# Neuromodulatory Control and Language Recovery in Bilingual Aphasia: An Active Inference Approach

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## Abstract

**:**

## 1. Introduction

#### 1.1. Recovery Patterns and Control

#### 1.2. Active Inference, Generative Models and Bayes-Optimality

## 2. Methods

#### 2.1. Active Inference

_{τ}|s

_{τ}):

#### 2.2. Generative Model of Picture Naming, Word Repetition and Translation

#### 2.3. In-Silico Lesions

#### 2.4. Paradigm Procedure

## 3. Results

## 4. Discussion

#### 4.1. Neuromodulation and Precision

#### 4.2. Generalisation and Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(generative model) Graphical representation of the picture naming, word repetition and translation tasks. There are five outcome modalities: task, language, audition, visual and feedback, and five (hidden) state factors with the following levels (i.e., possible alternative states). Context (3 levels) indexes the current task (naming, repetition, translation). The heard language factor (2 levels) lists the languages the experimenter can use to test the participant (L1 or L2). The target language factor (2 levels) lists the languages the participant can respond in (L1 or L2). The concept factor (12 levels) lists the concepts that the experimenter can ask the participant to name, repeat or translate. The epoch (2 levels) indexes the phase of the trial (stimulus presentation, response and feedback). The lines from states to outcomes represent the likelihood mapping and the lines mapping states within a factor represent allowable state transitions. To avoid visual clutter, we have highlighted likelihoods and transition probabilities that are conserved over state factors and outcome modalities. For example, in the audition likelihood mapping for translation, the target language and concept (man) to audition (homme) is shown for epoch 1, but similar mappings apply when mapping between girl and fille, etc. One (out of two) example transition probability is highlighted (in darker brown shade) for the target language, i.e., the transition is always to L1, regardless of previous target language. This transition represents the choice to speak in L1. Similar mappings are applied when choosing to speak in L2, regardless of the previous state.

**Figure 2.**(precision) The figure plots two hypothetical probability distributions—one precise (narrow) and the other imprecise (flat).

**Figure 3.**(paradigm set-up) Schematic illustration of the task sequence the model was exposed to during each simulated day.

**Figure 4.**(simulated behavioural performance) The bar charts report the number of correct responses, for each task, across the 9 simulated days for two simulated subjects. Here, #1 is a control subject (dark and light blue bars) and #2 is a lesioned subject (green and yellow bars). The language (L1/L2) in the legend denotes the speaker language e.g., for #1-L1 the subject was asked to repeat the word in L1 but translate the word from L1 to L2. Similarly, for #2-L2 the object had to be named in L2 but translated from L2 to L1 during the translation task. The x-axis is the simulated day number and the y-axis denotes the number of correct responses. The maximum number of correct responses, for each task per day, is 5. Day 3 and 4, in the grey box, is highlighted, the pattern of alternate antagonism and paradoxical translation in subject #2, e.g., when L2 is accessible (yellow bars; day 3), the subject is unable to name pictures and translate from L1 but can repeat in both L2 and L1. However, day 4 shows an alternate recovery profile: L1 is accessible (green bars), the subject is unable to name pictures and translate from L2 but can repeat in both L2 and L1.

**Figure 5.**(belief updates) Each figure (

**A**–

**D**) reports belief updating, over two epochs of a single trial, for the two subjects: #1-control and #2-lesioned. These are shown for the target language and heard language factors when completing different tasks during the simulated day 3, when the model had access to L2. These tasks are picture naming in L1 (

**A**), word repetition in L1 (

**B**), word translation from L2 to L1 (

**C**) and word translation from L1 to L2 (

**D**). For each figure, the top row comprises an image showing the stage of the trial and the bottom two rows display the belief updates for heard and target language. The columns represent the two epochs for the two models. The first column represents the posterior expectations about each of the associated states at different epochs (current, future) at epoch 1, for subjects #1 and #2. Similarly, the second column represents the posterior expectations about each of the states at different epochs at epoch 2. For example, for the target language factor, in both panels there are 2 states, and a total of 2 × 2 (states times epochs) posterior expectations. Similarly, for the heard language factor there are two levels, and total of 2 × 2 expectations. Note that white represents an expected probability of zero, black of one, and grey indicates gradations between these extremes. For example, the first column, top row in A corresponds to expectations about the heard language in terms of two alternatives for the first epoch. The second column, top row reports the equivalent expectations for the second epoch. This means that at the beginning of the trial the second column reports beliefs about the future; namely, the next epoch. However, later in time, these beliefs refer to the past, i.e., beliefs currently held about the first epoch as seen in the second column. This aspect of (deep temporal) inference is effectively an implementation of working memory that enables our model to remember what it has heard—and accumulate evidence for the target language that is subsequently articulated; i.e., mediating a working memory for planning short-term responses. Note that most beliefs persist through time. For example, the heard language reveals itself almost immediately and this prospective belief is propagated into the future.

Term | Description |
---|---|

Probability distribution, $P(.)$ | The probability of a random variable taking a particular value. |

Variational distribution, $Q(.)$ | An approximate posterior distribution (i.e., Bayesian belief) over the causes of outcomes, given those outcomes. |

Hidden states, $s\in S$ | Latent or hidden states of the world generating outcomes. |

Outcomes, $o\in O$ | Outcomes or (sensory) observations. |

Action, $u\in U$ | A (control) state that can influence states of the world. |

Policy,$\pi \in \prod $ | Sequence of actions. |

Generative model, $P(o,s)$ | A joint probability distribution over hidden states and outcomes. |

Free energy, $F$ | An information theory measure that bounds the surprise when sampling and outcome, given a generative model. |

Complexity, ${D}_{KL}[Q(s)||P(s)]$ | A measure of how much the posterior beliefs have to move away from prior beliefs to provide an accurate account of sensory data. |

Accuracy, ${\mathbb{E}}_{Q(s)}[\mathrm{log}P(o|s)]$ | The expected log likelihood of the sensory outcomes, given some posterior beliefs about the causes of those data. |

Expected free energy, $G$ | Free energy expected under future outcomes—an uncertainty measure, associated with a particular policy. |

KL-Divergence, ${D}_{KL}[.||.]$ | A measure of how one probability distribution differs from a second, reference probability distribution. |

Temporal horizon, $\tau \in T$ | Number of timesteps in a sequence of actions, i.e., policy depth. |

Posterior | Beliefs about their causes of outcomes after they are observed. The products of belief updating. |

Prior | Beliefs about the causes of outcomes before they are observed. A likelihood and prior beliefs constitute the generative model. |

Likelihood, $P({o}_{\tau}|{s}_{\tau},\eta )$ | Probabilistic mapping between states and outcomes. |

Transitions, $P({s}_{t}|{s}_{t-1},\pi )$ | Probabilistic transitions from one state to another over time. |

Expectation, $E[.]$ | The average of a random variable. |

Precision, $\omega $ | Confidence or inverse uncertainty. |

Sufficient statistics | Quantities which are sufficient to parameterise a probability distribution. |

Gradient Descent | An optimisation scheme used to minimise a particular function by iteratively moving in the direction of steepest descent. |

Softmax function, $\sigma $ | A function that converts a set of real values into probabilities that sum to 1. |

**Table 2.**(Alternate antagonism and Paradoxical translation) The alternate antagonism and paradoxical translation recovery patterns seen in two bilingual aphasic subjects; adapted from [10].

Language (Naming, etc.) | Translation | |
---|---|---|

First Patient (A.D.) | ||

1st Period | Total aphasia | |

2nd Period | L1 > L2 | |

+1 Day | L2 > L1 | |

+2 Day | L1 > L2 | L2 → L1 Bad; L1 → L2 Good |

+3 Day | L2 > L1 | L2 → L1 Excellent; L1 → L2 Poor |

+4 Day | L1 = good | |

+11 Day | L2 > L1 | L2 → L1 Very poor; L1 → L2 Very poor |

+24 Day | L2 ≥ L1 | L2 → L1 Poor; L1 → L2 Poor |

+25 Day | L2 ≥ L1 | L2 → L1 Poor; L1 → L2 Good |

Second Patient | ||

1st Week | L1 > L2 | |

2nd Week | L2 > L1 | |

3rd Week | L2 ≥ L1 | L2 → L1 Excellent; L1 → L2 Very poor |

4th Week | L2 = L1 | L2 → L1 Excellent; L1 → L2 Excellent |

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**MDPI and ACS Style**

Sajid, N.; Friston, K.J.; Ekert, J.O.; Price, C.J.; Green, D.W.
Neuromodulatory Control and Language Recovery in Bilingual Aphasia: An Active Inference Approach. *Behav. Sci.* **2020**, *10*, 161.
https://doi.org/10.3390/bs10100161

**AMA Style**

Sajid N, Friston KJ, Ekert JO, Price CJ, Green DW.
Neuromodulatory Control and Language Recovery in Bilingual Aphasia: An Active Inference Approach. *Behavioral Sciences*. 2020; 10(10):161.
https://doi.org/10.3390/bs10100161

**Chicago/Turabian Style**

Sajid, Noor, Karl J. Friston, Justyna O. Ekert, Cathy J. Price, and David W. Green.
2020. "Neuromodulatory Control and Language Recovery in Bilingual Aphasia: An Active Inference Approach" *Behavioral Sciences* 10, no. 10: 161.
https://doi.org/10.3390/bs10100161