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Limits of optimal decoding under synaptic coarse-tuning

Ori Hendler, Ronen Segev, Maoz Shamir

Abstract

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.

Limits of optimal decoding under synaptic coarse-tuning

Abstract

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 () for binary stimulus discrimination under two decoding schemes: a naive population average and an optimized linear decoder. For the naive decoder, we found that 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, scales linearly with population size . Under moderate coarse-tuning, scaling becomes sublinear. Under strong coarse-tuning, the regime most consistent with observed neuronal heterogeneity, 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.
Paper Structure (19 sections, 86 equations, 4 figures, 3 tables)

This paper contains 19 sections, 86 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Statistical Model of the neural response
  3. The Readout Model
  4. Readout Performance
  5. Naïve Decoder Performance
  6. Optimal Decoder Performance
  7. Coarse-tuned readout model
  8. Impact of Coarse-Tuning on Readout Performance
  9. Readout Layer and Further Processing
  10. Feedforward Neural Network
  11. Recurrent Neural Network
  12. Discussion
  13. $SNR^2$ of the fine-tuned na$\ddot{\i}$ve decoder
  14. $SNR^2$ of fine-tuned Optimal decoder
  15. The effect of coarse-tuning on the na$\ddot{\i}$ve decoder
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Readout model of the naïve and optimal decoders.(a) Schematic illustration of the model architecture. (b) The signal-to-noise ratio ($SNR$) is plotted as a function of population size $N$ for the optimal (blue) and naïve (black) decoders. Different values of the pairwise correlation coefficient $c=0, 0.05, 0.1$ are depicted by solid, dashed, and dotted lines, respectively.
  • Figure 2: Histograms of signal, noise$\bm{^2}$, and SNR. Distributions of the naïve (black) and optimal (blue) decoders across population sizes $N\in\{100,1000,4000\}$ under coarse-tuning with $\kappa=1$ and $\gamma=-1$. (a)$signal$ distribution. (b)$noise^2$ distribution. (c)$SNR$ distribution. Solid vertical lines indicate the mean; dashed lines indicate the $\pm1$ standard deviation. Red curves show analytical predictions derived in the main text.
  • Figure 3: $\boldsymbol{ SNR}$ scaling with population size under coarse-tuning.(a)$SNR$ versus population size $N$ for the optimal decoder, with varying magnitudes of coarse-tuning, $\kappa\in\{1, 3, 5, 7, 10\}$ at fixed $\gamma=-1$. (b)$SNR$ versus $N$ for the optimal decoder, with varying scalings of coarse-tuning, $\gamma\in\{-1, -0.75, -0.5, -0.2, 0\}$ at fixed $\kappa=1$. (c,d) Same as (a,b), but for the naïve decoder. (e)$SNR$ versus $\gamma$ at fixed population size $N=8000$ and $\kappa=1$. In all panels, the color gradient from dark to light indicates increased coarse-tuning.
  • Figure 4: Coarse-tuning of the Feedforward Neural Network and the Recurrent Neural Network.(a,b) Schematic illustration of the (a) Feedforward Neural Network and (b) Recurrent Neural Network architectures. (c,d) Susceptibility in the $T/J$--$J_0/J$ parameter space for (c) $\Delta=0.5$ and (d) $\Delta=1$. The solid black line marks the phase transition. (e,f) Magnetization heat maps for (e) $\Delta=0.5$ and (f) $\Delta=1$. The dashed black line indicates the phase transition for the corresponding $h_0=0$ case. (g,h) Projection of the signal onto (g) the uniform direction and (h) the random local field.