Conditioned Direct Feedback Alignment via Activity and Error Geometry

2026-07-20

AI Summary

This work addresses the training instability in Direct Feedback Alignment (DFA) caused by anisotropy in either presynaptic activities or local error signals. To mitigate this issue, the authors propose a normalized DFA approach that conditionally normalizes both activities and error signals. They introduce a symmetric, block-wise dual-factor normalization framework, decoupling and empirically validating the independent contributions of activity and error conditioning for the first time. The method is theoretically supported by linearized spectral analysis and implemented via inverse second-moment preconditioning and Kronecker-factor approximations. Controlled experiments on MNIST and Fashion-MNIST demonstrate that activity conditioning alone yields performance gains of up to 40 percentage points, while error conditioning improves accuracy by 1.77–7.53 percentage points; combining both strategies provides further modest improvements.

Abstract

Direct feedback alignment (DFA) trains hidden layers with fixed random projections of the output error, avoiding the transposed-weight backward pass of backpropagation (BP). We study a failure mode of DFA training that is distinct from feedback quality: the local weight update is calculated by an outer product, so anisotropy can enter through either its presynaptic-activity factor or its local-error factor. Our analyses with controlled synthetic regimes isolate the first failure mode and show an approximately 40-percentage-point activity-conditioning gain when high-variance directions contain task-irrelevant nuisance. Three clean confirmations isolate a different regime: error conditioning improves raw DFA by 1.77--7.53 percentage points, and combining independently selected activity and error factors adds 0.40--0.90 points over activity conditioning. The signs hold for tanh/one-vs-rest MNIST and preregistered Fashion-MNIST, and replicate on eight fresh seeds in a ReLU/softmax MNIST model. This factorization yields a symmetric block-local family of normalized DFA (nDFA): activity nDFA right-preconditions by an inverse activity second moment, error nDFA left-preconditions by an inverse local-error second moment, and K-nDFA applies both factors with separately tuned damping. A linearized post-alignment calculation gives an exact input-side spectral identity and a Kronecker-factor motivation for the two-sided rule, whereas norm matching rules out a scalar step-size explanation. The error factor is fragile when under-damped, BatchNorm is a strong activity-side alternative, and convnet gains remain partial. We therefore frame conditioned DFA as a factor-level study of when local outer-product rules fail, not as a general replacement for BP or a solution to all-layer convolutional credit assignment.

Problem

• Direct Feedback Alignment
• anisotropy
• outer-product update
• activity conditioning
• error conditioning

Innovation

• Direct Feedback Alignment
• Conditioning
• Activity-Error Factorization
• Normalized DFA
• Credit Assignment