6 papers
The Universe Learning Itself: On the Evolution of Dynamics from the Big Bang to Machine Intelligence
Pradeep Singh, Mudasani Rushikesh, Bezawada Sri Sai Anurag +1
We develop a unified, dynamical-systems narrative of the universe that traces a continuous chain of structure formation from the Big Bang to contemporary human societies and their…
HypER: Hyperbolic Echo State Networks for Capturing Stretch-and-Fold Dynamics in Chaotic Flows
Pradeep Singh, Sutirtha Ghosh, Ashutosh Kumar +2
Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but…
Frozen in Time: Parameter-Efficient Time Series Transformers via Reservoir-Induced Feature Expansion and Fixed Random Dynamics
Pradeep Singh, Mehak Sharma, Anupriya Dey +1
Transformers are the de-facto choice for sequence modelling, yet their quadratic self-attention and weak temporal bias can make long-range forecasting both expensive and brittle. W…
Echo State Networks as State-Space Models: A Systems Perspective
Pradeep Singh, Balasubramanian Raman
Echo State Networks (ESNs) are typically presented as efficient, readout-trained recurrent models, yet their dynamics and design are often guided by heuristics rather than first pr…
Contraction, Criticality, and Capacity: A Dynamical-Systems Perspective on Echo-State Networks
Pradeep Singh, Lavanya Sankaranarayanan, Balasubramanian Raman
Echo-State Networks (ESNs) distil a key neurobiological insight: richly recurrent but fixed circuitry combined with adaptive linear read-outs can transform temporal streams with re…
Dynamics and Computational Principles of Echo State Networks: A Mathematical Perspective
Pradeep Singh, Ashutosh Kumar, Sutirtha Ghosh +2
Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps…