Search papers, labs, and topics across Lattice.
This paper investigates the limitations of Direct Feedback Alignment (DFA) by analyzing the effects of anisotropy in weight updates derived from outer products of presynaptic activity and local error factors. The authors demonstrate that conditioning on high-variance activity can yield a significant performance improvement of approximately 40 percentage points in specific scenarios, while error conditioning further enhances DFA performance by 1.77 to 7.53 percentage points. Their findings suggest that combining both activity and error conditioning can lead to additional gains, establishing a new family of normalized DFA methods that address the failure modes of traditional DFA without fully replacing backpropagation.
Conditioning on activity can boost DFA performance by nearly 40 percentage points, revealing critical insights into the geometry of weight updates in neural networks.
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.
