Paradoxical lesions, plasticity and active inference

Abstract Paradoxical lesions are secondary brain lesions that ameliorate functional deficits caused by the initial insult. This effect has been explained in several ways; particularly by the reduction of functional inhibition, or by increases in the excitatory-to-inhibitory synaptic balance within perilesional tissue. In this article, we simulate how and when a modification of the excitatory–inhibitory balance triggers the reversal of a functional deficit caused by a primary lesion. For this, we introduce in-silico lesions to an active inference model of auditory word repetition. The first in-silico lesion simulated damage to the extrinsic (between regions) connectivity causing a functional deficit that did not fully resolve over 100 trials of a word repetition task. The second lesion was implemented in the intrinsic (within region) connectivity, compromising the model’s ability to rebalance excitatory–inhibitory connections during learning. We found that when the second lesion was mild, there was an increase in experience-dependent plasticity that enhanced performance relative to a single lesion. This paradoxical lesion effect disappeared when the second lesion was more severe because plasticity-related changes were disproportionately amplified in the intrinsic connectivity, relative to lesioned extrinsic connections. Finally, this framework was used to predict the physiological correlates of paradoxical lesions. This formal approach provides new insights into the computational and neurophysiological mechanisms that allow some patients to recover after large or multiple lesions.


Supplementary materials
In order to simulate the word repetition task, we used a partially observable Markov decision process for discrete state space and time, as defined under active inference. In what follows, we provide a brief overview of the model and the accompanying optimisation scheme (S.1-S.3) (Friston et al 2017a). We then describe the particular causes i.e., hidden states (Target Word, Repeated Word and Epoch) and outcome modalities (Proprioception, Evaluation and Word) of interest for a word repetition paradigm (S.4). Using this, we simulate the word repetition task presented in this paper.

S.1 Model parameterisation
Active inference rests on: where uU  and u is a particular action.
• An approximate posterior: By taking an additional expectation under ( | ) P o s  , we can predict future outcomes given hidden states (expected free energy) where:

S.2 Belief update equations:
We optimise expectations about hidden states (including policies and precision) through inference and optimise model parameters (likelihood, transition states) through learning after a series of observations. This learning and inference entails finding the sufficient statistics of posterior beliefs that minimise variational free energy. This is usually achieved using a gradient descent on free energy (under some policy):

S.3 Learning:
The generative model formulation, can be extended to include prior beliefs, over these model parameter priors (i.e., hyperpriors), which are learned through Bayesian belief-updating (Friston et al 2017a, Friston et al 2017b). The natural choice for the conjugate prior is a Dirichlet distribution, given that the probability distributions are specified as a categorical distribution. This means that the probability can be represented simply in terms of Dirichlet concentration parameters (Parr 2019). This allows us to represent each outcome-state (for A ) and state-state ( B ) mapping with Dirichlet parameters: here  is the digamma function.
These Dirichlet parameters can be thought of as 'pseudo-counts' i.e., as observations are made the model is able to accumulate Dirichlet parameters that best fit the data.

Supplementary Figure 1. Generative model of word repetition
Supplementary Figure 1 is a graphical representation of the generative model for word repetition.
There are three (hidden) state factors: Epoch, Target Word, and Repeated Word, and three outcome modalities: Proprioception, Evaluation and Word. The hidden factors had the following levels (i.e., possible alternative states). Epoch (3 levels) indexes the phase of the trial. During the first epoch, the target word is heard. The second epoch involves repeating the word. The third phase elicits a positive evaluation, if the repeated word matches the target word, and a negative evaluation otherwise. The repeated word factor includes the words that model can choose to say (4 levels). The target word factor (4 levels) lists the words the model has to repeat. The lines from states to outcomes represent the likelihood mapping and lines mapping states within a factor represent allowable state transitions. For clarity, we have highlighted likelihoods and transition probabilities that are conserved across the different factors and outcome modalities. For example, the 'audition' likelihood mapping target word (square) and audition (square) is shown for Epoch 1, but similar mappings would be applied, when mapping between blue and blue or triangle and triangle. One (out of a total of 4) example transition probability is highlighted for the repeated word, i.e., the transition is always to blue, regardless of previously spoken word (red, triangle, square or blue). This transition represents the choice to say 'blue'. Similar mappings are applied when choosing to say 'triangle', regardless of the previous word. Alternative actions then correspond to alternative choices of transition probability. Note that the lines represent plausible connections (and their absence reflects implausible connections), with the arrow denoting direction. For example, the line mapping hidden state epoch '1' to outcome modality proprioception '…' suggests that '…' is only plausible at epoch '1', but not '2' or '3'. Similarly, the line for hidden state target word 'blue' to itself reflects that level 'blue' can only transition to itself and no other word, throughout the trial.