Low-Rank Adaptation

We propose a novel gradient-based framework for learning parameterized quantum circuits (PQCs) in the presence of Pauli noise in gate operation. The key innovation in our framework is the simultaneous optimization of model parameters and learning of an inverse noise channel, specifically designed to mitigate Pauli noise. Our parametrized inverse noise model utilizes the Pauli-Lindblad equation and relies on the principle underlying the Probabilistic Error Cancellation (PEC) protocol to learn an effective and scalable mechanism for noise mitigation. In contrast to conventional approaches that apply predetermined inverse noise models during execution, our method systematically mitigates Pauli noise by dynamically updating the inverse noise parameters in conjunction with the model parameters, facilitating task-specific noise adaptation throughout the learning process. We employ proximal stochastic gradient descent (proximal SGD) to ensure that updates are bounded within a feasible range to ensure stability. This approach allows the model to converge efficiently to a stationary point, balancing the trade-off between noise mitigation and computational overhead, resulting in a highly adaptable quantum model that performs robustly in noisy quantum environments. Our framework is well-suited to near-term quantum devices in the noisy intermediate-scale quantum (NISQ) era, where noise is a significant challenge.

While sparse coding plays an important role in promoting the efficiency of biological neural systems, it has not been fully utilized by artificial models as the activation sparsity is not well suited to the current structure of deep networks. Spiking Neural Networks (SNNs), with their event-driven characteristics, offer a more natural platform for leveraging activation sparsity. In this work, we specifically target the reduction of neuronal activity, which directly leads to lower computational cost and facilitates efficient SNN deployment on Neuromorphic hardware. We begin by analyzing the limitations of existing activity regularization methods and identifying critical challenges in training sparse SNNs. To address these issues, we propose a modified neuron model, AT-LIF, coupled with a threshold adaptation technique that stabilizes training and effectively suppresses spike activity. Through extensive experiments on multiple datasets, we demonstrate that our approach achieves significant reductions in average firing rates and synaptic operations without sacrificing much accuracy. Furthermore, we show that our method complements weight-based pruning techniques and successfully trains an SNN with only 0.06 average firing rate and 2.22M parameters on ImageNet, highlighting its potential for building highly efficient and scalable SNN models. Code is available at https://github.com/putshua/Activity-Pruning-SNN.

Accurate estimation of background error (i.e., forecast error) distribution is critical for effective data assimilation (DA) in numerical weather prediction (NWP). In state-of-the-art operational DA systems, it is common to account for the temporal evolution of background errors by employing hybrid methods, which blend a static climatological covariance with a flow-dependent ensemble-derived component. While effective to some extent, these methods typically assume Gaussian-distributed errors and rely heavily on hand-crafted covariance structures and domain expertise, limiting their ability to capture the complex, non-Gaussian nature of atmospheric dynamics. In this work, we propose LoRA-EnVar, a novel hybrid ensemble variational DA algorithm that integrates low-rank adaptation (LoRA) into a deep generative modeling framework. We first learn a climatological background error distribution using a variational autoencoder (VAE) trained on historical data. To incorporate flow-dependent uncertainty, we introduce LoRA modules that efficiently adapt the learned distribution in response to flow-dependent ensemble perturbations. Our approach supports online finetuning, enabling dynamic updates of the background error distribution without catastrophic forgetting. We validate LoRA-EnVar in high-resolution assimilation settings using the FengWu forecast model and simulated observations from ERA5 reanalysis. Experimental results show that LoRA-EnVar significantly improves assimilation accuracy over models assuming static background error distribution and achieves comparable or better performance than full finetuning while reducing the number of trainable parameters by three orders of magnitude. This demonstrates the potential of parameter-efficient adaptation for scalable, non-Gaussian DA in operational meteorology.

Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and noticeable performance degradation, due to inconsistent and imbalanced weight updates induced by its nonunique low-rank factorizations. To overcome these limitations, this article identifies the optimal low-rank factorization per step that minimizes an upper bound on the loss. The resultant refactored low-rank adaptation (RefLoRA) method promotes a flatter loss landscape, along with consistent and balanced weight updates, thus speeding up stable convergence. Extensive experiments evaluate RefLoRA on natural language understanding, and commonsense reasoning tasks with popular large language models including DeBERTaV3, LLaMA-7B, LLaMA2-7B and LLaMA3-8B. The numerical tests corroborate that RefLoRA converges faster, outperforms various benchmarks, and enjoys negligible computational overhead compared to state-of-the-art LoRA variants.

Ultra-high dynamic range (UHDR) scenes exhibit pronounced exposure disparities between bright and dark regions. Such conditions are Ultra-high dynamic range (UHDR) scenes exhibit significant exposure disparities between bright and dark regions. Such conditions are commonly encountered in nighttime scenes with light sources. Even with standard exposure settings, a bimodal intensity distribution with boundary peaks often emerges, making it difficult to preserve both highlight and shadow details simultaneously. RGB-based bracketing methods can capture details at both ends using short-long exposure pairs, but are susceptible to misalignment and ghosting artifacts. We found that a short-exposure image already retains sufficient highlight detail. The main challenge of UHDR reconstruction lies in denoising and recovering information in dark regions. In comparison to the RGB images, RAW images, thanks to their higher bit depth and more predictable noise characteristics, offer greater potential for addressing this challenge. This raises a key question: can we learn to see everything in UHDR scenes using only a single short-exposure RAW image? In this study, we rely solely on a single short-exposure frame, which inherently avoids ghosting and motion blur, making it particularly robust in dynamic scenes. To achieve that, we introduce UltraLED, a two-stage framework that performs exposure correction via a ratio map to balance dynamic range, followed by a brightness-aware RAW denoiser to enhance detail recovery in dark regions. To support this setting, we design a 9-stop bracketing pipeline to synthesize realistic UHDR images and contribute a corresponding dataset based on diverse scenes, using only the shortest exposure as input for reconstruction. Extensive experiments show that UltraLED significantly outperforms existing single-frame approaches. Our code and dataset are made publicly available at https://srameo.github.io/projects/ultraled.

Mixture-of-experts networks (MoEs) have demonstrated remarkable efficiency in modern deep learning. Despite their empirical success, the theoretical foundations underlying their ability to model complex tasks remain poorly understood. In this work, we conduct a systematic study of the expressive power of MoEs in modeling complex tasks with two common structural priors: low-dimensionality and sparsity. For shallow MoEs, we prove that they can efficiently approximate functions supported on low-dimensional manifolds, overcoming the curse of dimensionality. For deep MoEs, we show that $\mathcal{O}(L)$-layer MoEs with $E$ experts per layer can approximate piecewise functions comprising $E^L$ pieces with compositional sparsity, i.e., they can exhibit an exponential number of structured tasks. Our analysis reveals the roles of critical architectural components and hyperparameters in MoEs, including the gating mechanism, expert networks, the number of experts, and the number of layers, and offers natural suggestions for MoE variants.

Deploying large language models (LLMs) often faces challenges from substantial memory and computational costs. Quantization offers a solution, yet performance degradation in the sub-1-bit regime remains particularly difficult. This paper introduces LittleBit, a novel method for extreme LLM compression. It targets levels like 0.1 bits per weight (BPW), achieving nearly 31$\times$ memory reduction, e.g., Llama2-13B to under 0.9 GB. LittleBit represents weights in a low-rank form using latent matrix factorization, subsequently binarizing these factors. To counteract information loss from this extreme precision, it integrates a multi-scale compensation mechanism. This includes row, column, and an additional latent dimension that learns per-rank importance. Two key contributions enable effective training: Dual Sign-Value-Independent Decomposition (Dual-SVID) for quantization-aware training (QAT) initialization, and integrated Residual Compensation to mitigate errors. Extensive experiments confirm LittleBit's superiority in sub-1-bit quantization: e.g., its 0.1 BPW performance on Llama2-7B surpasses the leading method's 0.7 BPW. LittleBit establishes a new, viable size-performance trade-off—unlocking a potential 11.6$\times$ speedup over FP16 at the kernel level—and makes powerful LLMs practical for resource-constrained environments.

Large Language Models (LLMs) capable of handling extended contexts are in high demand, yet their inference remains challenging due to substantial Key-Value (KV) cache size and high memory bandwidth requirements. Previous research has demonstrated that KV cache exhibits low-rank characteristics within the hidden dimension, suggesting the potential for effective compression. However, due to the widely adopted Rotary Position Embedding (RoPE) mechanism in modern LLMs, naive low‑-rank compression suffers severe accuracy degradation or creates a new speed bottleneck, as the low-rank cache must first be reconstructed in order to apply RoPE. In this paper, we introduce two key insights: first, the application of RoPE to the key vectors increases their variance, which in turn results in a higher rank; second, after the key vectors are transformed into the latent space, they largely maintain their representation across most layers. Based on these insights, we propose the Sparse Attention in Latent Space (SALS) framework. SALS projects the KV cache into a compact latent space via low-rank projection, and performs sparse token selection using RoPE-free query--key interactions in this space. By reconstructing only a small subset of important tokens, it avoids the overhead of full KV cache reconstruction. We comprehensively evaluate SALS on various tasks using two large-scale models: LLaMA2-7b-chat and Mistral-7b, and additionally verify its scalability on the RULER-128k benchmark with LLaMA3.1-8B-Instruct. Experimental results demonstrate that SALS achieves SOTA performance by maintaining competitive accuracy. Under different settings, SALS achieves 6.4-fold KV cache compression and 5.7-fold speed-up in the attention operator compared to FlashAttention2 on the 4K sequence. For the end-to-end throughput performance, we achieves 1.4-fold and 4.5-fold improvement compared to GPT-fast on 4k and 32K sequences, respectively. The source code will be publicly available in the future.

Test-time adaptation aims to improve model robustness under distribution shifts by adapting models with access to unlabeled target samples. A primary cause of performance degradation under such shifts is the model’s reliance on features that lack a direct causal relationship with the prediction target. We introduce Test-time Adaptation by Causal Trimming (TACT), a method that identifies and removes non-causal components from representations for test distributions. TACT applies data augmentations that preserve causal features while varying non-causal ones. By analyzing the changes in the representations using Principal Component Analysis, TACT identifies the highest variance directions associated with non-causal features. It trims the representations by removing their projections on the identified directions, and uses the trimmed representations for the predictions. During adaptation, TACT continuously tracks and refines these directions to get a better estimate of non-causal features. We theoretically analyze the effectiveness of this approach and empirically validate TACT on real-world out-of-distribution benchmarks. TACT consistently outperforms state-of-the-art methods by a significant margin.

Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: \textit{can we identify/synthesize linear transformations from a minimal set of geometric primitives?} Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors---geometric objects encoding oriented planes---and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only $\mathcal{O}(\log^2 d)$ parameters, versus $\mathcal{O}(d^2)$ required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, our rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.

Recent studies suggest that context-aware low-rank approximation is a useful tool for compression and fine-tuning of modern large-scale neural networks. In this type of approximation, a norm is weighted by a matrix of input activations, significantly improving metrics over the unweighted case. Nevertheless, existing methods for neural networks suffer from numerical instabilities due to their reliance on classical formulas involving explicit Gram matrix computation and their subsequent inversion. We demonstrate that this can degrade the approximation quality or cause numerically singular matrices. To address these limitations, we propose a novel _inversion-free regularized framework_ that is based entirely on stable decompositions and overcomes the numerical pitfalls of prior art. Our method can handle all possible challenging scenarios: (1) when calibration matrices exceed GPU memory capacity, (2) when input activation matrices are nearly singular, and even (3) when insufficient data prevents unique approximation. For the latter, we prove that our solution converges to a desired approximation and derive explicit error bounds.

Graph Neural Networks \texttt{(GNNs)} excel at jointly modeling node features and topology, yet their \emph{black-box} nature limits their adoption in real-world applications where interpretability is desired. Inspired by the success of interpretable Neural Additive Models \texttt{(NAM)} for tabular data, Graph Neural Additive Network \texttt{(GNAN)} extends the additive modeling approach to graph data to overcome limitations of GNNs. While being interpretable, \texttt{GNAN} representation learning overlooks the importance of local aggregation and more importantly suffers from parameter complexity. To mitigate the above challenges, we introduce Graph Neural Additive Model with Random Fourier Features (\texttt{G-NAMRFF}), a lightweight, self‐interpretable graph additive architecture. \texttt{G-NAMRFF} represents each node embedding as the sum of feature‐wise contributions where contributions are modeled via a \emph{Gaussian process} \texttt{(GP)} with a graph- and feature-aware kernel. Specifically, we construct a kernel using Radial Basis Function (\texttt{RBF}) with graph structure induced by Laplacian and learnable Finite Impulse Response (\texttt{FIR}) filter. We approximate the kernel using Random Fourier Features (\texttt{RFFs}) which transforms the \texttt{GP} prior to a Bayesian formulation, which are subsequently learnt using a single layer neural network with size equal to number of \texttt{RFF} features. \texttt{G-NAMRFF} is light weight with $168\times$ fewer parameters compared to \texttt{GNAN}. Despite its compact size, \texttt{G-NAMRFF} matches or outperforms state-of-the-art \texttt{GNNs} and \texttt{GNAN} on node and graph classification tasks, delivering real-time interpretability without sacrificing accuracy.

Low-bit floating-point (FP) formats, such as FP8, provide significant acceleration and memory savings in model training thanks to native hardware support on modern GPUs and NPUs. However, we analyze that FP8 quantization offers speedup primarily for large-dimensional matrix multiplications, while inherent quantization overheads diminish speedup when applied to low-rank adaptation (LoRA), which uses small-dimensional matrices for efficient fine-tuning of large language models (LLMs). To address this limitation, we propose FALQON, a novel framework that eliminates the quantization overhead from separate LoRA computational paths by directly merging LoRA adapters into an FP8-quantized backbone during fine-tuning. Furthermore, we reformulate the forward and backward computations for merged adapters to significantly reduce quantization overhead, and introduce a row-wise proxy update mechanism that efficiently integrates substantial updates into the quantized backbone. Experimental evaluations demonstrate that FALQON achieves approximately a 3$\times$ training speedup over existing quantized LoRA methods with a similar level of accuracy, providing a practical solution for efficient large-scale model fine-tuning. Moreover, FALQON’s end-to-end FP8 workflow removes the need for post-training quantization, facilitating efficient deployment. Code is available at https://github.com/iamkanghyunchoi/falqon.

Learning-to-learn or meta-learning focuses on developing algorithms that leverage prior experience to quickly acquire new skills or adapt to novel environments. A crucial component of meta-learning is representation learning, which aims to construct data representations capable of transferring knowledge across multiple tasks—a critical advantage in data-scarce settings. We study how representation learning can improve the efficiency of bandit problems. We consider $T$ $d$-dimensional linear bandits that share a common low-dimensional linear representation. We provide provably fast, sample-efficient algorithms to address the two key problems in meta-learning: (1) learning a common set of features from multiple related bandit tasks and (2) transferring this knowledge to new, unseen bandit tasks. We validated the theoretical results through numerical experiments using real-world and synthetic datasets, comparing them against benchmark algorithms.

In this paper, we address the challenges associated with merging low-rank adaptations of large neural networks. With the rise of parameter-efficient adaptation techniques, such as Low-Rank Adaptation (LoRA), model fine-tuning has become more accessible. While fine-tuning models with LoRA is highly efficient, existing merging methods often sacrifice this efficiency by merging fully-sized weight matrices. We propose the Core Space merging framework, which enables the merging of LoRA-adapted models within a common alignment basis, thereby preserving the efficiency of low-rank adaptation while substantially improving accuracy across tasks. We further provide a formal proof that projection into Core Space ensures no loss of information and provide a complexity analysis showing the efficiency gains. Extensive empirical results demonstrate that Core Space significantly improves existing merging techniques and achieves state-of-the-art results on both vision and language tasks while utilizing a fraction of the computational resources. Codebase is available at https://github.com/apanariello4/core-space-merging.

Many online learning applications adopt the stochastic bandit problem with a linear reward model, where the unknown parameter exhibits a succinct structure. We study minimax regret lower bounds which allow to know whether more efficient algorithms can be proposed. We introduce a general definition of succinctness and propose a novel framework for constructing minimax regret lower bounds based on an information-regret trade-off. When applied to entry-sparse vectors, our framework sharpens a recent lower bound by (Hao et al, NeurIPS 2020). We further apply our framework to derive novel results. To the best of our knowledge, we provide the first lower bounds for the group-sparse and low-rank matrix settings.

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, \emph{are their learned solutions really equivalent?} We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension -- by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.

Current AI advances largely rely on scaling neural models and expanding training datasets to achieve generalization and robustness. Despite notable successes, this paradigm incurs significant environmental, economic, and ethical costs, limiting sustainability and equitable access. Inspired by biological sensory systems, where adaptation occurs dynamically at the input (e.g., adjusting pupil size, refocusing vision)—we advocate for adaptive sensing as a necessary and foundational shift. Adaptive sensing proactively modulates sensor parameters (e.g., exposure, sensitivity, multimodal configurations) at the input level, significantly mitigating covariate shifts and improving efficiency. Empirical evidence from recent studies demonstrates that adaptive sensing enables small models (e.g., EfficientNet-B0) to surpass substantially larger models (e.g., OpenCLIP-H) trained with significantly more data and compute. We (i) outline a roadmap for broadly integrating adaptive sensing into real-world applications spanning humanoid, healthcare, autonomous systems, agriculture, and environmental monitoring, (ii) critically assess technical and ethical integration challenges, and (iii) propose targeted research directions, such as standardized benchmarks, real-time adaptive algorithms, multimodal integration, and privacy-preserving methods. Collectively, these efforts aim to transition the AI community toward sustainable, robust, and equitable artificial intelligence systems.

Learned control policies often fail when deployed in real-world environments with changing dynamics. When system dynamics shift unexpectedly, performance degrades until models are retrained on new data. We introduce Reflexive World Models (RWM), a dual control framework that uses world model predictions as implicit reference trajectories for rapid adaptation. Our method separates the control problem into long-term reward maximization through reinforcement learning and robust motor execution through reward-free rapid control in latent space. This dual architecture achieves significantly faster adaptation with low online computational cost compared to model-based RL baselines, while maintaining near-optimal performance. The approach combines the benefits of flexible policy learning through reinforcement learning with rapid error correction capabilities, providing a theoretically grounded method for maintaining performance in high-dimensional continuous control tasks under varying dynamics.

In this paper, we propose a novel tube-wise local tensor compressed sensing (CS) model, where sensing operators are independently applied to each tube of a third-order tensor. To recover the low-rank ground truth tensor, we minimize a non-convex objective via Burer–Monteiro factorization and solve it using gradient descent with spectral initialization. We prove that this approach achieves exact recovery with a linear convergence rate. Notably, our method attains provably lower sample complexity than existing TCS methods. Our proof leverages the leave-one-out technique to show that gradient descent generates iterates implicitly biased towards solutions with bounded incoherence, which ensures contraction of optimization error in consecutive iterates. Empirical results validate the effectiveness of GD in solving the proposed local TCS model.