally intensive methods to adapt compression parameters. Instead of the hard-to-tune hyperparameters required by adaptive compressors, this paper investigates the impact of two fundamental factors in DNN training—the layer size of the networks and their training phases—to design a simple yet efficient dynamic scheduler for any compressor, guiding the selection of compression parameters. We present a **L**ightweight **E**fficient **G**r**A**dient **C**ompression strategy**Y** or LEGACY, which, in theory, can work with any compression technique to produce a simple dynamic counterpart. We benchmark LEGACY on distributed and federated training, involving seven different DNN architectures, ranging from ResNet, Transformer-XL, to GPT-2, across large and challenging datasets, including ImageNet, WikiText-103, and OpenWebText. On ImageNet-1K, with an equivalent average data volume, LEGACY's dynamic compression strategies improve the Top-1 accuracy of ResNet-50 by 7-11% compared to uniform Top-0.1% compression, while on WikiText-103, the layer-based dynamic strategy reduces the perplexity of Transformer-XL by ~26% relative to the same baseline. In addition, we evaluate LEGACY under constrained and federated settings, and demonstrate that it scales effectively to a 100-worker configuration while maintaining strong accuracy under aggressive compression. We publish anonymized code at: https://github.com/LEGACY-compression/LEGACY.

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present $\textit{Panda}$, $\textit{P}$atched $\textit{A}$ttention for $\textit{N}$onlinear $\textit{D}$yn$\textit{A}$mics. We train $\textit{Panda}$ on a novel synthetic, extensible dataset of $2 \times 10^4$ chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, $\textit{Panda}$ exhibits emergent properties: zero-shot forecasting of unseen chaotic systems preserving both short-term accuracy and long-term statistics. Despite having been trained only on low-dimensional ordinary differential equations, $\textit{Panda}$ spontaneously develops the ability to predict partial differential equations without retraining. We also demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

Estimating relative free energy differences between multiple thermodynamic states lies at the core of numerous problems in computational biochemistry. Traditional estimators, such as Free Energy Perturbation and its non-equilibrium counterpart based on the Jarzynski equality, rely on defining a switching protocol between thermodynamic states and computing the free energy difference from the work performed during this process. In this work, we present a method for learning such switching protocols within the class of escorted protocols that combine deterministic and stochastic steps. For this purpose, we use Conditional Flow Matching, and introduce Conditional Density Matching (CDM) for the purpose of estimating the change in Free-Energy. We further reduce the variance in the multistate setting by coupling multiple flows between thermodynamic states into a Flow Graph, enforcing estimator consistency across different transition paths.