Arjun Karuvally

Postdoctoral Researcher

Salk Institute for Biological Studies

I’m a postdoctoral researcher interested in how intelligence works—both in the brain and in artificial systems. I study machine learning, mathematical models, and the dynamics of neural activity to uncover simple principles that explain complex behavior. I enjoy ideas that connect different fields and reveal the deeper structure behind how we learn, remember, and reason. My long-term aim is to understand the computational rules of the brain and use those insights to build better, more principled AI. If you have any comments, thoughts or queries, you can reach me at arjun.k018@gmail.com.

news

Oct 11, 2025	Our paper Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators is published at MDPI Analytics. Check out the paper here https://doi.org/10.3390/analytics4040028
Sep 21, 2025	Bridging Expressivity and Scalability with Adaptive Unitary SSMs. is accepted at NeurIPS 2025. Check out the final version at https://openreview.net/pdf?id=s4zitEu2R8
Sep 21, 2025	Exponential Dynamic Energy Network for High Capacity Sequence Memory. is accepted at NeurIPS 2025. Check out the final version at https://openreview.net/pdf?id=GyOrgWZZKO
Jun 8, 2025	New preprint released! Transient Dynamics in Lattices of Differentiating Ring Oscillators. Check it out at https://arxiv.org/pdf/2506.07253
Mar 10, 2025	Defended my Phd thesis titled Beyond the Hopfield Memory Theory: Dynamic Energy Landscapes and Traveling Waves in RNNs. Thank you for my advisors Hava T. Siegelmann, Terry Sejnowski, and committee members Cameron Musco and Ina Fiterau.

latest posts

Oct 18, 2023	Fractals
Sep 14, 2023	Memory and the Energy Paradigm

selected publications

2025

Bridging Expressivity and Scalability with Adaptive Unitary SSMs

Arjun Karuvally, Franz Nowak, Anderson T. Keller, and 3 more authors

2025
Exponential Dynamic Energy Network for High Capacity Sequence Memory

Arjun Karuvally, Pichsinee Lertsaroj, Terrence J. Sejnowski, and 1 more author

2025

2024

Hidden Traveling Waves bind Working Memory Variables in Recurrent Neural Networks

Arjun Karuvally, Terrence Sejnowski, and Hava T Siegelmann

In Proceedings of the 41st International Conference on Machine Learning, 21–27 jul 2024

Abs PDF

Traveling waves are a fundamental phenomenon in the brain, playing a crucial role in short-term information storage. In this study, we leverage the concept of traveling wave dynamics within a neural lattice to formulate a theoretical model of neural working memory in Recurrent Neural Networks (RNNs), study its properties, and its real world implications in AI. The proposed model diverges from traditional approaches, which assume information storage in static, register-like locations updated by interference. Instead, the model stores data as waves that is updated by the wave’s boundary conditions. We rigorously examine the model’s capabilities in representing and learning state histories, which are vital for learning history-dependent dynamical systems. The findings reveal that the model reliably stores external information and enhances the learning process by addressing the diminishing gradient problem of RNNs. To understand the model’s real-world applicability, we explore two cases: linear boundary condition and non-linear, self-attention-driven boundary condition. The experiments reveal that the linear scenario is effectively learned by RNNs through backpropagation when modeling history-dependent dynamical systems. Conversely, the non-linear scenario parallels an attention-only transformer. Collectively, our findings suggest the broader relevance of traveling waves in AI and its potential in advancing neural network architectures.