arXiv subjects

Sandra Zilles

Publications and source records attributed to Sandra Zilles.

At least 19 recordsLinked to original sources

arXiv2026

Learning Erasing Equal-Length Relational Pattern Languages in the Limit from Positive Data over Binary Alphabets

Relational pattern languages generalize Angluin's pattern languages by requiring the strings substituted for repeated occurrences of a variable to stand in a given relation, rather than to be identical. We study erasing pattern languages under the equal-length relation, where all occurrences of a variable must be replaced by strings of the same length. Over alphabets with at least three letters, this class is known to be learnable in the limit from positive data. We show that over a binary alphabet it is not, which resolves an open question from earlier work. Our proof reveals that non-learnability already holds for the restricted subclass of languages generated by patterns that have exactly three maximal substrings of variables. We then show that patterns with at most two maximal substrings of variables are learnable in the limit from positive data for every alphabet of size at least two. If the target pattern is known to have at most one maximal substring of variables, this can even be achieved by an iterative learner, which updates its hypothesis using only the current example and its previous hypothesis.

cs.LO↗

arXiv2026

Positive Characteristic Sets for Relational Pattern Languages

In the context of learning formal languages, data about an unknown target language L is given in terms of a set of (word,label) pairs, where a binary label indicates whether or not the given word belongs to L. A (polynomial-size) characteristic set for L, with respect to a reference class L of languages, is a set of such pairs that satisfies certain conditions allowing a learning algorithm to (efficiently) identify L within L. In this paper, we introduce the notion of positive characteristic set, referring to characteristic sets of only positive examples. These are of importance in the context of learning from positive examples only. We study this notion for classes of relational pattern languages, which are of relevance to various applications in string processing.

cs.FL↗

arXiv2026

Query Feedback and Teaching for Stable and Certifiable Language Generation

Language generation in the limit studies whether a learner observing an enumeration of an unknown target language can eventually generate only valid, previously unseen elements. We study stability, introduced by Kalavasis, Mehrotra, and Velegkas (2025), which requires the generator's infinite output set to eventually remain unchanged, and introduce the stronger notion of certifiability, which requires the generator to determine from its observations that its current output is valid. Drawing on teaching sets in learning theory, we introduce a hierarchy of teaching dimensions for generation under three increasingly strict success criteria: correctness, stability, and certifiability. These dimensions measure the minimum number of selected examples whose appearance guarantees the corresponding success condition. We also study stability and certifiability in the membership-query model of Charikar and Pabbaraju (2025). We characterize stable and certifiable generation, both with and without query feedback, and establish their relationships with uniform generation and identification in the limit. In particular, we give a finite-witness characterization of stable generation, analogous to Angluin's tell-tale characterization of identification, resolving a gap left open by Kalavasis, Mehrotra, and Velegkas (2025). We further compare these generation notions with identification in the limit and contrast their teaching requirements on well-studied language families, including regular and erasing pattern languages.

cs.LG↗

arXiv2026

Burning Signed Graphs

We introduce and analyze a new model of graph burning, in which two competing fires (coloured yellow and green) ignite vertices of a given signed graph and propagate along its edges. The boolean sign of an edge determines whether a fire spreading along the edge changes colour or not. In each step, a player ignites a new vertex in a colour of their choice, while previously activated fires continue to spread. Given a signed graph $Γ$, the objective is to burn the maximum possible number of vertices in a single colour; the optimal achievable value is called the plurality number of $Γ$. We express the plurality number through Hamming distances to a binary code associated with $Γ$. In particular, the minimum plurality number over the switching class of $Γ$ equals the number of vertices minus the covering radius of this code. Under certain conditions on the signature, we determine exact values of the plurality number of signed paths. By contrast, we prove hardness results for multiple variants of the problem of determining or approximating the plurality number.

math.CO↗

arXiv2026

Learning Shuffle Ideals with Membership Queries and Contrastive Examples

This paper studies learning of shuffle ideals with membership queries as well as with contrastive queries---a form of membership query that reveals not only whether a selected word $w$ is in the target language or not, but also provides a most similar word $w'$ that belongs to the target language if %and only if $w$ does not. For both settings, it is shown that even some very simple classes of shuffle ideals cannot be learned efficiently. By contrast, we obtain positive learnability results for classes of shuffle ideals that meet certain structural conditions. In the case of membership queries, these structural conditions are related to the previously studied notion of universal words, and raise new questions in word combinatorics. In the case of contrastive queries, the structural conditions relate to partitioning sets of words that are listed in shortlex order.

cs.FL↗

arXiv2026

Gradient-Discrepancy Acquisition for Pool-Based Active Learning

The effectiveness of active learning hinges on the choice of the acquisition criterion by which a learning algorithm selects potentially informative data points whose label is subsequently queried. This paper proposes a novel gradient-based acquisition criterion, derived from a generalization bound introduced by Luo et al. (2022). This criterion can be applied in lieu of uncertainty measures in uncertainty sampling, or incorporated into diversity-based methods that consider the spread of sampled points in addition to the uncertainty of their labels. We provide a theoretical justification of the proposed acquisition criterion, and demonstrate its effectiveness in an empirical evaluation.

cs.LG↗

arXiv2026

On the Semantics of Primary Cause in Hybrid Dynamic Domains

Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where change due to actions can be both discrete and continuous, that is, hybrid. Yet, despite extensive research on actual causation, only few recent studies looked into causation with continuous change. Building on recent progress, in this paper we propose two definitions of primary cause in a hybrid action-theoretic framework, namely the hybrid temporal situation calculus. One of these is foundational in nature while the other formalizes causation through contributions, which can then be verified from a counterfactual perspective using a modified ``but-for'' test. We prove that these two definitions are indeed equivalent. We then show that our definitions of causation have some intuitively justifiable properties.

cs.AI↗

arXiv2026

Learning Half-Spaces from Perturbed Contrastive Examples

We study learning under a two-step contrastive example oracle, as introduced by Mansouri et. al. (2025), where each queried (or sampled) labeled example is paired with an additional contrastive example of opposite label. While Mansouri et al. assume an idealized setting, where the contrastive example is at minimum distance of the originally queried/sampled point, we introduce and analyze a mechanism, parameterized by a non-decreasing noise function $f$, under which this ideal contrastive example is perturbed. The amount of perturbation is controlled by $f(d)$, where $d$ is the distance of the queried/sampled point to the decision boundary. Intuitively, this results in higher-quality contrastive examples for points closer to the decision boundary. We study this model in two settings: (i) when the maximum perturbation magnitude is fixed, and (ii) when it is stochastic. For one-dimensional thresholds and for half-spaces under the uniform distribution on a bounded domain, we characterize active and passive contrastive sample complexity in dependence on the function $f$. We show that, under certain conditions on $f$, the presence of contrastive examples speeds up learning in terms of asymptotic query complexity and asymptotic expected query complexity.

cs.LG↗

arXiv2026

Active learning from positive and unlabeled examples

Learning from positive and unlabeled data (PU learning) is a weakly supervised variant of binary classification in which the learner receives labels only for (some) positively labeled instances, while all other examples remain unlabeled. Motivated by applications such as advertising and anomaly detection, we study an active PU learning setting where the learner can adaptively query instances from an unlabeled pool, but a queried label is revealed only when the instance is positive and an independent coin flip succeeds; otherwise the learner receives no information. In this paper, we provide the first theoretical analysis of the label complexity of active PU learning.

cs.LG↗

arXiv2025

Distance-based Learning of Hypertrees

We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that we call orderly hypertrees. Our online algorithm can be transformed into a provably optimal offline algorithm. Orderly hypertrees can be positioned within the Fagin hierarchy of acyclic hypergraph (well-studied in database theory), and strictly encompass the broadest class in this hierarchy that is learnable with subquadratic SP-query complexity. Recognizing that in some contexts, such as evolutionary tree reconstruction, distance measurements can degrade with increased distance, we also consider a learning model that uses bounded distance queries. In this model, we demonstrate asymptotically tight complexity bounds for learning general hypertrees.

cs.LG↗

arXiv2025

The Computational Complexity of Almost Stable Clustering with Penalties

We investigate the complexity of stable (or perturbation-resilient) instances of $\mathrm{k-M\small{EANS}}$ and $\mathrm{k-M\small{EDIAN}}$ clustering problems in metrics with small doubling dimension. While these problems have been extensively studied under multiplicative perturbation resilience in low-dimensional Euclidean spaces (e.g., (Friggstad et al., 2019; Cohen-Addad and Schwiegelshohn, 2017)), we adopt a more general notion of stability, termed ``almost stable'', which is closer to the notion of $(α, \varepsilon)$-perturbation resilience introduced by Balcan and Liang (2016). Additionally, we extend our results to $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ with penalties, where each data point is either assigned to a cluster centre or incurs a penalty. We show that certain special cases of almost stable $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ (with penalties) are solvable in polynomial time. To complement this, we also examine the hardness of almost stable instances and $(1 + \frac{1}{poly(n)})$-stable instances of $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ (with penalties), proving super-polynomial lower bounds on the runtime of any exact algorithm under the widely believed Exponential Time Hypothesis (ETH).

cs.CC↗

arXiv2025

Formal Models of Active Learning from Contrastive Examples

Machine learning can greatly benefit from providing learning algorithms with pairs of contrastive training examples -- typically pairs of instances that differ only slightly, yet have different class labels. Intuitively, the difference in the instances helps explain the difference in the class labels. This paper proposes a theoretical framework in which the effect of various types of contrastive examples on active learners is studied formally. The focus is on the sample complexity of learning concept classes and how it is influenced by the choice of contrastive examples. We illustrate our results with geometric concept classes and classes of Boolean functions. Interestingly, we reveal a connection between learning from contrastive examples and the classical model of self-directed learning.

cs.LG↗

arXiv2025

Common Benchmarks Undervalue the Generalization Power of Programmatic Policies

Algorithms for learning programmatic representations for sequential decision-making problems are often evaluated on out-of-distribution (OOD) problems, with the common conclusion that programmatic policies generalize better than neural policies on OOD problems. In this position paper, we argue that commonly used benchmarks undervalue the generalization capabilities of programmatic representations. We analyze the experiments of four papers from the literature and show that neural policies, which were shown not to generalize, can generalize as effectively as programmatic policies on OOD problems. This is achieved with simple changes in the neural policies training pipeline. Namely, we show that simpler neural architectures with the same type of sparse observation used with programmatic policies can help attain OOD generalization. Another modification we have shown to be effective is the use of reward functions that allow for safer policies (e.g., agents that drive slowly can generalize better). Also, we argue for creating benchmark problems highlighting concepts needed for OOD generalization that may challenge neural policies but align with programmatic representations, such as tasks requiring algorithmic constructs like stacks.

cs.LG↗

arXiv2023

Approximation Algorithms for Preference Aggregation Using CP-Nets

This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called \emph{swaps}, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to $4/3$. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any $\varepsilon$, the trivial algorithm can\emph{not}\/ attain a $(2-\varepsilon)$-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than $2$.

cs.CC↗

arXiv2023

Using Sum-Product Networks to Assess Uncertainty in Deep Active Learning

The success of deep active learning hinges on the choice of an effective acquisition function, which ranks not yet labeled data points according to their expected informativeness. Many acquisition functions are (partly) based on the uncertainty that the current model has about the class label of a point, yet there is no generally agreed upon strategy for computing such uncertainty. This paper proposes a new and very simple approach to computing uncertainty in deep active learning with a Convolutional Neural Network (CNN). The main idea is to use the feature representation extracted by the CNN as data for training a Sum-Product Network (SPN). Since SPNs are typically used for estimating the distribution of a dataset, they are well suited to the task of estimating class probabilities that can be used directly by standard acquisition functions such as max entropy and variational ratio. The effectiveness of our method is demonstrated in an experimental study on several standard benchmark datasets for image classification, where we compare it to various state-of-the-art methods for assessing uncertainty in deep active learning.

cs.LG↗

arXiv2023

Inferring Symbolic Automata

We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all obtained results are positive. We provide a necessary condition for efficient learnability of SFAs in this paradigm, from which we obtain the first negative result. The main focus of our work lies in the learnability of SFAs under the paradigm of identification in the limit using polynomial time and data, and its strengthening efficient identifiability, which are concerned with the existence of a systematic set of characteristic samples from which a learner can correctly infer the target language. We provide a necessary condition for identification of SFAs in the limit using polynomial time and data, and a sufficient condition for efficient learnability of SFAs. From these conditions we derive a positive and a negative result. The performance of a learning algorithm is typically bounded as a function of the size of the representation of the target language. Since SFAs, in general, do not have a canonical form, and there are trade-offs between the complexity of the predicates on the transitions and the number of transitions, we start by defining size measures for SFAs. We revisit the complexity of procedures on SFAs and analyze them according to these measures, paying attention to the special forms of SFAs: normalized SFAs and neat SFAs, as well as to SFAs over a monotonic effective Boolean algebra. This is an extended version of the paper with the same title published in CSL'22.

cs.LO↗

arXiv2022

A Labelled Sample Compression Scheme of Size at Most Quadratic in the VC Dimension

This paper presents a construction of a proper and stable labelled sample compression scheme of size $O(\VCD^2)$ for any finite concept class, where $\VCD$ denotes the Vapnik-Chervonenkis Dimension. The construction is based on a well-known model of machine teaching, referred to as recursive teaching dimension. This substantially improves on the currently best known bound on the size of sample compression schemes (due to Moran and Yehudayoff), which is exponential in $\VCD$. The long-standing open question whether the smallest size of a sample compression scheme is in $O(\VCD)$ remains unresolved, but our results show that research on machine teaching is a promising avenue for the study of this open problem. As further evidence of the strong connections between machine teaching and sample compression, we prove that the model of no-clash teaching, introduced by Kirkpatrick et al., can be used to define a non-trivial lower bound on the size of stable sample compression schemes.

cs.LG↗

arXiv2021

On the Complexity of Symbolic Finite-State Automata

We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a state, and the size of the most complex transition predicate. We pay attention to the special forms of SFAs: {normalized SFAs} and {neat SFAs}, as well as to SFAs over a {monotonic} effective Boolean algebra.

cs.FL↗