Limits of optimal decoding under synaptic coarse-tuning
Sensory information propagates through successive processing stages in the brain, where synaptic weight patterns between stations determine how downstream neurons decode information from upstream populations. Although optimized synaptic connectivity can enhance information transmission, it requires precise weight tuning. Recent evidence depicting substantial synaptic volatility raises two fundamental questions: How does coarse-tuning of synaptic connectivity affect information transmission? What strategies could the nervous system employ to maintain reliable communication despite synaptic fluctuations? We addressed these questions by analyzing the signal-to-noise ratio ($SNR$) for binary stimulus discrimination under two decoding schemes: a naive population average and an optimized linear decoder. For the naive decoder, we found that $SNR$ remains largely insensitive to synaptic imprecision, since performance is already limited by correlated noise in neuronal responses. For the optimal decoder, we identified three distinct regimes. Under weak coarse-tuning, $SNR^2$ scales linearly with population size $N$. Under moderate coarse-tuning, scaling becomes sublinear. Under strong coarse-tuning, the regime most consistent with observed neuronal heterogeneity, $SNR$ saturates and can not be improved by recruiting larger populations. This limitation persists even when incorporating feedforward or recurrent network architectures. These findings suggest that in the biologically relevant regime of strong coarse-tuning, naive and optimal decoders can achieve qualitatively similar performance. The analysis shows that effective readout under synaptic volatility is constrained to an invariant low-dimensional manifold aligned with the naive decoder, potentially pointing to a fundamental principle for robust neural computation in the face of ongoing synaptic remodeling.