Conditioned Direct Feedback Alignment via Activity and Error Geometry
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Computer Science > Machine Learning
Title:Conditioned Direct Feedback Alignment via Activity and Error Geometry
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.
| Subjects: | Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Neurons and Cognition (q-bio.NC) |
| Cite as: | arXiv:2607.18574 [cs.LG] |
| (or arXiv:2607.18574v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.18574
arXiv-issued DOI via DataCite (pending registration)
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