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Santiago Cifuentes

Publications and source records attributed to Santiago Cifuentes.

16 recordsLinked to original sources
arXiv2026

Approximate Homomorphisms and Convergent Representations in Transducers

We study the stability of minimal representations of controlled stochastic processes (in particular, transducers) under perturbations. This question is motivated by recent experiments finding predictive-state structure in the latent representations of neural networks. We consider standard, linear and predictive transducers. We introduce notions of approximate homomorphism capturing local structural similarity between them, together with metrics comparing their induced dynamics (which we refer to as interfaces), and prove properties such as composability of the approximate homomorphisms. For standard transducers, we show that there exist simple interfaces for which there is no approximate homomorphism between the different implementations of the dynamics. In contrast, for every finite-rank interface $\mathcal I$, we prove that all minimal linear transducers implementing interfaces sufficiently close to $\mathcal I$ have an approximate homomorphism to the minimal implementation of $\mathcal I$, with error linear in the perturbation size. We prove an analogous stability result for predictive transducers under a residual metric using some mild hypothesis regarding the indistinguishability of the belief states. These results identify conditions under which canonical transducer representations are robust to perturbations, while showing that such convergence fails without additional structural restrictions. Under the assumption that these type of abstractions are embedded into the hidden layers of modern AI models, this gives some theoretical support to the hypothesis that their latent representations exhibit structural convergence.

cs.LG↗
arXiv2026

Beyond Shapley: Efficient Computation of Asymmetric Shapley Values

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

cs.AI↗
arXiv2026

Complexity of detecting large coefficients in the Pauli basis

We study the problem of deciding, given a mechanism to prepare a quantum state $ρ$ and a value $\varepsilon > 0$, whether there is some non-identity Pauli matrix $P$ such that $|Tr(P ρ)| \geq \varepsilon$. We consider that the state $ρ$ is described as the result of tracing out some of the qubits of a pure state prepared by a circuit $C$, and we assume the promise that either there is a Pauli matrix satisfying the stated condition or, instead, that for all non-identity Pauli matrices $P$ it is the case that $|Tr(Pρ)|\leq \varepsilon/2$. The problem is in $QCMA$, and we prove that if it belongs to $BQP$ then $NP \subseteq BQP$. The result is obtained through a reduction from the minimum-weight code problem, and it holds even when $ρ$ is assumed to be a pure state (i.e. when no qubits are discarded) and $\varepsilon$ is constant. This resolves an open question regarding the existence of efficient tomographic procedures to find the largest coefficients of a quantum state in the Pauli basis: namely, they do not exist under the standard hypothesis $NP \nsubseteq BQP$.

quant-ph↗
arXiv2026

Variational Quantum Models for Knowledge Graph Embeddings on NISQ Devices

Variational Quantum Algorithms (VQAs) combine quantum circuits with classical optimization to tackle problems that may benefit from the capabilities of near-term quantum hardware. In knowledge graph embedding, recent proposals based on this approach follow a similar overall architecture but differ in the way they compute the score function and in the number of qubits they require. One design uses $n+1$ qubits and obtains the score through a switch test on an ancillary qubit, while another employs $2n+1$ qubits and applies a swap test between two registers. In both cases, entities and relations are represented in a Hilbert space of dimension $d = 2^n$, with comparable computational cost and the same mean squared error loss. This work introduces a unified framework that captures the two schemes and makes it possible to explore new variants. Within this setting, we propose an alternative that keeps the intuitive meaning of the score function while dispensing with ancillary qubits and entangled measurements. The result is a model better suited to current NISQ devices, reducing hardware demands without sacrificing interpretability.

quant-ph↗
arXiv2026

Measuring the largest coefficients of a quantum state

We introduce a hierarchical algorithm for identifying the largest Pauli coefficients of an unknown $n$-qubit quantum state. The algorithm traverses a prefix-based tree whose nodes represent partial sums of squared Pauli coefficients, always expanding branches with the largest estimated weight and discarding the rest. Node weights are estimated using Bell sampling on two copies of the state, or alternatively via SWAP tests on subsystems. We analyze the sample complexity of each node estimation and derive bounds on the total number of nodes expanded as a function of the desired number of coefficients and the state's purity. For states admitting a sparse representation in the Pauli basis, the algorithm achieves a good reconstruction of the dominant components without requiring full state tomography. We validate the method with numerical simulations on Pauli-singleton states and random stabilizer states, showing that the algorithm's performance is competitive with other methods for structured states. Our work addresses an open problem in Pauli sampling and provides a practical tool for the targeted characterization of structured quantum states.

quant-ph↗
arXiv2026

Characterizing normality via automata and random matrix products

For a fixed alphabet A, an infinite sequence X is said to be normal if every word w over A appears in X with the same frequency as any other word of the same length. A classical result relates normality to finite automata as follows: a sequence X is normal if and only if all gambling strategies implementable with finite deterministic automata lose all their capital when trying to predict the next bit of X after seing the ones before. More precisely, Schnorr and Stimm (1972) proved that the capital goes exponentially fast to zero unless the automaton represents the gambler that never bets, in which case the capital remains constant. In this paper we show that an analogous result holds when considering probabilistic automata: a sequence X is normal if and only if for any gambling strategy implementable with probabilistic finite automaton it holds that the expected value of the capital of the gambler converges exponentially fast to a finite value when playing against X. To obtain this result, we show a more general statement related to the convergence of martingales given by finite sets of non-negative matrices {M a } a$\in$A . In particular, we show that X is normal if and only if ||vM X[1] . . . M X[n] || converges exponentially fast to a finite value for any non-negative starting vector v. Moreover, we distinguish three distinctive behaviours that this sequence can attain, and prove that the problem of recognizing, given a family of matrices, to which case it belongs, is decidable.

cs.FL↗
arXiv2026

General Agents Contain World Models, even under Partial Observability and Stochasticity

Deciding whether an agent possesses a model of its surrounding world is a fundamental step toward understanding its capabilities and limitations. In [10], it was shown that, within a particular framework, every almost optimal and general agent necessarily contains sufficient knowledge of its environment to allow an approximate reconstruction of it by querying the agent as a black box. This result relied on the assumptions that the agent is deterministic and that the environment is fully observable. In this work, we remove both assumptions by extending the theorem to stochastic agents operating in partially observable environments. Fundamentally, this shows that stochastic agents cannot avoid learning their environment through the usage of randomization. We also strengthen the result by weakening the notion of generality, proving that less powerful agents already contain a model of the world in which they operate.

cs.AI↗
arXiv2025

Feature Relevancy, Necessity and Usefulness: Complexity and Algorithms

Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic and the notion of \textit{sufficient reason}. Through this concept, the categories of relevant and necessary features were proposed in order to identify the crucial aspects of the input. This paper improves the existing techniques and algorithms for deciding which are the relevant and/or necessary features, showing in particular that necessity can be detected efficiently in complex models such as neural networks. We also generalize the notion of relevancy and study associated problems. Moreover, we present a new global notion (i.e. that intends to explain whether a feature is important for the behavior of the model in general, not depending on a particular input) of \textit{usefulness} and prove that it is related to relevancy and necessity. Furthermore, we develop efficient algorithms for detecting it in decision trees and other more complex models, and experiment on three datasets to analyze its practical utility.

cs.AI↗
arXiv2025

Quantum computational complexity of matrix functions

We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a Hermitian matrix $A$, compute a matrix element of $f(A)$ or compute a local measurement on $f(A)|0\rangle^{\otimes n}$, with $|0\rangle^{\otimes n}$ an $n$-qubit reference state vector, in both cases up to additive approximation error. We consider four functions -- monomials, Chebyshev polynomials, the time evolution function, and the inverse function -- and probe the complexity across a broad landscape covering different problem input regimes. Namely, we consider two types of matrix inputs (sparse and Pauli access), matrix properties (norm, sparsity), the approximation error, and function-specific parameters. We identify BQP-complete forms of both problems for each function and then toggle the problem parameters to easier regimes to see where hardness remains, or where the problem becomes classically easy. As part of our results, we make concrete a hierarchy of hardness across the functions; in parameter regimes where we have classically efficient algorithms for monomials, all three other functions remain robustly BQP-hard, or hard under usual computational complexity assumptions. In identifying classically easy regimes, among others, we show that for any polynomial of degree $\mathrm{poly}(n)$ both problems can be efficiently classically simulated when $A$ has $O(\log n)$ non-zero coefficients in the Pauli basis. This contrasts with the fact that the problems are BQP-complete in the sparse access model even for constant row sparsity, whereas the stated Pauli access efficiently constructs sparse access with row sparsity $O(\log n)$. Our work provides a catalog of efficient quantum and classical algorithms for fundamental linear-algebra tasks.

quant-ph↗
arXiv2024

The Distributional Uncertainty of the SHAP score in Explainable Machine Learning

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley value used in coalition game theory. The definition of this score relies on a probability distribution on the entity population. Since the exact distribution is generally unknown, it needs to be assigned subjectively or be estimated from data, which may lead to misleading feature scores. In this paper, we propose a principled framework for reasoning on SHAP scores under unknown entity population distributions. In our framework, we consider an uncertainty region that contains the potential distributions, and the SHAP score of a feature becomes a function defined over this region. We study the basic problems of finding maxima and minima of this function, which allows us to determine tight ranges for the SHAP scores of all features. In particular, we pinpoint the complexity of these problems, and other related ones, showing them to be NP-complete. Finally, we present experiments on a real-world dataset, showing that our framework may contribute to a more robust feature scoring.

cs.AI↗
arXiv2024

Computational Complexity of Preferred Subset Repairs on Data-Graphs

Preferences are a pivotal component in practical reasoning, especially in tasks that involve decision-making over different options or courses of action that could be pursued. In this work, we focus on repairing and querying inconsistent knowledge bases in the form of graph databases, which involves finding a way to solve conflicts in the knowledge base and considering answers that are entailed from every possible repair, respectively. Without a priori domain knowledge, all possible repairs are equally preferred. Though that may be adequate for some settings, it seems reasonable to establish and exploit some form of preference order among the potential repairs. We study the problem of computing prioritized repairs over graph databases with data values, using a notion of consistency based on GXPath expressions as integrity constraints. We present several preference criteria based on the standard subset repair semantics, incorporating weights, multisets, and set-based priority levels. We show that it is possible to maintain the same computational complexity as in the case where no preference criterion is available for exploitation. Finally, we explore the complexity of consistent query answering in this setting and obtain tight lower and upper bounds for all the preference criteria introduced.

cs.DB↗
arXiv2023

Towards exact algorithmic proofs of maximal mutually unbiased bases sets in arbitrary integer dimension

In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in discrete quantum systems. It is known that for dimensions $d$ that are powers of prime numbers, there exists a set of up to $d+1$ bases that form an MUB set. However, the maximum number of MUBs in dimensions that are not powers of prime numbers is not known. To address this issue, we introduce three algorithms based on First-Order Logic that can determine the maximum number of bases in an MUB set without numerical approximation. Our algorithms can prove this result in finite time, although the required time is impractical. Additionally, we present a heuristic approach to solve the semi-decision problem of determining if there are $k$ MUBs in a given dimension $d$. As a byproduct of our research, we demonstrate that the maximum number of MUBs in any dimension can be achieved with definable complex parameters, computable complex parameters, and other similar fields.

quant-ph↗
arXiv2023

Data-graph repairs: the preferred approach

Repairing inconsistent knowledge bases is a task that has been assessed, with great advances over several decades, from within the knowledge representation and reasoning and the database theory communities. As information becomes more complex and interconnected, new types of repositories, representation languages and semantics are developed in order to be able to query and reason about it. Graph databases provide an effective way to represent relationships among data, and allow processing and querying these connections efficiently. In this work, we focus on the problem of computing preferred (subset and superset) repairs for graph databases with data values, using a notion of consistency based on a set of Reg-GXPath expressions as integrity constraints. Specifically, we study the problem of computing preferred repairs based on two different preference criteria, one based on weights and the other based on multisets, showing that in most cases it is possible to retain the same computational complexity as in the case where no preference criterion is available for exploitation.

cs.DB↗
arXiv2023

An epistemic approach to model uncertainty in data-graphs

Graph databases are becoming widely successful as data models that allow to effectively represent and process complex relationships among various types of data. As with any other type of data repository, graph databases may suffer from errors and discrepancies with respect to the real-world data they intend to represent. In this work we explore the notion of probabilistic unclean graph databases, previously proposed for relational databases, in order to capture the idea that the observed (unclean) graph database is actually the noisy version of a clean one that correctly models the world but that we know partially. As the factors that may be involved in the observation can be many, e.g, all different types of clerical errors or unintended transformations of the data, we assume a probabilistic model that describes the distribution over all possible ways in which the clean (uncertain) database could have been polluted. Based on this model we define two computational problems: data cleaning and probabilistic query answering and study for both of them their corresponding complexity when considering that the transformation of the database can be caused by either removing (subset) or adding (superset) nodes and edges.

cs.DB↗
arXiv2022

On the complexity of finding set repairs for data-graphs

In the deeply interconnected world we live in, pieces of information link domains all around us. As graph databases embrace effectively relationships among data and allow processing and querying these connections efficiently, they are rapidly becoming a popular platform for storage that supports a wide range of domains and applications. As in the relational case, it is expected that data preserves a set of integrity constraints that define the semantic structure of the world it represents. When a database does not satisfy its integrity constraints, a possible approach is to search for a 'similar' database that does satisfy the constraints, also known as a repair. In this work, we study the problem of computing subset and superset repairs for graph databases with data values using a notion of consistency based on a set of Reg-GXPath expressions as integrity constraints. We show that for positive fragments of Reg-GXPath these problems admit a polynomial-time algorithm, while the full expressive power of the language renders them intractable.

cs.DB↗