Adam J. Eisen

selected publications

1. 

   Propofol anesthesia destabilizes neural dynamics across cortex

   Adam J. Eisen*, Leo Kozachkov*, Andre M. Bastos, Jacob A. Donoghue, Meredith K. Mahnke, Scott L. Brincat, Sarthak Chandra, Emery N. Brown, Ila R. Fiete, and Earl K. Miller

   Neuron Jul 2024

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   Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is that anesthesia disrupts dynamic stability-the ability of the brain to balance excitability with the need to be stable and controllable. To test this hypothesis, we developed a method for quantifying changes in population-level dynamic stability in complex systems: delayed linear analysis for stability estimation (DeLASE). Propofol was used to transition animals between the awake state and anesthetized unconsciousness. DeLASE was applied to macaque cortex local field potentials (LFPs). We found that neural dynamics were more unstable in unconsciousness compared with the awake state. Cortical trajectories mirrored predictions from destabilized linear systems. We mimicked the effect of propofol in simulated neural networks by increasing inhibitory tone. This in turn destabilized the networks, as observed in the neural data. Our results suggest that anesthesia disrupts dynamical stability that is required for consciousness.

2. 

   Delay Embedding Theory of Neural Sequence Models

   Mitchell B. Ostrow, Adam J. Eisen, and Ila R. Fiete

   In ICML Workshop on Next Generation Sequence Models Jun 2024

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   To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed variables. To test whether language models are effectively constructing delay embeddings, we measure the capacities of sequence models to reconstruct unobserved dynamics. We trained 1-layer transformer decoders and state-space sequence models on next-step prediction from noisy, partially-observed time series data. We found that each sequence layer can learn a viable embedding of the underlying system. However, state-space models have a stronger inductive bias than transformers-in particular, they more effectively reconstruct unobserved information at initialization, leading to more parameter-efficient models and lower error on dynamics tasks. Our work thus forges a novel connection between dynamical systems and deep learning sequence models via delay embedding theory.

3. 

   Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis

   Mitchell B. Ostrow, Adam J. Eisen, Leo Kozachkov, and Ila R. Fiete

   In Advances in Neural Information Processing Systems Dec 2023

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   How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic interpretability, and brain-machine interfaces. Standard approaches for comparing neural networks focus on the spatial geometry of latent states. Yet in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry. To bridge this gap, we introduce a novel similarity metric that compares two systems at the level of their dynamics, called Dynamical Similarity Analysis (DSA). Our method incorporates two components: Using recent advances in data-driven dynamical systems theory, we learn a high-dimensional linear system that accurately captures core features of the original nonlinear dynamics. Next, we compare different systems passed through this embedding using a novel extension of Procrustes Analysis that accounts for how vector fields change under orthogonal transformation. In four case studies, we demonstrate that our method disentangles conjugate and non-conjugate recurrent neural networks (RNNs), while geometric methods fall short. We additionally show that our method can distinguish learning rules in an unsupervised manner. Our method opens the door to comparative analyses of the essential temporal structure of computation in neural circuits.