Cortical representation learning
& Bayes-optimal cue integration
Deperrois, N., Petrovici, M.A., Senn, W., & Jordan, J. (2021). Learning cortical representations through perturbed and adversarial dreaming. arXiv preprint arXiv:2109.04261.
Jordan, J., Sacramento, J., Wybo, W. A., Petrovici, M. A., & Senn, W. (2021). Learning
Bayes-optimal dendritic opinion pooling. arXiv preprint arXiv:2104.13238.
Jakob Jordan
Department of Physiology, University of Bern, Switzerland
03.03.2022, SCN Retreat, Crans-Montana, Switzerland
- structured neuronal representations underlie our capacity to behave successfully, and our fast/flexible learning capabilities
- latent representations emerge from unsupervised learning principles
- here: we propose that sleep and in particular REM dreams implement adversarial learning
Motivation
[Illing et al., 2021]
[Goetschalckx et al., 2021]
GenerativeAdversarial
Networks
Learning during sleep (sketch)
- sensory experiences are encoded & stored during wakefulness
- preturbed replay during NREM robustifies encoding
- "creative" replay" during REM organizes encoding space
Nicolas Deperrois
Different, but complementary objectives govern learning during wakefulness and sleep
- discriminator: external
- data reconstruction
- latent reconstruction
- discriminator: internal
- generator: external
Objectives:
Dreams become more realistic with training
(remark: FID uses an Inception-v3 network, hence likely
focuses on local image statistics, e.g., Brendel & Bethge, 2019)
Adversarial dreaming during REM improves the structure of latent representations
Perturbed dreaming during NREM improves the robustness of latent representations
Cortical correlates of adversarial learning
- (trained) discriminator neurons are in different activity regimes during wakefulness and REM sleep; distinguish external from internal, hence may be involved in reality monitoring systems (ACC, mPFC?); impaired discriminator function could thus lead to the formation of delusions
- discriminator learning predicts opposite weight changes on feedforward synapses during wakefulness and REM sleep for identical low-level activity
- generator learning predicts opposite plasticity rule on feedback synapses during wakefulness and REM sleep
(High-level) neuronal representations reflect contributions from multiple modalities
How to (optimally) combine uncertain information from different sources?
\bm z
visual
auditory
olfactory
\frac{1}{\sigma_\text{v}^2}
\frac{1}{\sigma_\text{a}^2}
\frac{1}{\sigma_\text{o}^2}
Neurons with conductance-based synapses
naturally implement probabilistic cue integration
An observation
Bayes-optimal inference
Bidirectional voltage dynamics
Membrane potential dynamics from noisy gradient ascent
\begin{array}{rl}
p(u_\text{s}|W,r) =& \frac{1}{Z'} \prod_{d=0}^D p_d(u_\text{s}|W_d,r) \\
=& \frac{1}{Z} e^{-\frac{\bar g_\text{s}}{2}\left( u_\text{s} - \bar E_\text{s}\right)^2}
\end{array}
\begin{array}{rl}
C \dot u_\text{s} =& \frac{\partial}{\partial u_\text{s}} \log p(u_\text{s}| W,r) + \xi \\
=& \sum_{d=0}^D \left( g_d^\text{L} (E^\text{L} - u_\text{s}) + g_d^\text{E} (E^\text{E} - u_\text{s}) + g_d^\text{I} (E^\text{I} - u_\text{s}) \right) + \xi
\end{array}
\mathbb{E}[u_\text{s}] = \bar E_\text{s}
Average membrane potentials
= reliability-weighted opinions
Membrane potential variance
= 1/total reliability
\text{Var}[u_\text{s}] = \frac{1}{\bar g_\text{s}}
Synaptic plasticity from stochastic gradient ascent
\begin{array}{rl}
\dot W_d^\text{E/I} \propto \frac{\partial}{\partial W_d^\text{E/I}} \log p(u_\text{s}^*|W,r) \\
\end{array}
\Delta \mu^{\text{E/I}} \propto (u_\text{s}^* - \bar E_\text{s}) \left( E^\text{E/I} - \bar E_\text{s} \right) \\
\Delta \sigma^2 \propto \frac{1}{2} \left( \frac{1}{\bar g_\text{s}} - (u_\text{s}^* - \bar E_\text{s})^2 \right)
Synaptic plasticity modifies excitatory/inhibitory synapses
- in approx. opposite directions to match the mean
- in identical directions to match the variance
\propto [ \; \Delta \mu^\text{E/I} \, + \, \Delta \sigma^2 \; ] \, r
\(u_\text{s}^*\): sample from target distribution \(p^*(u_\text{s})\)
target
actual
Synaptic plasticity performs
error-correction and reliability matching
Learning Bayes-optimal inference of orientations from multimodal stimuli
The trained model approximates ideal observers
and reproduces psychophysical signatures of experimental data
[Nikbakht et al., 2018]
Cross-modal suppression as
reliability-weighted opinion pooling
The trained model exhibits cross-modal suppression:
- at low stimulus intensities, firing rate is larger bimodal condition
- at high stimulus intensities, firing rate is smaller in bimodal condition
- example prediction for experiments: strength of suppression depends on relative reliabilities of the two modalities
[Ohshiro et al., 2017]
Summary
Adversarial learning during wakefulness and sleep allows the emergence of organized cortical representations.
Single neurons with conductance-based synapses learn to be optimal cue integrators.
Deperrois, N., Petrovici, M.A., Senn, W., & Jordan, J. (2021). Learning cortical representations through perturbed and adversarial dreaming. arXiv preprint arXiv:2109.04261.
Jordan, J., Sacramento, J., Wybo, W. A., Petrovici, M. A., & Senn, W. (2021). Learning
Bayes-optimal dendritic opinion pooling. arXiv preprint arXiv:2104.13238.
Representations & cue integration
By jakobj
