A characteristic feature of living systems is the ability to adapt based on limited feedback. However, from single cells to animal collectives, living systems operate well beyond the regime where traditional optimization principles apply, that is, sensory input and control output are often high-dimensional. An animal cannot hope to learn a control strategy from scratch by exploring a high-dimensional control space within its lifetime. For example, a simple grasping movement involves more than 20 degrees of freedom; learning this movement through trial-and-error would require finding a specific trajectory from point A to point B in a 20-dimensional state space with unknown constraints and nonlinear dynamics. Artificial neural networks face a similar problem, with very large numbers of parameters and internal states. However, the space of possible ways one can modify the system is vast, and yet useful adaptations often have to be found quickly. How can complex systems learn and adapt without exhaustively exploring all of their possibilities? Does experience over long timescales shape the ability to respond on shorter timescales?

We approach these questions using mathematical theory, numerics and data-driven modeling, often in collaboration with experimental biologists and machine-learning researchers. Modern AI systems are particularly valuable because they provide complex learning systems that can be trained and probed in ways that are often impossible in biology. Our current work is centered on three broad themes: (1) cognition and intelligence, (2) collective behavior in multicellular systems, and (3) mapping genotypes to phenotypes.

Cognition and intelligence

How do higher-order cognitive abilities emerge from the dynamics of many interacting components?

Abilities such as reasoning, few-shot learning, intuitive understanding of the physical world can be well-characterized at the level of behavior. Yet we have very little understanding of how such abilities arise from the underlying circuitry, or how learning gives rise to the mechanisms that implement them. Bridging this gap—from cognitive phenomena to circuit-level mechanisms—is one of the central challenges in understanding intelligence.

Until recently, this question could be addressed primarily by examining living systems. Large artificial neural networks now exhibit sophisticated cognitive behaviors while remaining systems that are easy to train and leverage as fully accessible experimental systems. Modern artificial intelligence thus creates an exciting opportunity for identifying essential aspects of intelligence. 

Our goal is to use these systems to develop theory for how complex circuits acquire cognitive abilities through learning. We would like to understand what internal computations support particular behaviors, how these computations emerge during training, and which principles extend across architectures and potentially across biological and artificial systems. 

Selected references: Hamou, Gershman & Reddy, Reconciling time and prediction error theories of associative learning, Nature Communications (2025); Reddy, A reinforcement-based mechanism for discontinuous learning, PNAS (2022); Reddy, The mechanistic basis of data dependence and abrupt learning in an in-context classification task, ICLR (2024); Gibson, Cui & Reddy, Distinct mechanisms underlying in-context learning in transformers, arXiv (2026); Raj & Reddy, Adaptive inference and function vectors in deep transformers, arXiv (2026).

Collective behavior in multicellular systems

A multicellular system is made up of many heterogeneous units, each with access to only part of the state of the whole system. Yet these units collectively generate remarkably coordinated behaviors. A distinctive aspect of collective behavior in such systems is that individual units have relatively sophisticated internal states and exchange information with other units through diverse signaling modalities. We are interested in formulating this decentralized control process as a form of distributed computation: what information must individual units exchange, and how can local interactions generate robust behavior without a centralized controller?

During development, cells grow, communicate, change their identities and apply forces to pattern and shape tissues. In recent work, partly inspired by development, we have explored connections between generative modeling and models of cell-fate specification. More recently, we have explored a control theoretic framework for self-organization in mean-field interacting systems. 

Other nascent work on extrasynaptic communication in nervous systems is motivated by recent experiments which show that the connectome of synaptic wiring is not necessarily a good predictor of neural signal propagation. These experiments show extensive diversity in neuromodulators expressed across a similarly diverse set of cell types. Neuromodulators diffuse outside synapses, presumably persist for minutes or longer in the extracellular milieu, and affect different neurons differently depending on which receptors these neurons express. The biophysics of transport and the computational role played by most neuromodulators is not known. In principle, such signals could convey a compact representation of the animal's internal state, allowing the organism to reconfigure how a static synaptic circuit operates in response to changes in context. Similar questions arise in the immune system and, plausibly, in other multicellular systems. We collaborate with experimental neuroscientists and develop methods in multi-agent reinforcement learning to identify organizational principles of such distributed systems. 

Selected references: Reddy, Dynamic landscapes and statistical limits on growth during cell fate specification, Physical Review E (2025); Blumenthal & Reddy, Self-organized robustness in mean-field interacting systems, arXiv (2026).

Mapping genotypes to phenotypes

How does variation at the level of genes or molecular sequence give rise to variation in phenotype?

This mapping is difficult because genetic changes do not generally act independently, that is, their effects can depend on other mutations and on the environment. The number of possible combinations quickly becomes enormous. Yet this complexity often contains simpler structure. For example, widespread interactions among mutations can generate systematic patterns at the level of fitness, and many genetic variants may act through a much smaller number of shared cellular processes. We are interested in identifying when such simplifications occur and how they can be inferred from data. We develop methods that uncover hidden structure in genotype–phenotype data, as well as flexible machine-learning models that can capture higher-order genetic interactions and changes across environments. 

Selected references: Reddy & Desai, Global epistasis emerges from a generic model of a complex trait, eLife (2021); Petti, Reddy & Desai, Inferring sparse structure in genotype–phenotype maps, Genetics (2023); Rijal et al., Inferring genotype–phenotype maps using attention models, PNAS Nexus (2026); George, Wingreen & Reddy, Phenotypic Heterogeneity in Lag Reflects an Evolutionarily Stable Bet-Hedging Strategy, PRX Life (2026); Liu et al., A thermodynamic metric quantitatively predicts disordered protein partitioning and multicomponent phase behavior, arXiv (2026).