Many biological systems have evolved to embody solutions to complex inverse problems to produce desired outputs or functions; others have evolved strategies to learn solutions to complex inverse problems on much shorter (e.g. physiological or developmental) time scales. Another class of systems that solves complex inverse problems for desired outputs is artificial neural networks. A critical distinction between the biological systems and neural networks is that the former are not associated with processors that carry out algorithms such as gradient descent to solve the inverse problems. They must solve them using local rules that only approximate gradient descent. Thus a key challenge is to understand how biological systems encode local rules for experience-dependent modification in physical hardware to implement robust solutions to complex
inverse problems. A similar challenge is faced by a growing community of researchers interested in developing physical systems that can solve inverse problems on their own. Despite the differences between physical/biological systems that solve inverse problems via local rules on one hand, and neural networks that solve them using global algorithms like gradient descent on the other hand, each has the potential to inform the other. For example, the insight that overparameterization is important for obtaining good solutions generalizes from neural networks to physical/biological learning systems.

Examples of biological systems that learn at different scales include (1) biological filament networks such as the actin cortex, collagen extracellular matrix and fibrin blood clots, which maintain rigidity homeostasis as an output under constantly varying and often extreme stresses as inputs. (2) Epithelial tissues during various stages of development, which can undergo large shape changes and controlled cellular flows as desired outputs. (3) Immune systems, which constantly adapt to bind to invading pathogens as desired outputs. (4) Ecological systems, in which species can change their interactions (eg. learn to consume new species) in order to bolster their population as an output.
The goal of this workshop is to discover new core principles and mathematical tools/approaches shared across physical learning systems, biological learning systems and neural networks that will inform deeper understanding and future discovery in all 3 fields. To this end, we will bring together researchers interested in viewing biological problems through the lens of inverse problems, researchers working on physical learning, and researchers studying neural networks for a week of intensive discussion and cross-fertilization.

We envision a unique format for this workshop, focused on framing and discussing open questions rather than on recitations of recent results. We will ask a subset of participants to present pedagogical overviews of key topics to help members of disparate communities establish common intellectual ground for discussion.

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