Living systems, from single cells to humans, receive information from the external world, and process that information to move and shape the processes within them. Information theory offers an excellent framework for placing limits on what an organism can sense, and serves as a design principle that can be used to rationalize what we observe in nature. Most organisms, however, self-organize and move, which breaks the limits of passive sensing and leads to a tight coupling between information processing and decision-making. Active information acquisition is an inherently non-stationary process, while organismal decision-making emerges as a sum of numerous microscopic computations occurring out of equilibrium, rendering canonical thermodynamic descriptions inapplicable. Our hope is to find a common mathematical framework that offers testable predictions and normative explanations for empirical decision-making phenomena, much like the role information theory has played for describing passive sensory systems. 

Additional complexity arises from the fact that living systems are not static but constantly learn, that is, make long-term changes to their core processes that allow them to adapt and anticipate future scenarios. Most biological learning operates in "high-dimensions" -- the number of tunable parameters is often exceedingly large, and the sensory-action response functions involve high-dimensional sensory inputs (say, from diverse receptors) and high-dimensional action outputs (say, control of muscles or gene regulation). A (seemingly) fundamental limitation of learning in this regime is that the larger the number of knobs one can tune, the longer it takes to find the optimal solution. However, this "limitation", known as the curse of dimensionality, does not appear to apply in practice -- modern machine learning models and extant biological complexity are prime examples. Presumably, most high-dimensional systems, through learning, acquire implicit low-dimensional structure that reflects the task they are meant to solve. How is the curse of dimensionality circumvented in high-dimensional learning systems and under what conditions does low-dimensional structure emerge? 

Learning by itself is not enough -- living systems need to learn quickly -- to survive, populations should rapidly acquire strongly beneficial mutations before they go extinct and animals should rapidly learn the structure of the environment that they are born into. How should biological systems be organized so that they learn quickly? Much like meta-trained machine learning systems, biological systems encounter and survive a diverse array of environments ("tasks") on organismal and evolutionary timescales. Does learning across many tasks over long timescales create a scaffold for adaptation on shorter timescales? 

We are a group of physicists contributing towards addressing these foundational questions in biological physics through a combination of theory and data-driven modeling. We collaborate closely with both machine learning researchers and experimental biologists. Machine learning models are excellent 'experimental' systems to probe principles of high-dimensional learning and test out new conceptual ideas. We believe that understanding how these models work will get us further along the path towards understanding how life works. 

We work on a diverse set of problems spanning animal behavior, neuroscience, evolution and machine learning. Below is a selected list of ongoing and future projects -- please reach out to greddy AT princeton DOT edu if you're interested in joining or collaborating with us. 

Representation learning for decision-making: 

Most sensory information that we receive is redundant, making compression an important part of information processing systems. Information theory provides a statistical measure of information by taking into account correlations between variables, yet does not account for meaning. How should high-dimensional information be compressed to preserve the maximal amount of information for downstream decision-making and reward maximization? Recent advances in machine learning have provided various contrastive and predictive coding-based methods that work well on high-dimensional synthetic tasks, but the geometry of representations they learn and why particular methods work better than others remains unclear. We are leading a theory effort in collaboration with computer scientists and neuroscientists at Princeton to generalize neuroscientific theories of representation learning to the high-dimensional domain. 

In-context learning in attention-based networks: 

Attention-based networks (e.g. the transformers that underlie large language models such as ChatGPT) exhibit a powerful ability known as in-context learning -- the ability to learn from examples provided in the context with no additional weight updates. In-context learning is a form of meta-learning, where slow learning over a diverse array of tasks enables near-optimal learning on a new task given only a few examples. This offers a potential new paradigm for redefining and making precise long-standing notions of evolvability and learnability in biological systems. By reproducing this phenomenon in simple models trained on synthetic tasks, we hope to reverse-engineer the algorithms implemented by these networks and identify why certain network architectures and data-distributional properties lead to in-context learning. 

Fundamentals of biological associative learning: 

An animal placed in a novel environment (say, a mouse in a Skinnerian box) should quickly figure out its structure (say, what each lever does in the experimentalist's box) to acquire reward. Classic theories from psychology have proposed basic laws or learning rules for how an animal learns how its environment works. An important component of these rules is how associations are formed across long spatial and temporal scales -- how does an animal learn that pulling a lever at one location determines the appearance of reward at another location a few seconds later? Recent behavioral data necessitates revisiting these basic laws and the development of a unifying, quantitative theory of associative learning that captures a rich set of learning phenomena. 

Evolvability in fluctuating environments: 

In past work, we showed that predictable macroscopic patterns emerge due to large numbers of microscopic interactions between mutational effects (‘epistasis’). However, this poses a puzzle: in a typical evolution experiment, these patterns also appear when individual lineages acquire relatively few (~10-20) mutations, which, if chosen from random pathways, are unlikely to interact. An emerging hypothesis, supported by sequencing data and our computational work, is that the genotype-to-fitness map is modular and low-dimensional, that is, only a few pathways matter/are evolvable in any given laboratory condition. Consequently, fixed mutations primarily affect this much smaller set of pathways and their effects show strong epistasis. But, why should the genotype-fitness map be low-dimensional or modular? Past theoretical arguments relate modularity to evolvability, that is, how quickly an organism adapts to a new environment. However, we lack a mechanistic understanding of what these functional modules are, what functional constraints determine dimensionality and which modules are evolutionary targets when environmental statistics change. We are addressing these questions by developing: 1) Computational tools to infer low-dimensional modular structure in genotype-phenotype maps, 2) A theoretical framework for bridging fitness landscape models with mechanistic resource allocation models, and 3) Spin-glass-like fitness landscape models, informed by recent evolution and quantitative  genetics data, that combine epistasis and pleiotropy.