Variable spontaneous dynamics in the experimental data.
(A) The power-law distributions of both avalanche duration and size of the experimental data in the spontaneous state. (B) Average avalanche size 〈S〉 given avalanche duration T. The relationship between the three power-law exponents aligns with theoretical predictions, i.e., DCC = |1/σvz − (τ − 1)/(α − 1)| = 0.05 . The black line refers to the theoretical prediction with the slope equal to (τ − 1)/(α − 1) . (C) The probability distribution of correlation of mean firing rate of neurons within-session (orange curve) and cross-session (olive curve). (D) The distance between the functional connectivity, i.e., correlation between the neuronal activity, within-session and cross-session (t- test, p = 0.025, see Method for detail).
Representational drift and the restricted representational geometry in the experimental data.
(A) The set of active neurons for a given stimulus changed across sessions (days). Red, green, and purple dots represent active neurons on the corresponding sessions, with overlapping colors indicating neurons active across multiple sessions. (B) The correlation between the mean population response vector across sessions of the same signal. (C) The low-dimensional representation of the population response vector of different signals and different trials in two sessions (top panel and bottom panel, respectively). Each color represents a different stimulus, with individual points of the same color representing different trials of that stimulus. (D) The representation similarity matrix, i.e., the correlation matrix between mean population response vectors for all stimulus pairs within session. (E) The cross-session correlation of the representation similarity matrices across signals obtained on different sessions (e.g., the two matrices shown in Figure 3D) as a function of the temporal distance between these sessions. (F) Illustration of the representational geometry of population response with different stimuli (nodes), defined by the angles between edges of the mean population response, where each edge is denoted as difference between mean population response vectors of two signals (see Method). For reliable representational geometry across sessions, the angles between all the edges are supposed to be preserved. (G) Representational geometry undergoes subtle changes over time but remains confined within a restricted space, manifested by time-invariant drift distances.
The self-organized criticality (SOC) in the E-I network with homeostatic plasticity.
(A) The synaptic strength dynamics of a randomly initialized network with homeostatic plasticity, converged to a relatively stable state characterized by a nearly constant mean synapse strength from inhibitory neuron to excitatory neuron, as shown in the grey region. To study representational drift in this model, we selected network configurations at several time points ({Ti}i=1,2..10) within this stable state. These time points are referred to sessions in experimental data. (B) The raster plot of neural activity in the stable state. (C) The near power-law distribution of the avalanche duration (blue) and avalanche size (red), indicating that the homeostatic plasticity organizes the neural dynamics into the (near) criticality. (D) The relationship between the average avalanche size with respect to avalanche duration follows the theoretical prediction (DCC = |1/σvz − (τ − 1)/(ρ − 1)| = 0.04 ± 0.016). (E) The probability distribution of correlation of mean firing rate of neurons within (olive curve) and across (orange-curve) sessions. (F) The distance between the functional connectivity, i.e., correlation between the neural activity, within and cross-session.
Representational drift and the restricted representational geometry in the self-organized critical (SOC) model.
(A) The set of active neurons for a given stimulus changed across sessions. Red, green, and purple dots represent active neurons on the corresponding sessions, with overlapping colors indicating neurons active across multiple sessions. (B) The correlation between the mean population response vector across sessions of the same signal. (C) The low-dimensional representation of the population response vector of different signals and different trials in two sessions (top panel and bottom panel, respectively). Each color represents a different stimulus, with individual points of the same color representing different trials of that stimulus. (D) The representation similarity matrix, i.e., the correlation matrix between mean population response vectors for all stimulus pairs. (E) The cross-session correlation of the representation similarity matrices across signals obtained on different sessions (e.g., the two matrices shown in Figure 4D) as a function of the temporal distance between these sessions. (F) Representational geometry undergoes subtle changes over time but remains confined within a restricted space, manifested by time-invariant drift distances.
Random shuffled plasticity biases the network from criticality and breaks down restricted representational geometry.
(A) The distribution of synaptic weight changes (ΔWij) obtained from numerical simulations of the self-organized critical network with homeostatic plasticity (as described in Figure 2A). To create the “random shuffled plasticity” condition, we replaced the original homeostatic plasticity rule with random sampling from the empirically observed ΔWij distribution. Each connection was updated independently using this distribution. (B) The shuffled plasticity shifts the network into a slightly subcritical regime compared to the near-critical dynamics observed with homeostatic plasticity. This shift is further supported by an increase in DCC value for the shuffled plasticity network compared to the self-organized critical network with homeostatic plasticity (DCChomeo = 0.040 ± 0.016, DCCshuffled = 0.072 ± 0.022). (C) The randomly shuffled plasticity disrupts the restricted representation geometry observed with homeostatic plasticity. This is evidenced by a reduction in representational similarity across time (upper panel) and an increase in the distance between representational geometries (lower panel).
Self-organized critical (SOC) state maximizes cross-session low-dimensional representation reliability.
(A) The distribution of avalanche durations for three representative values of . (B) The p-value obtained from comparing each avalanche duration distribution to the optimal power-law distribution. A higher p-value indicates a closer fit to the power law, suggesting closer proximity to criticality. The network with = 6 ms (black dashed line) exhibits the closest fit to the power law, indicating a near-critical state. (C) Low dimensional representation of the linear discriminant analysis (LDA) results for four example stimuli (represented by different colors). Circles, stars and squares denote the trails of three different sessions. The close alignment of markers for the same stimulus cross-session indicates that the LDA decoder successfully captured stimulus-relevant features that are invariant to session-to-session variability. The upper and low panels show the results for the experimental data and model simulation, respectively. (D) The performance of the LDA decoder as a function of in the model. Decoding performance was quantified as the classification accuracy. The SOC state ( = 6 ms) exhibited the highest cross-session decoding performance. The shade area in (B) and (D) represents the standard deviation across 10 network realizations.
(A) The change in synaptic weight patterns (ΔW, blue) and the change in inhibitory degree (ΔC, red) for each excitatory neuron over time in the SOC network ( = 6 ms). Both ΔW and ΔC rapidly stabilize after a brief period of initial fluctuations. (B) The static state value of ΔW and ΔC as the functions of . The near-critical state ( = 6 ms) exhibited the lowest ΔW and ΔC indicating that the network structure is most stable at criticality.
The estimated effective connectivity from neural activity using inverse of co-variance matrix.
Both experimental data (two sample t test, p ≈ 0.03 < 0.2) and balanced model (two sample t test, p ≈ 0) show larger change in effective connectivity for the cross-session than the within-session.
The statistics of representational drift of the experimental data.
The overlap refers to the overlap ratio of the active neurons under the same signal across different sessions, and the correlation refers to the correlation between the population response vectors under the same signal across different sessions. The statistics of response pattern is based on 78 mice and 30 signals.
Raster plots of plasticity model in different state.
The blue, orange, and red raster plots correspond to spikes of the excitatory neurons in the subcritical (), critical state (), and supercritical state (), respectively.
Raster plot of the plasticity model at the supercritical state with and the corresponding dynamics of the average synapse strength.
Accuracy of different decoders with different input durations.
We use two decoders to evaluate the reliability of signal representation across sessions. For common decoder, we put the neural response from different sessions together, and used the LDA analysis to obtain the decoder from the training set, then evaluated the accuracy on the test set. For the transfer decoder, we used the neural response in one session to obtain the LDA-based decoder, and examined the decoding accuracy on the neural response in another session. The different color refers to different signal durations, and vertical black dash line indicates the critical state.
The synapse strength and indegree patterns of the shuffled plasticity model.
We use the same shuffled plasticity model as the Fig. 5. Since the ΔW in each step follows the random distribution, then the distance of synapse strength and indegree patterns naturally increase with the ΔT.
