ICLR 2026 Papers

Post-training of large language models involves a fundamental trade-off between supervised fine-tuning (SFT), which efficiently mimics demonstrations but tends to memorize, and reinforcement learning (RL), which achieves better generaliza- tion at higher computational cost. Dynamic Fine-Tuning (DFT) recently emerged as a promising middle ground, reweighting SFT objectives with token probabili- ties and achieving improvements in certain reasoning domains, though it exhibits instability in other tasks. We provide a analysis of DFT through the reward- weighted regression (RWR) framework, revealing that it corresponds to a spe- cific auxiliary distribution choice that yields provably tighter RL bounds than standard SFT. However, our analysis also uncovers a critical limitation: this con- struction lacks distributional anchoring, leading to progressive drift that under- mines training stability. To address this, we propose Anchored Supervised Fine- Tuning (ASFT), which augments DFT’s reweighting with lightweight KL regu- larization to preserve tightness while ensuring stability. Empirically, ASFT con- sistently outperforms both SFT and DFT across mathematical reasoning, medical knowledge grounding, and code generation, achieving substantial improvements with minimal computational overhead. Our RWR framework provides a system- atic lens for understanding post-training methods and demonstrates that principled theoretical analysis leads to both stronger guarantees and practical gains.

Existing language model benchmarks provide contradictory model rankings, even for benchmarks that aim to capture similar skills. This dilemma of conflicting rankings hampers model selection, clouds model comparisons, and adds confusion to a growing ecosystem of competing models. In this paper, we take a different perspective on model comparison: instead of relying on out-of-the-box performance via direct evaluation, we compare model potential by providing each model with identical benchmark-specific fine-tuning before evaluation. We call this approach train-before-test. Our primary contribution is a comprehensive empirical evaluation of model potential across 24 benchmarks and 61 models. First, we demonstrate that model potential rankings obtained through train-before-test exhibit remarkable consistency across all benchmarks. Whereas traditional rankings demonstrate little external validity under direct evaluation, they enjoy a significant degree of external validity when applying train-before-test: model potential rankings transfer gracefully from one benchmark to another. Second, train-before-test restores the connection between perplexity and downstream task performance, lost under direct evaluation. Remarkably, even pre-finetuning perplexity of a base model predicts post-finetuning downstream performance, suggesting that ranking consistency reflects inherent model potential rather than fine-tuning artifacts. Finally, train-before-test reduces the model-score matrix to essentially rank one, indicating that model potential is dominated by one latent factor, uncovered by train-before-test. While direct evaluation remains useful for assessing deployment-ready performance, train-before-test provides a complementary lens for understanding achievable performance of models after adaptation.

Reinforcement learning (RL) algorithms are highly sensitive to reward function specification, which remains a central challenge limiting their broad applicability. We present ARM-FM: Automated Reward Machines via Foundation Models, a framework for automated, compositional reward design in RL that leverages the high-level reasoning capabilities of foundation models (FMs). Reward machines (RMs) - an automata-based formalism for reward specification - are used as the mechanism for RL objective specification, and are automatically constructed via the use of FMs. The structured formalism of RMs yields effective task decompositions, while the use of FMs enables objective specifications in natural language. Concretely, we (i) use FMs to automatically generate RMs from natural language specifications; (ii) associate language embeddings with each RM automata-state to enable generalization across tasks; and (iii) provide empirical evidence of ARM-FM's effectiveness in a diverse suite of challenging environments, including evidence of zero-shot generalization.

Large Language Models have demonstrated strong performance across a wide range of tasks, but adapting them efficiently to new domains remains a key challenge. Parameter-Efficient Fine-Tuning (PEFT) methods address this by introducing lightweight, trainable modules while keeping most pre-trained weights fixed. The prevailing approach, LoRA, models updates using a low-rank decomposition, but its expressivity is inherently constrained by the rank. Recent methods like HiRA aim to increase expressivity by incorporating a Hadamard product with the frozen weights, but still rely on the structure of the pre-trained model. We introduce ABBA, a new PEFT architecture that reparameterizes the update as a Hadamard product of two independently learnable low-rank matrices. In contrast to prior work, ABBA fully decouples the update from the pre-trained weights, enabling both components to be optimized freely. This leads to significantly higher expressivity under the same parameter budget, a property we validate through matrix reconstruction experiments. Empirically, ABBA achieves state-of-the-art results on arithmetic and commonsense reasoning benchmarks, consistently outperforming existing PEFT methods by a significant margin across multiple models. Our code is publicly available at: https://github.com/CERT-Lab/abba.

We propose \textbf{ABSignSGD}, a block‑coordinate variant of sign-based descent with flexible block selection that enables memory‑ and runtime‑efficient full‑parameter fine‑tuning of large language models. We present a unified convergence analysis under mild conditions, covering both the base method and a \textit{majority‑vote} extension for distributed training. The latter improves communication efficiency by aggregating only gradient signs rather than averaging full gradients. Experiments on \textcolor{blue}{Qwen3‑8B, Llama3-8B, and Qwen3-32B}, spanning mathematical reasoning and general instruction‑following tasks, show that ABSignSGD converges faster per iteration and delivers superior downstream performance while reducing both runtime and memory usage compared to existing methods. Ablation studies further indicate that the memoryless sign-based update naturally complements block‑wise updates, explaining the method’s strong empirical performance.

Fine-tuning large language models (LLMs) often faces GPU memory bottlenecks: the backward pass of first-order optimizers like Adam increases memory usage to more than 10 times the inference level (e.g., 633~GB for OPT-30B). Zeroth-order (ZO) optimizers avoid this cost by estimating gradients only from forward passes, yet existing methods like MeZO usually need tens of times more steps to converge. Can this trade-off between speed and memory in ZO be fundamentally improved? Normalized-SGD, for instance, demonstrates strong empirical performance with greater memory efficiency than Adam. In light of this, we introduce FZOO, a Fast Zeroth-Order Optimizer towards Adam-Scale Speed. On the one hand, FZOO reduces the total forward passes needed for convergence by employing batched one-sided estimates that adapt step-sizes based on the standard deviation of batch losses. On the other hand, it accelerates per-batch computation through the use of Rademacher random vector (±1) perturbations, which also enables further speedups through batched evaluation. Extensive experiments on diverse models (including RoBERTa-large, the OPT family (350M-66B), Phi-2, and Llama3) across 11 varied downstream tasks validate FZOO's effectiveness. On average, FZOO outperforms MeZO by +3% in accuracy while requiring 3$\times$fewer forward passes. Notably, for the RoBERTa-large model, FZOO achieves average improvements of +5.6% in accuracy and 18$\times$reduction in forward passes compared to MeZO, achieving convergence speeds comparable to Adam. We also provide theoretical analysis proving FZOO’s formal equivalence to a normalized-SGD update rule and establishing its convergence guarantees. Beyond full-parameter tuning, FZOO plugs smoothly into PEFT techniques, unlocking even larger memory savings. Taken together, our results make single-GPU, high-speed, full-parameter fine-tuning realistic today and point toward future work on memory-efficient pre-training. Code: https://github.com/DKmiyan/FZOO

Visual prompt tuning offers significant advantages for adapting pre-trained visual foundation models to specific tasks. However, current research provides limited insight into the interpretability of this approach, which is essential for enhancing AI reliability and enabling AI-driven knowledge discovery. In this paper, rather than learning abstract prompt embeddings, we propose the first framework, named Interpretable Visual Prompt Tuning (IVPT), to explore interpretability for visual prompts by introducing cross-layer concept prototypes. Specifically, visual prompts are linked to human-understandable semantic concepts, represented as a set of category-agnostic prototypes, each corresponding to a specific region of the image. IVPT then aggregates features from these regions to generate interpretable prompts for multiple network layers, allowing the explanation of visual prompts at different network depths and semantic granularities. Comprehensive qualitative and quantitative evaluations on fine-grained classification benchmarks show its superior interpretability and performance over visual prompt tuning methods and existing interpretable methods. Our code is available at https://github.com/ThomasWangY/IVPT.

As large language models (LLMs) scale to billions of parameters, full-parameter fine-tuning becomes compute- and memory-prohibitive. Parameter-efficient fine-tuning (PEFT) mitigates this issue by updating only a small set of task-specific parameters while keeping the base model frozen. Among PEFT approaches, low-rank adaptation (LoRA) is widely adopted; however, it enforces a uniform rank across layers despite substantial variation in layer importance, motivating layerwise rank allocation. Recent adaptive-rank variants (e.g., AdaLoRA) allocate ranks based on importance scores, yet typically rely on instantaneous gradients that capture only local sensitivity, overlooking non-local, pathwise effects within the same layer, which yields unstable and biased scores. To address this limitation, we introduce IGU-LoRA, an adaptive-rank LoRA that (i) computes within-layer Integrated Gradients (IG) sensitivities and aggregates them into a layer-level score for rank allocation, and (ii) applies an uncertainty-aware scheme using exponential moving averages with deviation tracking to suppress noisy updates and calibrate rank selection. Theoretically, we prove an upper bound on the composite trapezoidal rule approximation error for parameter-space IG under a pathwise Hessian-Lipschitz condition, which informs the quadrature budget. Across diverse tasks and architectures, IGU-LoRA consistently outperforms strong PEFT baselines at matched parameter budgets, improving downstream accuracy and robustness. Ablations confirm the contributions of pathwise within-layer sensitivity estimates and uncertainty-aware selection to effective rank allocation.

Recent advances in large language model (LLM) reasoning have shown that reasoning ability can emerge through reinforcement learning (RL). However, despite these successes, RL in its current form remains insufficient to induce capabilities that exceed the limitations of the base model, as it is primarily optimized based on existing knowledge of the model. To address this limitation, we employ supervised fine-tuning (SFT) to learn what RL cannot, which enables the incorporation of new knowledge and reasoning patterns by leveraging high-quality demonstration data. We analyze the training dynamics of RL and SFT for LLM reasoning and find that RL excels at improving performance on questions within the model's original capabilities, while SFT is more effective at enabling progress on questions beyond the current scope of the model. Motivated by the complementary strengths of RL and SFT, we introduce \textbf{ReLIFT} (\textbf{Re}inforcement \textbf{L}earning \textbf{I}nterleaved with Online \textbf{F}ine-\textbf{T}uning), a novel training strategy. ReLIFT employs RL for general training, but interleaves it with targeted SFT on challenging questions for which high-quality solutions are collected online. By alternating between RL and SFT, ReLIFT addresses model weaknesses as they emerge. Empirically, ReLIFT outperforms previous RLVR methods by an average of +6.7 points across a suite of six benchmarks (five math reasoning and one out-of-distribution). More importantly, ReLIFT surpasses baselines such as individual RL, individual SFT, and various hybrid approaches while reducing the required training time. These results provide compelling evidence that ReLIFT is a powerful and resource-efficient paradigm for developing capable reasoning models. The code is available at \href{https://anonymous.4open.science/r/Learning-What-Reinforcement-Learning-Can-t-6AFF/}{here}.

Parameter-Efficient Fine-Tuning (PEFT) methods have become crucial for rapidly adapting large language models (LLMs) to downstream tasks. Prefix-Tuning, an early and effective PEFT technique, demonstrated the ability to achieve performance comparable to full fine-tuning with significantly reduced computational and memory overhead. However, despite its earlier success, its effectiveness in training modern state-of-the-art LLMs has been very limited. In this work, we demonstrate empirically that Prefix-Tuning underperforms on LLMs because of an inherent tradeoff between the contribution of input prompt and parameterized prefix within the attention head. This motivates us to introduce PrefixMemory-Tuning, an architecture that generalizes the principles of Prefix-Tuning while addressing its shortcomings by shifting the prefix module out of the attention head itself and improving its expressiveness. Our experiments show that, across diverse benchmarks, PrefixMemory-Tuning consistently outperforms existing Prefix-Tuning methods. Notably, it achieves competitive performance with modern PEFTs on several general benchmarks, highlighting a potential extension of Prefix-Tuning approaches to become state-of-the-art. Our findings suggest that by overcoming its inherent limitations, Prefix-Tuning can remain a competitive and relevant research direction in the landscape of parameter-efficient LLM adaptation.

Large Language Models (LLMs) currently respond to every prompt. However, they can produce incorrect answers when they lack knowledge or capability -- a problem known as hallucination. We instead propose post-training an LLM to generate content only when confident in its correctness and to otherwise (partially) abstain. Specifically, our method, HALT, produces capability-aligned post-training data that encodes what the model can and cannot reliably generate. We generate this data by splitting responses of the pretrained LLM into factual fragments (atomic statements or reasoning steps), and use ground truth information to identify incorrect fragments. We achieve capability-aligned finetuning responses by either removing incorrect fragments or replacing them with "Unsure from Here" -- according to a tunable threshold that allows practitioners to trade off response completeness and mean correctness of the response's fragments. We finetune four open-source models for biography writing, mathematics, coding, and medicine with HALT for three different trade-off thresholds. HALT effectively trades off response completeness for correctness, increasing the mean correctness of response fragments by 15% on average, while resulting in a 4% improvement in the F1 score (mean of completeness and correctness of the response) compared to the relevant baselines. By tuning HALT for highest correctness, we train a single reliable Llama3-70B model with correctness increased from 51% to 87% across all four domains while maintaining 53% of the response completeness achieved with standard finetuning.

Information processing in neural populations is inherently constrained by metabolic resource limits and noise properties, with dynamics that are not accurately described by existing mathematical models. Recent data, for example, shows that neurons in mouse visual cortex go into a "low power mode" in which they maintain firing rate homeostasis while expending less energy. This adaptation leads to increased neuronal noise and tuning curve flattening in response to metabolic stress. We have developed a theoretical population coding framework that captures this behavior using two novel, surprisingly simple constraints: an approximation of firing rate homeostasis and an energy limit tied to noise levels via biophysical simulation. A key feature of our contribution is an energy budget model directly connecting adenosine triphosphate (ATP) use in cells to a fully explainable mathematical framework that generalizes existing optimal population codes. Specifically, our simulation provides an energy-dependent dispersed Poisson noise model, based on the assumption that the cell will follow an optimal decay path to produce the least-noisy spike rate that is possible at a given cellular energy budget. Each state along this optimal path is associated with properties (resting potential and leak conductance) which can be measured in electrophysiology experiments and have been shown to change under prolonged caloric deprivation. We analytically derive the optimal coding strategy for neurons under varying energy budgets and coding goals, and show how our method uniquely captures how populations of tuning curves adapt while maintaining homeostasis, as has been observed empirically.

Different time-series tasks benefit from distinct cues at various spaces and abstractions, yet existing time-series pre-trained models entangle these signals within large, monolithic embeddings, limiting transferability and zero-shot usability. Moreover, massive model sizes demand heavy compute, restricting practical deployments and real-time applications. To address this, we propose TSPulse, an ultra-light pre-trained model (1M parameters) that performs disentangled masked reconstruction across spaces and abstraction levels, explicitly learning three disentangled views: temporal embeddings for fine-grained time analysis, spectral embeddings for frequency-aware fidelity, and semantic embeddings for high-level task understanding. A hybrid masking scheme further randomizes mask style and span length to avoid pre-training bias and improve robustness. Despite its compact size, TSPulse achieves strong gains across four time-series tasks: +20\% and rank-1 on TSB-AD leaderboard benchmark for reliable anomaly detection through multi-head triangulation, which correlates complementary cues across disentangled views; +25\% in similarity search as the disentangled semantic embedding remain invariant to time, scale and noise shifts, making retrieval more robust; +50\% improvement in imputation since hybrid masking exposes the model to diverse real-world corruption patterns; and +5–16\% gains in multivariate classification with TSLens, a lightweight module that selectively attends to the most informative signals across variates. Overall, TSPulse outperform models that are 10–100× larger on 75+ datasets across tasks, while delivering state-of-the-art zero-shot results with GPU-free support and efficient fine-tuning. Models and source code will be open-sourced and currently shared in the supplementary material.

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures that are trained end-to-end for specific imaging problems. Iterative methods in the first class are computationally costly and often yield suboptimal reconstruction performance, whereas unrolled architectures are generally problem-specific and require expensive training. In this work, we propose a novel non-iterative, lightweight architecture that incorporates knowledge about the forward operator (acquisition physics and noise parameters) without relying on unrolling. Our model is trained to solve a wide range of inverse problems, such as deblurring, magnetic resonance imaging, computed tomography, inpainting, and super-resolution, and works on arbitrary image sizes and channels, such as grayscale, complex, and color data. The proposed model can be easily adapted to unseen inverse problems or datasets with a few fine-tuning steps (up to a few images) in a self-supervised way, without ground-truth references. Throughout a series of experiments, we demonstrate state-of-the-art performance from medical imaging to low-photon imaging and microscopy.

Rote learning is a memorization technique based on repetition. Many researchers argue that rote learning hinders generalization because it encourages verbatim memorization rather than deeper understanding. This concern extends even to factual knowledge, which inevitably requires a certain degree of memorization. In this work, we challenge this view and demonstrate that large language models (LLMs) can, in fact, generalize over rote memorized data. We introduce a two-phase “memorize-then-generalize” framework, where the model first rote memorizes factual subject-object associations using a synthetic semantically meaningless key token and then learns to generalize by fine-tuning on a small set of semantically meaningful prompts. Extensive experiments over 8 LLMs show that the models can reinterpret rote memorized data through the semantically meaningful prompts, as evidenced by the emergence of structured, semantically aligned latent representations between the key token and the semantically meaningful prompts. This surprising finding opens the door to both effective and efficient knowledge injection as well as possible risks of repurposing the memorized data for malicious usage.

We investigate the role of learning rate scheduling in the large-scale pre-training of large language models, focusing on its influence on downstream performance after supervised fine-tuning (SFT). Decay-based learning rate schedulers are widely used to minimize pre-training loss. However, despite their widespread use, how these schedulers affect performance after SFT remains underexplored. In this paper, we examine Warmup-Stable-Only (WSO), which maintains a constant learning rate after warmup without any decay. Through experiments with 1B and 8B parameter models, we show that WSO consistently outperforms decay-based schedulers in terms of performance after SFT, even though decay-based schedulers may exhibit better performance after pre-training. The result also holds across different regimes with mid-training and over-training. Loss landscape analysis further reveals that decay-based schedulers lead models into sharper minima, whereas WSO preserves flatter minima that support adaptability. These findings indicate that applying LR decay to improve pre-training metrics may compromise downstream adaptability. Our work also provides practical guidance for training and model release strategies, highlighting that pre-training models with WSO enhances their adaptability for downstream tasks.

Large language models (LLMs) achieve strong performance across diverse tasks but suffer from high inference latency due to their autoregressive generation. Speculative Decoding (SPD) mitigates this issue by verifying candidate tokens from a smaller draft model in parallel, yet its strict exact-match verification discards many semantically valid continuations. We propose Training-Free Loosely Speculative Decoding (FLy), a novel method that loosens the rigid verification criterion by leveraging the target model’s own corrective behavior to judge whether a draft–target mismatch remains semantically valid. FLy introduces a two-tier mechanism: an entropy-level gate that identifies whether the current token allows multiple plausible alternatives or is nearly deterministic, and a token-level deferred window that distinguishes genuine errors from differently worded yet semantically correct variants. To further reduce latency, we design a multi-level acceleration strategy that accelerates not only the target model but also the drafter itself. Owing to its training-free design, FLy composes seamlessly with arbitrary draft–target pairs and generalizes across models and domains without hyperparameter re-tuning. Experiments show that FLy preserves $\geq$99\% of the target model’s accuracy while achieving an average 2.81$\times$ speedup on Llama-3.1-70B-Instruct and 5.07$\times$ speedup on the 405B variant. Notably, on out-of-domain datasets, our method remains highly effective and outperforms the training-based method EAGLE-3 by 1.62$\times$.

Most existing Time Series Foundation Models (TSFMs) use channel independent modeling and focus on capturing and generalizing temporal dependencies, while neglecting the correlations among channels or overlook the different aspects of correlations. However, these correlations play a vital role in Multivariate time series forecasting. To address this, we propose a Correlation-aware Adapter (**CoRA**), a lightweight plug-and-play method that requires only fine-tuning with TSFMs and is able to capture different types of correlations, so as to improve forecast performance. Specifically, to reduce complexity, we innovatively decompose the correlation matrix into low-rank Time-Varying and Time-Invariant components. For the Time-Varying component, we further design learnable polynomials to learn dynamic correlations by capturing trends or periodic patterns. To learn positive and negative correlations that appear only among some variables, we introduce a novel dual contrastive learning method that identifies correlations through projection layers, regulated by a Heterogeneous-Partial contrastive loss during training, without introducing additional complexity in the inference stage. Extensive experiments on 10 real-world datasets demonstrate that CoRA improves the state-of-the-art TSFMs in average forecast performance.

As large pre-trained models rapidly scale, Parameter-Efficient Fine-Tuning (PEFT) through methods like Low-Rank Adaptation (LoRA) becomes increasingly crucial. While LoRA has emerged as a cornerstone of PEFT, excelling at preserving performance with minimal additional parameters, exploring parameter-sharing mechanisms of LoRA remains critical to pushing efficiency boundaries. However, existing naive LoRA sharing methods often degrade performance due to sacrificed representational diversity and weakened model expressiveness. To overcome this issue, we conduct an in-depth analysis of pre-trained models using gradient-based proxy entropy, and uncover two critical, previously overlooked properties: Local Similarity and Layer-wise Information Heterogeneity. Building on these insights, we propose E²LoRA, a novel dual-adaptive sharing framework. It enables adaptive sharing interval partitioning, guided by inter-layer proxy entropy similarity, and adaptive rank allocation, informed by layer-wise absolute proxy entropy. This unique design leverages inherently informative properties of pre-trained models to significantly reduce parameter redundancy while maintaining or enhancing expressiveness. Comprehensive evaluations across diverse tasks, modalities, and models consistently demonstrate that E²LoRA achieves an excellent balance of efficiency and effectiveness, consistently matching or surpassing baselines with approximately 50% fewer trainable parameters.