Game Theory seminars

Which nodes in a brain network causally influence one another, and how do such interactions utilize the underlying structural connectivity? One of the fundamental goals of neuroscience is to pinpoint such causal relations. Conventionally, these relationships are established by manipulating a node while tracking changes in another node. A causal role is then assigned to the first node if this intervention led to a significant change in the state of the tracked node. In this presentation, I use a series of intuitive thought experiments to demonstrate the methodological shortcomings of the current ‘causation via manipulation’ framework. Namely, a node might causally influence another node, but how much and through which mechanistic interactions? Therefore, establishing a causal relationship, however reliable, does not provide the proper causal understanding of the system, because there often exists a wide range of causal influences that require to be adequately decomposed. To do so, I introduce a game-theoretical framework called Multi-perturbation Shapley value Analysis (MSA). Then, I present our work in which we employed MSA on an Echo State Network (ESN), quantified how much its nodes were influencing each other, and compared these measures with the underlying synaptic strength. We found that: 1. Even though the network itself was sparse, every node could causally influence other nodes. In this case, a mere elucidation of causal relationships did not provide any useful information. 2. Additionally, the full knowledge of the structural connectome did not provide a complete causal picture of the system either, since nodes frequently influenced each other indirectly, that is, via other intermediate nodes. Our results show that just elucidating causal contributions in complex networks such as the brain is not sufficient to draw mechanistic conclusions. Moreover, quantifying causal interactions requires a systematic and extensive manipulation framework. The framework put forward here benefits from employing neural network models, and in turn, provides explainability for them.

Aram Harrow connects the Unique Games conjecture, especially small-set expansion, with the quantum separability problem. The Lasserre hierarchy used for Unique Games and the k-extendible relaxation of quantum separability turn out to be closely equivalent algorithmic approaches. The talk examines how quantum-information conjectures could yield quasipolynomial algorithms or hardness results for Unique Games, and discusses promising research directions. It introduces the necessary quantum mechanics, Unique Games, and hierarchy background rather than presupposing it. The presentation draws partly on the papers arXiv:1205.4484 and arXiv:1210.6367.