Can Transfer Entropy Infer Information Flow in Neuronal Circuits for Cognitive Processing?

TL;DR

The paper questions whether Transfer Entropy can reliably infer information flow and causality in neural circuits. It tests TE against ground-truth causal influence in Markov Brains evolved to perform motion detection and sound localization, formalizing TE as $TE_{X\rightarrow Y} = I(Y_{t+1}: X_{t-k:t} \mid Y_{t-l:t})$. Results show TE can both miss existing relations and falsely infer non-existent ones, with accuracy that depends on the cognitive task and the presence of cryptographic-like dependencies (e.g., XOR/XNOR gates) and polyadic obfuscation. The study combines analytical gate-level misestimation with TE measurements on simulated neural recordings, highlighting the need for task-specific validation of causality measures in neuroscience and guiding the development of more robust information-flow metrics.

Abstract

To infer information flow in any network of agents, it is important first and foremost to establish causal temporal relations between the nodes. Practical and automated methods that can infer causality are difficult to find, and the subject of ongoing research. While Shannon information only detects correlation, there are several information-theoretic notions of "directed information" that have successfully detected causality in some systems, in particular in the neuroscience community. However, recent work has shown that some directed information measures can sometimes inadequately estimate the extent of causal relations, or even fail to identify existing cause-effect relations between components of systems, especially if neurons contribute in a cryptographic manner to influence the effector neuron. Here, we test how often cryptographic logic emerges in an evolutionary process that generates artificial neural circuits for two fundamental cognitive tasks: motion detection and sound localization. We also test whether activity time-series recorded from behaving digital brains can infer information flow using the transfer entropy concept, when compared to a ground-truth model of causal influence constructed from connectivity and circuit logic. Our results suggest that transfer entropy will sometimes fail to infer causality when it exists, and sometimes suggest a causal connection when there is none. However, the extent of incorrect inference strongly depends on the cognitive task considered. These results emphasize the importance of understanding the fundamental logic processes that contribute to information flow in cognitive processing, and quantifying their relevance in any given nervous system.

Figures (7)

• Figure 1: (A) A network where processes $X$ and $Y$ influence future state of $Z$. (B) A feedback network in which processes $X$ and $Y$ influence future state $X$.
• Figure 2: (A) A Reichardt detector circuit. In these circuits, the results of the multiplications from each half circuit are subtracted to generate the response. (B) Schematic examples of three types of input patterns received by the two sensory neurons at two consecutive time steps. Grey squares show presence of the stimuli in those neurons.
• Figure 3: (A) Schematic of 5 sound sources at different angles with respect to a listener (top view) and Jeffress model of sound localization. (B) Schematic examples of 5 time sequences of input patterns received by the two sensory neurons (receptors of two ears) at three consecutive time steps. Black squares show presence of the stimuli in those neurons.
• Figure 4: Frequency distribution of all, as well as essential, gates in evolved Markov Brains that perform the motion detection or sound localization task perfectly. (A) All gates, motion detection. (B) Essential gates, motion detection. (C) All gates, sound localization. (D) Essential gates, sound localization.
• Figure 5: Transfer entropy measures, exact measures and misestimates by transfer entropy, on essential gates of perfect circuits for motion detection, and sound localization task. Columns show mean values and 95% confidence interval of misestimates and exact measures (A) per Brain, and (B) per gate.