Feedback Alignment Meets Low-Rank Manifolds: A Structured Recipe for Local Learning

• URL: http://arxiv.org/abs/2510.25594v1
• Date: Wed, 29 Oct 2025 15:03:46 GMT
• Title: Feedback Alignment Meets Low-Rank Manifolds: A Structured Recipe for Local Learning
• Authors: Arani Roy, Marco P. Apolinario, Shristi Das Biswas, Kaushik Roy,
• Abstract summary: Training deep neural networks (DNNs) with backpropagation (BP) achieves state-of-the-art accuracy but requires global error propagation and full parameterization.<n>Direct Feedback Alignment (DFA) enables local, parallelizable updates with lower memory requirements.<n>We propose a structured local learning framework that operates directly on low-rank manifold.
• Score: 7.034739490820967
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Training deep neural networks (DNNs) with backpropagation (BP) achieves state-of-the-art accuracy but requires global error propagation and full parameterization, leading to substantial memory and computational overhead. Direct Feedback Alignment (DFA) enables local, parallelizable updates with lower memory requirements but is limited by unstructured feedback and poor scalability in deeper architectures, specially convolutional neural networks. To address these limitations, we propose a structured local learning framework that operates directly on low-rank manifolds defined by the Singular Value Decomposition (SVD) of weight matrices. Each layer is trained in its decomposed form, with updates applied to the SVD components using a composite loss that integrates cross-entropy, subspace alignment, and orthogonality regularization. Feedback matrices are constructed to match the SVD structure, ensuring consistent alignment between forward and feedback pathways. Our method reduces the number of trainable parameters relative to the original DFA model, without relying on pruning or post hoc compression. Experiments on CIFAR-10, CIFAR-100, and ImageNet show that our method achieves accuracy comparable to that of BP. Ablation studies confirm the importance of each loss term in the low-rank setting. These results establish local learning on low-rank manifolds as a principled and scalable alternative to full-rank gradient-based training.

Related papers

• Information-Theoretic Greedy Layer-wise Training for Traffic Sign Recognition [0.5024983453990065]
  layer-wise training eliminates the need for cross-entropy loss and backpropagation.<n>Most existing layer-wise training approaches have been evaluated only on relatively small datasets.<n>We propose a novel layer-wise training approach based on the recently developed deterministic information bottleneck (DIB) and the matrix-based R'enyi's $alpha$-order entropy functional.
  arXiv  Detail & Related papers  (2025-10-31T17:24:58Z)
• Eigen Neural Network: Unlocking Generalizable Vision with Eigenbasis [5.486667906157719]
  Eigen Neural Network (ENN) is a novel architecture that re parameterizes each layer's weights in a layer-shared, learned orthonormal eigenbasis.<n>When integrated with standard BP, ENN consistently outperforms state-of-the-art methods on large-scale image classification benchmarks.
  arXiv  Detail & Related papers  (2025-08-02T06:33:58Z)
• Regularizing Subspace Redundancy of Low-Rank Adaptation [54.473090597164834]
  We propose ReSoRA, a method that explicitly models redundancy between mapping subspaces and adaptively Regularizes Subspace redundancy of Low-Rank Adaptation.<n>Our proposed method consistently facilitates existing state-of-the-art PETL methods across various backbones and datasets in vision-language retrieval and standard visual classification benchmarks.<n>As a training supervision, ReSoRA can be seamlessly integrated into existing approaches in a plug-and-play manner, with no additional inference costs.
  arXiv  Detail & Related papers  (2025-07-28T11:52:56Z)
• Stochastic Layer-wise Learning: Scalable and Efficient Alternative to Backpropagation [1.0285749562751982]
  Backpropagation underpins modern deep learning, yet its reliance on global synchronization limits scalability and incurs high memory costs.<n>In contrast, fully local learning rules are more efficient but often struggle to maintain the cross-layer coordination needed for coherent global learning.<n>We introduce Layer-wise Learning (SLL), a layer-wise training algorithm that decomposes the global objective into coordinated layer-local updates.
  arXiv  Detail & Related papers  (2025-05-08T12:32:29Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture.<n>Non-smooth regularization is often incorporated into machine learning tasks.<n>We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• Towards Interpretable Deep Local Learning with Successive Gradient Reconciliation [70.43845294145714]
  Relieving the reliance of neural network training on a global back-propagation (BP) has emerged as a notable research topic. We propose a local training strategy that successively regularizes the gradient reconciliation between neighboring modules. Our method can be integrated into both local-BP and BP-free settings.
  arXiv  Detail & Related papers  (2024-06-07T19:10:31Z)
• Structure-Preserving Network Compression Via Low-Rank Induced Training Through Linear Layers Composition [11.399520888150468]
  We present a theoretically-justified technique termed Low-Rank Induced Training (LoRITa) LoRITa promotes low-rankness through the composition of linear layers and compresses by using singular value truncation. We demonstrate the effectiveness of our approach using MNIST on Fully Connected Networks, CIFAR10 on Vision Transformers, and CIFAR10/100 and ImageNet on Convolutional Neural Networks.
  arXiv  Detail & Related papers  (2024-05-06T00:58:23Z)
• Reparameterization through Spatial Gradient Scaling [69.27487006953852]
  Reparameterization aims to improve the generalization of deep neural networks by transforming convolutional layers into equivalent multi-branched structures during training. We present a novel spatial gradient scaling method to redistribute learning focus among weights in convolutional networks.
  arXiv  Detail & Related papers  (2023-03-05T17:57:33Z)
• Learning an Invertible Output Mapping Can Mitigate Simplicity Bias in Neural Networks [66.76034024335833]
  We investigate why diverse/ complex features are learned by the backbone, and their brittleness is due to the linear classification head relying primarily on the simplest features. We propose Feature Reconstruction Regularizer (FRR) to ensure that the learned features can be reconstructed back from the logits. We demonstrate up to 15% gains in OOD accuracy on the recently introduced semi-synthetic datasets with extreme distribution shifts.
  arXiv  Detail & Related papers  (2022-10-04T04:01:15Z)
• Biologically Plausible Training Mechanisms for Self-Supervised Learning in Deep Networks [14.685237010856953]
  We develop biologically plausible training mechanisms for self-supervised learning (SSL) in deep networks. We show that learning can be performed with one of two more plausible alternatives to backpagation.
  arXiv  Detail & Related papers  (2021-09-30T12:56:57Z)
• Efficient Micro-Structured Weight Unification and Pruning for Neural Network Compression [56.83861738731913]
  Deep Neural Network (DNN) models are essential for practical applications, especially for resource limited devices. Previous unstructured or structured weight pruning methods can hardly truly accelerate inference. We propose a generalized weight unification framework at a hardware compatible micro-structured level to achieve high amount of compression and acceleration.
  arXiv  Detail & Related papers  (2021-06-15T17:22:59Z)
• DessiLBI: Exploring Structural Sparsity of Deep Networks via Differential Inclusion Paths [45.947140164621096]
  We propose a new approach based on differential inclusions of inverse scale spaces. We show that DessiLBI unveils "winning tickets" in early epochs.
  arXiv  Detail & Related papers  (2020-07-04T04:40:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.