ICLR 2026 Papers

Recently, Ainsworth et al. empirically demonstrated that, given two independently trained models, applying a parameter permutation that preserves the input–output behavior allows the two models to be connected by a low-loss linear path. When such a path exists, the models are said to achieve linear mode connectivity (LMC). Prior studies, including Ainsworth et al., have reported that achieving LMC requires not only an appropriate permutation search but also sufficiently wide models (e.g., a 32 $\times$ width multiplier for ResNet-20). This is broadly believed to be because increasing the model width ensures a large enough space of candidate permutations, increasing the chance of finding one that yields LMC. In this work, we empirically demonstrate that, even without any permutations, simply widening the models is sufficient for achieving LMC when using a suitable softmax temperature calibration. We further explain why this phenomenon arises by analyzing intermediate layer outputs. Specifically, we introduce layerwise exponentially weighted connectivity (LEWC), which states that the output of each layer of the merged model can be represented as an exponentially weighted sum of the outputs of the corresponding layers of the original models. Consequently the merged model's output matches that of an ensemble of the original models, which facilitates LMC. To the best of our knowledge, this work is the first to show that widening the model not only facilitates nonlinear mode connectivity, as suggested in prior research, but also significantly increases the possibility of achieving linear mode connectivity.

Permutation equivariant neural networks employing parameter-sharing schemes have emerged as powerful models for leveraging a wide range of data symmetries, significantly enhancing the generalization and computational efficiency of the resulting models. Recently, Kolmogorov-Arnold Networks (KANs) have demonstrated promise through their improved interpretability and expressivity compared to traditional architectures based on MLPs. While equivariant KANs have been explored in recent literature for a few specific data types, a principled framework for applying them to data with permutation symmetries in a general context remains absent. This paper introduces Function Sharing KAN (FS-KAN), a principled approach to constructing equivariant and invariant KA layers for arbitrary permutation symmetry groups, unifying and significantly extending previous work in this domain. We derive the basic construction of these FS-KAN layers by generalizing parameter-sharing schemes to the Kolmogorov-Arnold setup and provide a theoretical analysis demonstrating that FS-KANs have the same expressive power as networks that use standard parameter-sharing layers, allowing us to transfer well-known and important expressivity results from parameter-sharing networks to FS-KANs. Empirical evaluations on multiple data types and symmetry groups show that FS-KANs exhibit superior data efficiency compared to standard parameter-sharing layers, by a wide margin in certain cases, while preserving the interpretability and adaptability of KANs, making them an excellent architecture choice in low-data regimes.

Large Language Models (LLM) have gained significant attention. KV cache, stored to avoid quadratic complexity of attention, becomes a bottleneck due to the demands for long-context. Sparse attention (SA) has been proposed to address this by only selecting critical KVs for attention, which may degrade model quality in less sparse scenarios. To improve quality, rather than selecting more KVs, this paper reveals another perspective by estimating the contributions of remaining KVs, called Residual Estimation. We find that attention logits (before softmax) exhibit substantial redundancy due to its inherent low-rank nature. We perform Singular Value Decomposition (SVD) on logits matrix in prefilling and find the spectral dominance of principal singular value and its linearly scaling property with sequence length. These imply that increasing sequence length leads to replication-like logits growth with significant redundancy. However, it is impossible to perform SVD at each decoding step in practice due to its heavy costs. To this end, we propose RESA, a training-free framework compensating SA's output with an estimated low-rank prior of logits. RESA introduces (i) a Prior Estimator that derives a prior distribution from a typical query as a rank-1 approximation at the end of prefilling, and (ii) an Online Aggregator that fuses the prior with SA at each decoding step via lightweight scaling and merging. Besides, we further show that RESA's effect comes from priors being used as attention bias for knowledge injection. Extensive experiments show that without extra overheads, RESA improves model quality by up to 26\% across various tasks with the same KV budget compared to state-of-the-art. Moreover, RESA maintains the same quality with up to 33.2\% KV budget reduction and 1.23$\times$ attention throughput improvement.

Parameter-efficient fine-tuning techniques such as Low-rank Adaptation (LoRA) enable large language models (LLMs) to adapt to downstream tasks efficiently. Federated learning (FL) further facilitates this process by enabling collaborative fine-tuning across distributed clients without sharing private data. However, the use of two separate low-rank matrices in LoRA for federated fine-tuning introduces two types of challenges. The first challenge arises from the error induced by separately aggregating those two low-rank matrices. The second challenge occurs even when the product of two low-rank matrices is aggregated. The server needs to recover factors via matrix decomposition, which is non-unique and can introduce decomposition drift. To tackle the aforementioned challenges, we propose FLoRG, a federated fine-tuning framework which employs a single low-rank matrix for fine-tuning and aggregates its Gram matrix (i.e., the matrix of inner products of its column vectors), eliminating the aggregation error while also reducing the communication overhead. FLoRG minimizes the decomposition drift by introducing a Procrustes alignment approach which aligns the decomposed matrix between consecutive fine-tuning rounds for consistent updates. We theoretically analyze the convergence of FLoRG and prove that adopting the Procrustes alignment results in a tighter convergence bound. Experimental results across multiple LLM fine-tuning benchmarks demonstrate that FLoRG outperforms four state-of-the-art baseline schemes in the downstream task accuracy and can reduce the communication overhead by up to 2041$\times$.

Large language models, constrained by the fixed-depth Transformer architecture, struggle to solve complex reasoning tasks in an end-to-end manner. Existing approaches, such as Chain of Thought, improve reasoning depth to some extent but rely heavily on natural language generation, with computational costs increasing rapidly as the length of the generated sequence grows. To address these limitations, we propose ChainGPT, a dual-reasoning model that shifts reasoning into latent computational space. Within each layer, ChainGPT employs multi-substep state updates combined with state-guided sparse attention, enabling deep local computation and efficient long-range modeling without quadratic costs. Across layers, recurrent depth approach iteratively refine latent states, supported by adaptive training and stopping strategies that balance reasoning depth against computational budget. Theoretically, we show that ChainGPT can, in principle, simulate general computation, and empirically it delivers consistent improvements over comparable models, including on reasoning tasks that remain challenging for existing systems. By unifying efficiency and reasoning ability, ChainGPT provides a principled foundation for next-generation language models.

Neural audio codecs are foundational to speech language models. It is expected to have a low frame rate and decoupled semantic and acoustic information. A lower frame rate codec can reduce the computational cost of speech language models by shortening the sequence length. Recent studies have developed 12.5Hz low-frame-rate audio codecs, but even lower frame rate codecs remain underexplored. We find that pushing existing audio codecs to very low frame rates loses much semantic information. We suggest that low-frame-rate codecs' limitations are in both insufficient semantic decoupling and insufficient time resolution at capturing transient phonetic details. This paper introduces **FlexiCodec** to address this limitation. FlexiCodec improves semantic preservation with a **dynamic frame rate** approach and introduces a novel architecture featuring an **ASR feature-assisted dual stream** encoding and Transformer bottlenecks. With dynamic frame rates, it uses less frames at information-sparse regions through adaptively merging semantically similar frames. A dynamic frame rate also allows FlexiCodec to support inference-time **controllable frame rates** between 3Hz and 12.5Hz. Experiments on **6.25Hz, 8.3Hz and 12.5Hz** average frame rates confirm that FlexiCodec excels over baseline systems in semantic information preservation and delivers a high audio reconstruction quality. We also validate the effectiveness of FlexiCodec in language model-based TTS. Demos are available at: https://flexicodec.github.io.

In this paper, we propose a novel node-level graph diffusion method with low-rank feature learning for few-shot node classification (FSNC), termed Low-Rank Few-Shot Graph Diffusion Model or LR-FGDM. LR-FGDM first employs a novel Few-Shot Graph Diffusion Model (FGDM) as a node-level graph generative method to generate an augmented graph with an enlarged support set, then performs low-rank transductive classification to obtain the few-shot node classification results. Our graph diffusion model, FGDM, comprises two components, the Hierarchical Graph Autoencoder (HGAE) with an efficient hierarchical edge reconstruction method and a new prototypical regularization, and the Latent Diffusion Model (LDM). The low-rank regularization is robust to the noise inherently introduced by the diffusion model and empirically inspired by the Low Frequency Property. We also provide a strong theoretical guarantee justifying the low-rank regularization for the transductive classification in few-shot learning. Extensive experimental results evidence the effectiveness of LR-FGDM for few-shot node classification, which outperforms the current state-of-the-art. The code of the LR-FGDM is available at \url{https://anonymous.4open.science/r/LR-FGDM/}.

Quantization techniques such as BitsAndBytes, AWQ, and GPTQ are widely used as a standard method in deploying large language models but often degrades accuracy when using low-bit representations, e.g., 4 bits. Low-rank correction methods (e.g., LQER, QERA, ASER) has been proposed to mitigate this issue, however, they restore all layers and insert error-correction modules into every decoder block, which increases latency and memory overhead. To address this limitation, we propose GlowQ, a group-shared low-rank approximation for quantized LLMs that caches a single shared right factor per input-sharing group and restores only the groups or layers that yield the highest accuracy benefit. GlowQ computes the high-precision projection once per input-sharing group and reuses it across its modules, reducing parameter and memory overhead, and retaining the expressivity of layer-specific corrections. We also propose a selective variant, GlowQ-S, that applies the cached shared module only where it provides the largest benefit. Compared with strong baselines, our approach reduces TTFB by \(5.6\%\) and increases throughput by \(9.6\%\) on average, while reducing perplexity on WikiText-2 by \(0.17\%\) and increasing downstream accuracy by 0.42 percentage points. The selective model GlowQ-S further reduces latency, cutting TTFB by \(23.4\%\) and increasing throughput by \(37.4\%\), while maintaining accuracy within 0.2 percentage points on average.

Parameter-Efficient Fine-Tuning (PEFT) techniques, such as Low-Rank Adaptation (LoRA) and its variants, have emerged as critical tools for adapting large pretrained models under limited computational resources. However, a notable performance gap persists between these LoRA methods and Full Fine-Tuning (FFT). In this paper, we investigate a key yet overlooked cause of this gap: the relationship between LoRA's low-rank adaptation subspace and true effective update directions of FFT gradients, which we define as the **gradient intrinsic dimensionality**. To systematically quantify this dimension, we first propose a novel entropy-based estimator, uncovering substantial discrepancies (up to more than 100x) between the rank of LoRA and the gradient intrinsic dimensionality. Motivated by this finding, we introduce **RaLoRA**, which adaptively aligns the ranks of LoRA adapters with layer-specific gradient intrinsic dimensions, without increasing the number of overall parameters. We further extend this approach into **RaLoRA-Pro**, integrating intra-layer rank alignment and inter-layer parameter reallocation guided by loss sensitivity, enabling finer-grained capacity relocation under comparable parameters. Extensive experiments demonstrate the effectiveness of our methods. Specifically, compared to vanilla LoRA, our methods achieve more than +5\% improvement on GLUE, +0.57 on MT-Bench, +5.23\% on GSM8K, +5.69\% on HumanEval, and +1.58\% on image classification, confirming consistent and substantial performance gains across diverse tasks and modalities.

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph (IBG), a low-rank factorization of large directed graphs based on combinations of intersecting bipartite components, each consisting of a pair of communities, for source and target nodes. By giving less weight to non-edges, we show how an IBG can efficiently approximate any graph, sparse or dense. Specifically, we prove a constructive version of the weak regularity lemma: for any chosen accuracy, every graph can be approximated by a dense IBG whose rank depends only on that accuracy. This improves over prior versions of the lemma, where the rank depended on the number of nodes for sparse graphs. Our method allows for efficient approximation of large graphs that are both directed and sparse, a crucial capability for many real-world applications. We then introduce a graph neural network architecture operating on the IBG representation of the graph and demonstrating competitive performance on node classification, spatio-temporal graph analysis, and knowledge graph completion, while having memory and computational complexity linear in the number of nodes rather than edges.

Dual Modular Redundancy (DMR) is a highly effective mechanism for detecting silent data corruption (SDC)—a critical reliability concern in large language model (LLM) training—by executing each operation twice. However, its high computation overhead has prevented practical deployment at scale. In this paper, we present SpareTrain, an LLM training system that achieves complete DMR with minimal overhead by repurposing the activation checkpointing mechanism and exploiting idle GPU time. Evaluations on up to 32 H200 GPUs show that SpareTrain improves throughput by 12–35\% over naive DMR, corresponding to only 3–14\% overhead compared to unprotected training, while maintaining full DMR error detection capabilities.

We introduce MoSA, a new parameter-efficient fine-tuning (PEFT) method that replaces low-rank factorization with randomized, fine-grained sharing of weight updates. Each adapted weight matrix is constructed by broadcasting a small set of learned scalars over a fixed tessellation, a pre-defined group assignment of weight entries of the weight matrix, producing expressive changes under the same parameter budget as low-rank adaptation (LoRA). MoSA requires no architectural changes and can be merged into the base model for zero-overhead inference. Across diverse language understanding and generation tasks, MoSA matches or surpasses strong PEFT baselines under strictly matched budgets. Analyses and ablations indicate that non-local parameter sharing acts as an effective regularizer, and that grouping design and budget allocation govern the expressivity–efficiency trade-off. These results position MoSA as a simple, scalable alternative to LoRA.

With the rapid development of large language models (LLMs), identifying efficient strategies for training such large-scale systems has become increasingly critical. Although LLMs have achieved remarkable success across diverse applications, the necessity of maintaining full dense matrices during pre-training has been questioned, giving rise to parameter-efficient sparse pre-training methods which retains parameter-efficiency in both training and inference. These methods can be further divided into connectivity sparse training and spectral sparse training, with dynamic connectivity sparse training and low-rank factorization emerging as representative approaches for the two branches. However, a unified framework that effectively combines the strengths of both has yet to be established. In this work, we observe that the cancellation effect between the sparse and low-rank branches may limit the expressivity of the model, manifesting as output conflicts when the two components are combined. To address this issue, we propose a novel scheme that integrates dynamic sparse training with low-rank training, introducing a simple yet effective $\textbf{alignment loss}$ to mitigate the disagreement between the two branches and promote better collaboration. We validate this scheme by combining a representative dynamic sparse training method, CHTs, with low-rank training, resulting in a new parameter-efficient training approach termed $\textbf{CHTsL}$. The method is evaluated on LLaMA60M and LLaMA130M using the OpenWebText and C4 datasets, where only 10\%, 20\%, and 30\% of the parameters are preserved compared to dense training. Experimental results demonstrate that our proposed scheme effectively alleviates the cancellation effect and improves training stability and performance compared to the naive combination of sparse and low-rank components. Also, the new scheme enables CHTsL to consistently outperform other parameter-efficient sparse training methods under the same parameter budget, achieving performance most close to dense training.

Using a nearly-frozen pretrained model, the continual representation learning paradigm reframes parameter updates as a similarity-matching problem to mitigate catastrophic forgetting. However, directly leveraging pretrained features for downstream tasks often suffers from multicollinearity in the similarity-matching stage, and more advanced methods can be computationally prohibitive for real-time, low-latency applications. Inspired by the fly olfactory circuit, we propose Fly-CL, a bio-inspired framework compatible with a wide range of pretrained backbones. Fly-CL substantially reduces training time while achieving performance comparable to or exceeding that of current state-of-the-art methods. We theoretically show how Fly-CL progressively resolves multicollinearity, enabling more effective similarity matching with low time complexity. Extensive simulation experiments across diverse network architectures and data regimes validate Fly-CL’s effectiveness in addressing this challenge through a biologically inspired design.

Deploying large language models (LLMs) on mobile platforms faces significant challenges due to the limited memory and shared computational resources of the device. Resource availability may be an issue as it is directly impacted by on the current device workload, adding to the uncertainty of model deployment. We introduce UniQL, a unified post-training quantization and low-rank compression framework, with on-device configurable pruning rates for edge LLMs. UniQL is a general framework that integrates quantization and low-rank compression for Transformers, State Space Models (SSMs), and hybrid models to cater to diverse edge applications. In our proposed joint framework, we introduce an efficient structured weight-sorting that speeds up the computation by 20×, quantization-aware singular value decomposition (SVD) decompositions to minimize the quantization errors, state-aware weight sorting for SSMs, and a fused rotary embedding (RoPE) kernel for the pruned models. Our framework performs weight-sorting, fine-tuning, and quantization in the cloud in a one-shot fashion, while enabling on-device configurable pruning rates up to 35%. Our experiments show that quantized and pruned models offer a memory reduction of 4×–5.7× and a token throughput improvement of 2.7×–3.4×, maintaining accuracy within 5% of the original models at 15% pruning rates across Transformers (Llama3 and Qwen2.5), SSMs (Mamba2), and hybrid models (Nemotron-H and Bamba-v2). The code and quantized models will be released at: https://github.com/.

Large language models are increasingly deployed in settings where newtasks arrive continuously, yet existing parameter-efficient finetuning (PEFT) methods either bloat linearly with the task horizon or sacrifice deep adaptation, leaving catastrophic forgetting unresolved. We aim to achieve memory-constant, on-the-fly adaptation for a frozen LLM facing an unbounded stream of tasks. To this end we propose Meta-Unified Contrastive Finetuning(Meta-UCF), which encodes each task into a lightweight layer-normalised mean embedding and feeds it to a single hypernetwork that instantly generates rank-r LoRA updates for every transformer layer; a meta-contrastive coupled with orthogonality objective further steers task embeddings into near-orthogonal directions, preserving past knowledge without inner-loop gradients. On four benchmark streams—Std-CL 5, Seq-GLUE 7, Long-CL 15 and TRACE-8—Meta-UCF raises average accuracy by up to 2.2 pp and cuts forgetting by 13% relative to the strongest LoRA baseline, while using the parameters of a single adapter. By decoupling continual learning from parameter growth, Meta-UCF provides a practical path toward scalable, low-resource lifelong language modelling.

Large Language Models (LLMs) have revolutionized numerous fields, yet their adaptation to specialized tasks in privacy-sensitive domains such as healthcare and finance remains constrained due to the scarcity of accessible training data caused by stringent privacy requirements. Secure Multi-party Computation (MPC)-based privacy-preserving machine learning provides theoretical guarantees for the privacy of model parameters and data. However, its application to LLMs has been predominantly limited to inference, as fine-tuning introduces significant efficiency challenges, particularly in backward propagation, optimizer, and self-attention operations. To address these challenges, we propose SecP-Tuning, the first MPC-based framework designed for efficient, privacy-preserving prompt tuning of LLMs. SecP-Tuning innovatively integrates Forward-only Tuning (FoT) through the ''data owner-server interaction" paradigm, effectively removing the need for privacy-preserving computations in backward propagation and optimization processes. Furthermore, it devises an efficient privacy-preserving Random Feature Attention (RFA), effectively mitigating the computational complexity of softmax-based self-attention and circumventing MPC-incompatible nonlinear operations. Experimental results demonstrate that, compared to full-Parameter Supervised Fine-Tuning (SFT) and gradient-based prompt tuning, SecP-Tuning achieves approximately 12$\times$ and 16$\times$ end-to-end acceleration, as well as 18$\times$ and 20$\times$ reductions in communication overhead, respectively. Moreover, it delivers performance comparable to gradient-based methods across multiple few-shot tasks. Additionally, the ''black-box/API-style" privacy-preserving tuning paradigm of SecP-Tuning effectively avoids memory leakage risks caused by gradient/parameter transmission, thereby striking an optimal balance between efficiency, accuracy, deployability, and privacy.

Parameter-efficient continual learning has emerged as a promising approach for large language models (LLMs) to mitigate catastrophic forgetting while enabling adaptation to new tasks. Current Low-Rank Adaptation (LoRA) continual learning techniques often retain and freeze previously learned LoRAs or generate data representations to overcome forgetting, typically utilizing these to support new LoRAs learn new tasks. However, these methods not only ignore growing computational memory with tasks and limited storage space but also suffer from potential task interference due to the lack of effective LoRA merging mechanisms. In this paper, we propose a novel continual learning method that orthogonally initializes and sequentially merges LoRAs updates into a single unified LoRA. Our method leverages orthogonal basis extraction from previously learned LoRA to initialize the learning of new tasks, further exploits the intrinsic asymmetry property of LoRA components by using a time-aware scaling mechanism to balance new and old knowledge during continual merging. Our approach maintains constant memory complexity with respect to the number of tasks, minimizes interference between past and new tasks via orthogonal basis initialization, and improves performance over asymmetric LoRA merging via adaptive scaling. We provide theoretical analysis to justify our design and conduct extensive experiments across diverse continual learning benchmarks using various Llama models, demonstrating the effectiveness and efficiency of our method.

Federated fine-tuning enables Large Language Models (LLMs) to adapt to downstream tasks while preserving data privacy, but its resource-intensive nature severely limits deployment on edge devices. In this paper, we introduce Developmental Federated Tuning (DevFT), a resource-efficient approach inspired by cognitive development that progressively builds a powerful LLM from a compact foundation. DevFT decomposes the fine-tuning process into developmental stages, each optimizing a submodel with increasing parameter capacity. Knowledge acquired in earlier stages is transferred to subsequent submodels, providing optimized initialization parameters that prevent convergence to local minima and accelerate training. This paradigm mirrors human learning, gradually constructing a comprehensive knowledge structure while refining existing skills. To efficiently build stage-specific submodels, DevFT introduces deconfliction-guided layer grouping and differential-based layer fusion to distill essential information and construct representative layers. Evaluations across multiple benchmarks demonstrate that DevFT significantly outperforms state-of-the-art methods, achieving up to $\textbf{4.59$\times$}$ faster convergence, $\textbf{10.67$\times$}$ reduction in communication overhead, and $\textbf{9.07}$\% average performance improvement, while maintaining compatibility with existing federated fine-tuning approaches.