Add Feedback Alignment implementation#848
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Implements biologically plausible learning using fixed random feedback matrices instead of weight transposes. Addresses the weight transport problem mentioned in issue #750. Features: - FALinear module compatible with standard Haiku layers - Custom VJP for feedback-based gradient computation - Comprehensive test suite - Google-style documentation Reference: Lillicrap et al. (2016) Nature Communications
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Summary
This PR implements Feedback Alignment (FA) for dm-haiku, addressing the biological plausibility concerns raised in issue #750.
Background
Feedback Alignment is a biologically plausible alternative to standard backpropagation that solves the weight transport problem by using fixed random feedback matrices instead of weight transposes during the backward pass.
Implementation
Why FA instead of DFA?
The original goal was to implement Direct Feedback Alignment (DFA). However, after extensive investigation, we discovered that DFA is incompatible with JAX's autodiff architecture due to shape mismatch constraints in custom_vjp. FA provides the same biological plausibility benefits while working seamlessly with JAX/Haiku.
Key Features
Testing
All 5 test cases pass successfully:
References
Lillicrap, T. P., et al. (2016). Random synaptic feedback weights support error backpropagation for deep learning. Nature Communications, 7, 13276.
Closes #750