37 citations · 75 across the 21 of their papers we have counts for
24 papers
The Reciprocal tau-Cell: A Log-Domain Circuit for On-Chip Learning
Craig Jin, Thomas Chaffey
Training hardware by gradient descent requires a gradient to be computed using a separate backwards pass. If a circuit is reciprocal, meaning every connection is symmetric, the bac…
Quantization Robustness of Monotone Operator Equilibrium Networks
James Li, Philip H. W. Leong, Thomas Chaffey
Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence.…
Circuit realization and hardware linearization of monotone operator equilibrium networks
Thomas Chaffey
It is shown that the port behavior of a resistor-diode network corresponds to the solution of a ReLU monotone operator equilibrium network (a neural network in the limit of infinit…
Operator-Splitting Methods for Neuromorphic Circuit Simulation
Amir Shahhosseini, Thomas Chaffey, Rodolphe Sepulchre
A novel splitting algorithm is proposed for the numerical simulation of neuromorphic circuits. The algorithm is grounded in the operator-theoretic concept of monotonicity, which be…
Graphical Dominance Analysis for Linear Systems: A Frequency-Domain Approach
Chao Chen, Thomas Chaffey, Rodolphe Sepulchre
We propose a frequency-domain approach to dominance analysis for multi-input multi-output (MIMO) linear time-invariant systems. The dominance of a MIMO system is defined to be the…
Symmetry in linear physical systems
Arjan van der Schaft, Rodolphe Sepulchre, Tom Chaffey
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input…
Convergence of energy-based learning in linear resistive networks
Anne-Men Huijzer, Thomas Chaffey, Bart Besselink +1
Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of…
A homotopy theorem for incremental stability
Thomas Chaffey, Andrey Kharitenko, Fulvio Forni +1
A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that increment…
Amplitude response and square wave describing functions
Thomas Chaffey, Fulvio Forni
An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is cha…
An Operator-Theoretic Framework to Simulate Neuromorphic Circuits
Amir Shahhosseini, Thomas Chaffey, Rodolphe Sepulchre
Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit…
Kernel Modelling of Fading Memory Systems
Yongkang Huo, Thomas Chaffey, Rodolphe Sepulchre
The paper is a follow-up of the recently introduced kernel-based framework to identify nonlinear input-output systems regularized by desirable input-output incremental properties.…
Relaxation systems and cyclic monotonicity
Thomas Chaffey, Henk J. van Waarde, Rodolphe Sepulchre
It is shown that an LTI system is a relaxation system if and only if its Hankel operator is cyclic monotone. Cyclic monotonicity of the Hankel operator implies the existence of a s…
Circuit Analysis using Monotone+Skew Splitting
Thomas Chaffey, Sebastian Banert, Pontus Giselsson +1
It is shown that the behavior of an -port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elemen…
Loop Shaping with Scaled Relative Graphs
Thomas Chaffey, Fulvio Forni, Rodolphe Sepulchre
The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphi…
On the incremental form of dissipativity
Rodolphe Sepulchre, Thomas Chaffey, Fulvio Forni
Following the seminal work of Zames, the input-output theory of the 70s acknowledged that incremental properties (e.g. incremental gain) are the relevant quantities to study in non…
Splitting algorithms and circuit analysis
Thomas Chaffey, Amritam Das, Rodolphe Sepulchre
The splitting algorithms of monotone operator theory find zeros of sums of relations. This corresponds to solving series or parallel one-port electrical circuits, or the negative f…
Circuit Model Reduction with Scaled Relative Graphs
Thomas Chaffey, Alberto Padoan
Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in lin…
Analog cross coupled controller for oscillations: modeling and design via dominant system theory
Weiming Che, Thomas Chaffey, Fulvio Forni
We propose a new analog feedback controller based on the classical cross coupled electronic oscillator. The goal is to drive a linear passive plant into oscillations. We model the…
Monotone one-port circuits
Thomas Chaffey, Rodolphe Sepulchre
Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed f…
A rolled-off passivity theorem
Thomas Chaffey
Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconne…
Graphical Nonlinear System Analysis
Thomas Chaffey, Fulvio Forni, Rodolphe Sepulchre
We use the recently introduced concept of a Scaled Relative Graph (SRG) to develop a graphical analysis of input-output properties of feedback systems. The SRG of a nonlinear opera…
Oscillations in Mixed-Feedback Systems
Amritam Das, Thomas Chaffey, Rodolphe Sepulchre
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-…
Scaled relative graphs for system analysis
Thomas Chaffey, Fulvio Forni, Rodolphe Sepulchre
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled rel…
Monotone RLC Circuits
Thomas Chaffey, Rodolphe Sepulchre
The circuit-theoretic origins of maximal monotonicity are revisited using modern optimization algorithms for maximal monotone operators. We present an algorithm for computing the p…