arXiv subjects

Javier Lopez-Piqueres

Publications and source records attributed to Javier Lopez-Piqueres.

10 recordsLinked to original sources

arXiv2026

MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning

We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This factorization indexes key structural dimensions, including layer and matrix type, and can optionally incorporate heads and tasks. This design allows MetaTT's parameter count to scale with the sum, rather than the product, of the modes, resulting in a substantially more compact adapter. Our benchmarks compare MetaTT with LoRA along with recent state-of-the-art matrix and tensor decomposition based fine-tuning methods. We observe that when tested on single-task standard language modeling benchmarks, MetaTT achieves competitive parameter efficiency to accuracy tradeoff. We further demonstrate that MetaTT performs competitively when compared to state-of-the-art methods on multi-task learning. Finally, we leverage the TT decomposition to design a rank adaptive optimizer inspired by the DMRG method from many-body physics. Our results demonstrate that integrating this approach with AdamW enhances optimization performance for a specified target rank.

cs.LG↗

arXiv2026

Tensor Network Estimation of Distribution Algorithms

Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into evolutionary optimization algorithms have appeared in the recent literature. In essence, these methods can be understood as replacing the traditional crossover operation of a genetic algorithm with a tensor network-based generative model. We investigate these methods from the point of view that they are Estimation of Distribution Algorithms (EDAs). We find that optimization performance of these methods is not related to the power of the generative model in a straightforward way. Generative models that are better (in the sense that they better model the distribution from which their training data is drawn) do not necessarily result in better performance of the optimization algorithm they form a part of. This raises the question of how best to incorporate powerful generative models into optimization routines. In light of this we find that adding an explicit mutation operator to the output of the generative model often improves optimization performance.

cs.LG↗

arXiv2025

Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints

In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures. These tensor networks are particularly tailored for modeling distributions with support strictly over the feasible space, offering benefits such as reducing the search space in optimization problems, alleviating overfitting, improving training efficiency, and decreasing model size. Central to our approach is the concept of a quantum region, an extension of quantum numbers traditionally used in U(1) symmetric tensor networks, adapted to capture any linear constraint, including the unconstrained scenario. We further develop a novel canonical form for these new MPS, which allow for the merging and factorization of tensor blocks according to quantum region fusion rules and permit optimal truncation schemes. Utilizing this canonical form, we apply an unsupervised training strategy to optimize arbitrary objective functions subject to discrete linear constraints. Our method's efficacy is demonstrated by solving the quadratic knapsack problem, achieving superior performance compared to a leading nonlinear integer programming solver. Additionally, we analyze the complexity and scalability of our approach, demonstrating its potential in addressing complex constrained combinatorial optimization problems.

math.NA↗

arXiv2023

Observing quantum measurement collapse as a learnability phase transition

The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware.

quant-ph↗

arXiv2023

Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization

Constrained combinatorial optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search space. In some heuristic solvers, these are typically addressed by introducing certain Lagrange multipliers in the cost function, by relaxing them in some way, or worse yet, by generating many samples and only keeping valid ones, which leads to very expensive and inefficient searches. In this work, we encode arbitrary integer-valued equality constraints of the form Ax=b, directly into U(1) symmetric tensor networks (TNs) and leverage their applicability as quantum-inspired generative models to assist in the search of solutions to combinatorial optimization problems. This allows us to exploit the generalization capabilities of TN generative models while constraining them so that they only output valid samples. Our constrained TN generative model efficiently captures the constraints by reducing number of parameters and computational costs. We find that at tasks with constraints given by arbitrary equalities, symmetric Matrix Product States outperform their standard unconstrained counterparts at finding novel and better solutions to combinatorial optimization problems.

quant-ph↗

arXiv2023

Integrability breaking from backscattering

We analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability and leads to a crossover from ballistic to diffusive transport, it preserves infinitely many conserved quantities corresponding to even moments of the velocity distribution of the gas. In the limit of small noise, we derive the exact expressions for the diffusion and structure factor matrices, and show that they generically have off-diagonal components in the presence of interactions. We find that the particle density structure factor is non-Gaussian and singular near the origin, with a return probability showing logarithmic deviations from diffusion.

cond-mat.stat-mech↗

arXiv2022

Integrability breaking in the Rule 54 cellular automaton

Cellular automata have recently attracted a lot of attention as testbeds to explore the emergence of many-body quantum chaos and hydrodynamics. We consider the Rule 54 model, one of the simplest interacting integrable models featuring two species of quasiparticles (solitons), in the presence of an integrability-breaking perturbation that allows solitons to backscatter. We study the onset of thermalization and diffusive hydrodynamics in this model, compute perturbatively the diffusion constant of tracer particles, and comment on its relation to transport coefficients.

cond-mat.stat-mech↗

arXiv2021

Operator front broadening in chaotic and integrable quantum chains

Operator spreading under unitary time evolution has attracted a lot of attention recently, as a way to probe many-body quantum chaos. While quantities such as out-of-time-ordered correlators (OTOC) do distinguish interacting from non-interacting systems, it has remained unclear to what extent they can truly diagnose chaotic {\it vs} integrable dynamics in many-body quantum systems. Here, we analyze operator spreading in generic 1D many-body quantum systems using a combination of matrix product operator (MPO) and analytical techniques, focusing on the operator {\em right-weight}. First, we show that while small bond dimension MPOs allow one to capture the exponentially-decaying tail of the operator front, in agreement with earlier results, they lead to significant quantitative and qualitative errors for the actual front -- defined by the maximum of the right-weight. We find that while the operator front broadens diffusively in both integrable and chaotic interacting spin chains, the precise shape and scaling of the height of the front in integrable systems is anomalous for all accessible times. We interpret these results using a quasiparticle picture. This provides a sharp, though rather subtle signature of many-body quantum chaos in the operator front.

cond-mat.str-el↗

arXiv2021

Hydrodynamics of nonintegrable systems from a relaxation-time approximation

We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is based on a generalized relaxation-time approximation; it gives a simple, but surprisingly accurate, prescription for computing nonequilibrium transport even in strongly interacting systems. This approximation reproduces the crossover from generalized to conventional hydrodynamics in interacting one-dimensional Bose gases with integrability-breaking perturbations, both with and without momentum conservation. It also predicts the hydrodynamics of chaotic quantum spin chains, in good agreement with matrix product operator calculations.

cond-mat.stat-mech↗

arXiv2020

Mean-field entanglement transitions in random tree tensor networks

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

cond-mat.stat-mech↗