Low-Rank Adaptation (LoRA) has become the de facto parameter-efficient finetuning (PEFT) method for large language models (LLMs) by constraining weight updates to low-rank matrices. Recent works such as Tied-LoRA, VeRA, and VBLoRA push efficiency further by introducing additional constraints to reduce the trainable parameter space. In this paper, we show that the parameter space reduction strategies employed by these LoRA variants can be formulated within a unified framework, Uni-LoRA, where the LoRA parameter space, flattened as a highdimensional vector space RD, can be reconstructed through a projection from a subspace Rd, with d D. We demonstrate that the fundamental difference among various LoRA methods lies in the choice of the projection matrix, P RD d. Most existing LoRA variants rely on layer-wise or structure-specific projections that limit cross-layer parameter sharing, thereby compromising parameter efficiency. In light of this, we introduce an efficient and theoretically grounded projection matrix that is isometric, enabling global parameter sharing and reducing computation overhead. Furthermore, under the unified view of Uni-LoRA, this design requires only a single trainable vector to reconstruct LoRA parameters for the entire LLM - making UniLoRA both a unified framework and a "one-vector-only" solution. Extensive experiments on GLUE, mathematical reasoning, and instruction tuning benchmarks demonstrate that Uni-LoRA achieves state-of-the-art parameter efficiency while outperforming or matching prior approaches in predictive performance.

We aim to provide a unified convergence analysis for permutation-based Stochastic Gradient Descent (SGD), where data examples are permuted before each epoch.

For the theoretical exposition, we first establish the following Lemmas. Lemma A.1 proves that the derivative of the function φis bounded in the `2-norm when the domain is restricted to the support of P. Lemma A.1. Lemma A.3 proves that the function fΘ, as a function of Θ, is Lipschitz with respect to the k k norm. Joint first authors contributed equally Corresponding author 35th Conference on Neural Information Processing Systems (NeurIPS 2021). Thus, from equation (1), h φ(PC(θ)) φ(θ),x PC(θ)i 0. (2) We now observe that, dφ(x,θ) dφ(x,PC(θ)) dφ(PC(θ),θ) = h φ(PC(θ)) φ(θ),x PC(θ)i 0. Hence the result.

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of Young's inequality in $L_{\psi_p}$ Orlicz spaces. Using the decorrelation lemma in combination with other techniques, such as symmetrization, couplings, and chaining in the space of probability measures, we obtain new upper bounds on the generalization error, both in expectation and in high probability, and recover as special cases many of the existing generalization bounds, including the ones based on mutual information, conditional mutual information, stochastic chaining, and PAC-Bayes inequalities. In addition, the Fernique--Talagrand upper bound on the expected supremum of a subgaussian process emerges as a special case.

Contrastive learning has recently emerged as a promising approach for learning data representations that discover and disentangle the explanatory factors of the data.Previous analyses of such approaches have largely focused on individual contrastive losses, such as noise-contrastive estimation (NCE) and InfoNCE, and rely on specific assumptions about the data generating process.This paper extends the theoretical guarantees for disentanglement to a broader family of contrastive methods, while also relaxing the assumptions about the data distribution.Specifically, we prove identifiability of the true latents for four contrastive losses studied in this paper, without imposing common independence assumptions.The theoretical findings are validated on several benchmark datasets.Finally, practical limitations of these methods are also investigated.

The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the rank-based loss is prevalent, replacing the empirical loss in many cases. The rank-based loss comprises a weighted sum of sorted individual losses, encompassing both convex losses like the spectral risk, which includes the empirical risk and conditional value-at-risk, and nonconvex losses such as the human-aligned risk and the sum of the ranked range loss. In this paper, we introduce a unified framework for the optimization of the rank-based loss through the utilization of a proximal alternating direction method of multipliers. We demonstrate the convergence and convergence rate of the proposed algorithm under mild conditions. Experiments conducted on synthetic and real datasets illustrate the effectiveness and efficiency of the proposed algorithm.

Our platform encompasses a diverse range of pre-existing and novel environments, including dexterous manipulation with the Shadow Hand, whole-arm manipulation tasks with Franka and Fetch robots, quadruped locomotion, among others. Included environments are organized within and cover multiple domains such as hand manipulation, locomotion, multi-task, multi-agent, muscles, etc. In comparison to prior works, RoboHive offers a streamlined and unified task interface taking dependency on only a minimal set of well-maintained packages, features tasks with high physics fidelity and rich visual diversity, and supports common hardware drivers for real-world deployment. The unified interface of RoboHive offers a convenient and accessible abstraction for algorithmic research in imitation, reinforcement, multi-task, and hierarchical learning. Furthermore, RoboHive includes expert demonstrations and baseline results for most environments, providing a standard for benchmarking and comparisons.

Diagnosing and cleaning data is a crucial step for building robust machine learning systems. However, identifying problems within large-scale datasets with real-world distributions is challenging due to the presence of complex issues such as label errors, under-representation, and outliers. In this paper, we propose a unified approach for identifying the problematic data by utilizing a largely ignored source of information: a relational structure of data in the feature-embedded space. To this end, we present scalable and effective algorithms for detecting label errors and outlier data based on the relational graph structure of data. We further introduce a visualization tool that provides contextual information of a data point in the feature-embedded space, serving as an effective tool for interactively diagnosing data. We evaluate the label error and outlier/out-of-distribution (OOD) detection performances of our approach on the large-scale image, speech, and language domain tasks, including ImageNet, ESC-50, and SST2. Our approach achieves state-of-the-art detection performance on all tasks considered and demonstrates its effectiveness in debugging large-scale real-world datasets across various domains.

The last few years have witnessed a surge in methods for symbolic regression, from advances in traditional evolutionary approaches to novel deep learning-based systems. Individual works typically focus on advancing the state-of-the-art for one particular class of solution strategies, and there have been few attempts to investigate the benefits of hybridizing or integrating multiple strategies. In this work, we identify five classes of symbolic regression solution strategies---recursive problem simplification, neural-guided search, large-scale pre-training, genetic programming, and linear models---and propose a strategy to hybridize them into a single modular, unified symbolic regression framework. Based on empirical evaluation using SRBench, a new community tool for benchmarking symbolic regression methods, our unified framework achieves state-of-the-art performance in its ability to (1) symbolically recover analytical expressions, (2) fit datasets with high accuracy, and (3) balance accuracy-complexity trade-offs, across 252 ground-truth and black-box benchmark problems, in both noiseless settings and across various noise levels. Finally, we provide practical use case-based guidance for constructing hybrid symbolic regression algorithms, supported by extensive, combinatorial ablation studies.

U-Nets are a go-to neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures.