Biological Plausibility and Representational Alignment of Feedback Alignment in Convolutional Networks

Backpropagation (BP) is widely viewed as biologically implausible, in part because it requires feedback weights to be the transpose of forward weights for error propagation. Interestingly, when training a network with fixed random feedback weights to circumvent this issue, learning aligns the forward weights with the feedback weights, leading the backpropagated error signal to become an approximation of the standard gradient used by BP. This process, called Feedback Alignment (FA), occurs in MLPs and very shallow CNNs but does not scale well to deeper architectures. In this work, we first investigated differences between BP and FA models, trained on CIFAR10, specifically focusing on the effective rank of the signal. We found that the FA error has a considerably lower rank and hence is constrained to a lower-dimensional subspace compared to BP, limiting exploration of the parameter space. Motivated by this observation, we evaluated two mechanisms for increasing the effective dimensionality of FA: Muon, an optimiser that orthogonalises weight updates; and hidden activity normalisation, which promotes activation orthogonality. Across larger architectures and benchmarks, we find that these methods consistently improve over FA baselines, for example, on CIFAR100 with a Resnet-18, accuracy increases by 9 percentage points. Our results identify low-dimensional gradient dynamics as a key obstacle to scaling FA and suggest that inducing higher-dimensional update geometry is a promising route toward scaling alternatives to backpropagation.

A central question in computational neuroscience is whether the learning rule used to train a neural network determines how well its internal representations align with those of the human visual cortex. We present a systematic comparison of four learning rules (backpropagation (BP), feedback alignment (FA), predictive coding (PC), and spike-timing-dependent plasticity (STDP)) applied to identical convolutional architectures and evaluated against human fMRI data from the THINGS-fMRI dataset (720 stimuli, 3 subjects) using Representational Similarity Analysis (RSA). All models process stimuli at 224 x 224 resolution; results are averaged across 5 random seeds. Crucially, we include an untrained random-weights baseline that reveals the dominant role of architecture. At V1/V2, the untrained baseline exceeds backpropagation (rho = 0.076 vs. rho = 0.034; Delta-rho = +0.044, p < 0.001), and STDP achieves the highest V1 alignment among trained rules (rho = 0.064). At LOC, only BP reliably exceeds the random baseline (rho = 0.012 vs. -0.005, p < 0.001). At IT, all five conditions converge (rho = 0.008-0.014) with no significant pairwise differences among trained rules (p > 0.05, FDR-corrected). FA consistently produces the lowest alignment at V1, V2, and LOC (rho = 0.012 at V1, below all other conditions). Partial RSA confirms all effects survive pixel-similarity control. Seed variability is small relative to between-rule differences at V1/V2. These results demonstrate that early visual alignment is architecture-driven, learning rules differentiate only at intermediate areas, and all rules converge at the highest levels of the hierarchy.

Despite the success of deep learning, training deep networks in biologically plausible and hardware-efficient ways remains an open challenge. Feedback alignment (FA) methods address this by replacing backpropagation's symmetric backward weights with fixed random matrices, but their effectiveness depends critically on whether they can be accurately evaluated. The standard evaluation relies on two quantities: task accuracy and cosine similarity between the method's credit signal and the backpropagation gradient. We show that this reporting pair is insufficient by identifying two independent failure modes, both silent under current reporting: (1) measurement degeneracy, where the BP reference gradient collapses to the numerical floor in terminal-LayerNorm residual architectures, rendering cosine uninterpretable; and (2) aggregation collapse, where the aggregate cosine masks layerwise heterogeneity that concentrates credit at one end of the network. To address these limitations, we propose a diagnostic evaluation protocol based on three checks -- scale stability, reference validity, and depth utility -- together with per-layer rather than aggregate cosine reporting. Across multiple architectures and methods, the standard reporting pair gives no signal of failure in any audited case, while our protocol identifies all failures with wide calibration margins. The two failure modes are causally independent: a per-block scale penalty alleviates Mode 1 (residual scale explosion driving reference collapse) without affecting Mode 2 (cosine ranking that contradicts every functional metric we measured). Identifying these silent failures prevents researchers from building on non-functional credit assignment and provides actionable guidance for developing FA methods that genuinely train deep layers.