15 papers
Network Topology Does Not Matter: The Breakdown of Classical Consensus in LLM Populations
Sahil Rajesh Dhayalkar
As multi-agent language model networks become widely deployed, predicting their collective behavior is a critical challenge. Classical distributed consensus theory relies on networ…
Kilobyte Models: Neural Networks as a Seed and a Quantized Latent
Sahil Rajesh Dhayalkar
The cost of storing and transmitting a trained neural network scales with its parameter count, a bottleneck for over-the-air updates, on-device libraries, and other bandwidth-bound…
Overcoming the Impedance Mismatch: A Theoretical Roadmap for Fusing Foundation Models and Knowledge Graphs
Sahil Rajesh Dhayalkar
Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowled…
Logic-Gated Time-Shared Feedforward Networks for Alternating Finite Automata: Exact Simulation and Learnability
Sahil Rajesh Dhayalkar
We present a formal and constructive framework for simulating Alternating Finite Automata (AFAs) using Logic-Gated Time-Shared Feedforward Networks (LG-TS-FFNs). Unlike prior neura…
Reasoning Stabilization Point: A Training-Time Signal for Stable Evidence and Shortcut Reliance
Sahil Rajesh Dhayalkar
Fine-tuning pretrained language models can improve task performance while subtly altering the evidence a model relies on. We propose a training-time interpretability view that trac…
Attention as Binding: A Vector-Symbolic Perspective on Transformer Reasoning
Sahil Rajesh Dhayalkar
Transformer-based language models display impressive reasoning-like behavior, yet remain brittle on tasks that require stable symbolic manipulation. This paper develops a unified p…
Particle Filter Made Simple: A Step-by-Step Beginner-friendly Guide
Sahil Rajesh Dhayalkar
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and s…
Symbolic Feedforward Networks for Probabilistic Finite Automata: Exact Simulation and Learnability
Sahil Rajesh Dhayalkar
We present a formal and constructive theory showing that probabilistic finite automata (PFAs) can be exactly simulated using symbolic feedforward neural networks. Our architecture…
Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs
Sahil Rajesh Dhayalkar
We extend the ReLU Transition Graph (RTG) framework into a comprehensive graph-theoretic model for understanding deep ReLU networks. In this model, each node represents a linear ac…
Neural Networks as Universal Finite-State Machines: A Constructive Deterministic Finite Automaton Theory
Sahil Rajesh Dhayalkar
We present a complete theoretical and empirical framework establishing feedforward neural networks as universal finite-state machines (N-FSMs). Our results prove that finite-depth…
The Geometry of ReLU Networks through the ReLU Transition Graph
Sahil Rajesh Dhayalkar
We develop a novel theoretical framework for analyzing ReLU neural networks through the lens of a combinatorial object we term the ReLU Transition Graph (RTG). In this graph, each…
A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization
Sahil Rajesh Dhayalkar
We propose a combinatorial and graph-theoretic theory of dropout by modeling training as a random walk over a high-dimensional graph of binary subnetworks. Each node represents a m…
A Constructive Framework for Nondeterministic Automata via Time-Shared, Depth-Unrolled Feedforward Networks
Sahil Rajesh Dhayalkar
We present a formal and constructive simulation framework for nondeterministic finite automata (NFAs) using time-shared, depth-unrolled feedforward networks (TS-FFNs), i.e., acycli…
Dynamic Context Adaptation and Information Flow Control in Transformers: Introducing the Evaluator Adjuster Unit and Gated Residual Connections
Sahil Rajesh Dhayalkar
Transformers have revolutionized various domains of artificial intelligence due to their unique ability to model long-range dependencies in data. However, they lack in nuanced, con…
Human Activity Recognition using Smartphones
Mayur Sonawane, Sahil Rajesh Dhayalkar, Siddesh Waje +3
Human Activity Recognition is a subject of great research today and has its applications in remote healthcare, activity tracking of the elderly or the disables, calories burnt trac…