CMSP Seminar (Joint ICTP/SISSA Statistical Physics): Statistical physics through the lens of real-space mutual information
Starts 2 Feb 2021 11:00
Ends 2 Feb 2021 12:00
Central European Time
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing effective theories. The celebrated renormalization group (RG) provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices. Machine learning approaches, on the other hand, though promising, often lack formal interpretability: it is unclear what relation, if any, the architecture- and training-dependent learned "relevant" features bear to standard objects of physical theory. I will present recent results addressing both issues. We develop a fast algorithm, the RSMI-NE, employing state-of-art results in machine-learning-based estimation of information-theoretic quantities to construct the optimal coarse-graining. We use it to develop a new approach to identifying the most relevant field theory operators describing a statistical system, which we validate on the example of interacting dimer model.
I will also discuss the formal results underlying our methods: we establish equivalence between the information-theoretic notion of relevance defined in the Information Bottleneck (IB) formalism of compression theory, and the field-theoretic relevance of the RG. We show analytically that for statistical physical systems the "relevant" degrees of freedom found using IB compression (and RSMI-NE) indeed correspond to operators with the lowest scaling dimensions. Our findings provide a dictionary connecting two distinct theoretical toolboxes, and conceptually pave the way towards automated theory-building.
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