arXiv subjects

Xavier Poncini

Publications and source records attributed to Xavier Poncini.

5 recordsLinked to original sources

arXiv2025

SCALAR: Benchmarking SAE Interaction Sparsity in Toy LLMs

Mechanistic interpretability aims to decompose neural networks into interpretable features and map their connecting circuits. The standard approach trains sparse autoencoders (SAEs) on each layer's activations. However, SAEs trained in isolation don't encourage sparse cross-layer connections, inflating extracted circuits where upstream features needlessly affect multiple downstream features. Current evaluations focus on individual SAE performance, leaving interaction sparsity unexamined. We introduce SCALAR (Sparse Connectivity Assessment of Latent Activation Relationships), a benchmark measuring interaction sparsity between SAE features. We also propose "Staircase SAEs", using weight-sharing to limit upstream feature duplication across downstream features. Using SCALAR, we compare TopK SAEs, Jacobian SAEs (JSAEs), and Staircase SAEs. Staircase SAEs improve relative sparsity over TopK SAEs by $59.67\% \pm 1.83\%$ (feedforward) and $63.15\% \pm 1.35\%$ (transformer blocks). JSAEs provide $8.54\% \pm 0.38\%$ improvement over TopK for feedforward layers but cannot train effectively across transformer blocks, unlike Staircase and TopK SAEs which work anywhere in the residual stream. We validate on a $216$K-parameter toy model and GPT-$2$ Small ($124$M), where Staircase SAEs maintain interaction sparsity improvements while preserving feature interpretability. Our work highlights the importance of interaction sparsity in SAEs through benchmarking and comparing promising architectures.

cs.LG↗

arXiv2023

Integrable models from singly generated planar algebras

Not all planar algebras can encode the algebraic structure of a Yang--Baxter integrable model described in terms of a so-called homogeneous transfer operator. In the family of subfactor planar algebras, we focus on the ones known as singly generated and find that the only such planar algebras underlying homogeneous Yang--Baxter integrable models are the so-called Yang--Baxter relation planar algebras. According to a result of Liu, there are three such planar algebras: the well-known Fuss--Catalan and Birman--Wenzl--Murakami planar algebras, in addition to one more which we refer to as the Liu planar algebra. The Fuss--Catalan and Birman--Wenzl--Murakami algebras are known to underlie Yang--Baxter integrable models, and we show that the Liu algebra likewise admits a Baxterisation. We also show that the homogeneous transfer operator describing a model underlied by a singly generated Yang--Baxter relation planar algebra is polynomialisable, meaning that it is polynomial in a spectral-parameter-independent element of the algebra.

math-ph↗

arXiv2022

Integrability of planar-algebraic models

The Quantum Inverse Scattering Method is a scheme for solving integrable models in $1+1$ dimensions, building on an $R$-matrix that satisfies the Yang--Baxter equation and in terms of which one constructs a commuting family of transfer matrices. In the standard formulation, this $R$-matrix acts on a tensor product of vector spaces. Here, we relax this tensorial property and develop a framework for describing and analysing integrable models based on planar algebras, allowing non-separable \textit{$R$-operators} satisfying \textit{generalised} Yang--Baxter equations. We also re-evaluate the notion of integrals of motion and characterise when an (algebraic) \textit{transfer operator} is polynomial in a single integral of motion. We refer to such models as {\em polynomially integrable}. In an eight-vertex model, we demonstrate that the corresponding transfer operator is polynomial in the natural hamiltonian. In the Temperley--Lieb loop model with loop fugacity $\beta\in\mathbb{C}$, we likewise find that, for all but finitely many $\beta$-values, the transfer operator is polynomial in the usual hamiltonian element of the Temperley--Lieb algebra $\mathrm{TL}_n(\beta)$, at least for $n\leq17$. Moreover, we find that this model admits a second canonical hamiltonian, and that this hamiltonian also acts as a polynomial integrability generator for small $n$ and all but finitely many $\beta$-values.

math-ph↗

arXiv2021

Approximations in transmon simulation

Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms that are too onerous to run in the loop with current-day quantum hardware, as well as for researchers without consistent access to hardware. However, if the model used to represent the system is not selected carefully, an optimised control protocol may be rendered futile when applied to hardware. We present a series of models, ordered in a hierarchy of progressive approximation, which appear in quantum control literature. The validity of each model is characterised experimentally by designing and benchmarking control protocols for an IBMQ cloud quantum device. This result demonstrates error amplification induced by the application of a first-order perturbative approximation. Furthermore, the emergence of errors that cannot be corrected by simple amplitude scaling of control pulses is demonstrated in simulation, due to an underlying mistreatment of noncomputational dynamics. Finally, an evaluation of simulated control dynamics reveals that despite the substantial variance in numerical predictions across the proposed models, the complexity of discovering local optimal control protocols appears invariant in the simple control scheme setting.

quant-ph↗

arXiv2021

Critical behaviour of loop models on causal triangulations

We introduce a dense and a dilute loop model on causal dynamical triangulations. Both models are characterised by a geometric coupling constant $g$ and a loop parameter $α$ in such a way that the purely geometric causal triangulation model is recovered for $α=1$. We show that the dense loop model can be mapped to a solvable planar tree model, whose partition function we compute explicitly and use to determine the critical behaviour of the loop model. The dilute loop model can likewise be mapped to a planar tree model; however, a closed-form expression for the corresponding partition function is not obtainable using the standard methods employed in the dense case. Instead, we derive bounds on the critical coupling $g_c$ and apply transfer matrix techniques to examine the critical behaviour for $α$ small.

hep-th↗