Papers › How Important is Weight Symmetry in Backpropagation?
How Important is Weight Symmetry in Backpropagation?
Qianli Liao, Joel Z. Leibo, Tomaso Poggio
Gradient backpropagation (BP) requires symmetric feedforward and feedback connections -- the same weights must be used for forward and backward passes. This "weight transport problem" (Grossberg 1987) is thought to be one of the main reasons to doubt BP's biologically plausibility. Using 15 different classification datasets, we systematically investigate to what extent BP really depends on weight symmetry. In a study that turned out to be surprisingly similar in spirit to Lillicrap et al.'s demonstration (Lillicrap et al. 2014) but orthogonal in its results, our experiments indicate that: (1) the magnitudes of feedback weights do not matter to performance (2) the signs of feedback weights do matter -- the more concordant signs between feedforward and their corresponding feedback connections, the better (3) with feedback weights having random magnitudes and 100% concordant signs, we were able to achieve the same or even better performance than SGD. (4) some normalizations/stabilizations are indispensable for such asymmetric BP to work, namely Batch Normalization (BN) (Ioffe and Szegedy 2015) and/or a "Batch Manhattan" (BM) update rule.
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Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Handwritten Digit Recognition | MNIST | Sign-symmetry | PERCENTAGE ERROR | 0.91 | #2 of 2 | Archive leaderboard | report |
| Image Classification | CIFAR-10 | Sign-symmetry | Percentage correct | 80.98 | #246 of 265 | Archive leaderboard | report |
| Image Classification | CIFAR-100 | Sign-symmetry | Percentage correct | 48.75 | #203 of 211 | Archive leaderboard | report |
| Image Classification | STL-10 | Sign-symmetry | Percentage correct | 57.32 | #115 of 117 | Archive leaderboard | report |
| Image Classification | SVHN | Sign-symmetry | Percentage error | 10.16 | #46 of 62 | Archive leaderboard | report |
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