Related papers: On the Hardness of Learning Regular Expressions

We prove hardness-of-learning results under a well-studied assumption on the existence of local pseudorandom generators. As we show, this assumption allows us to surpass the current state of the art, and prove hardness of various basic…

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…

We consider the problems of robust PAC learning from distributed and streaming data, which may contain malicious errors and outliers, and analyze their fundamental complexity questions. In particular, we establish lower bounds on the…

The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…

Significant work has been done on learning regular expressions from a set of data values. Depending on the domain, this approach can be very successful. However, significant time is required to learn these expressions and the resulting…

We study the learnability of languages in the Next Symbol Prediction (NSP) setting, where a learner receives only positive examples from a language together with, for every prefix, (i) whether the prefix itself is in the language and (ii)…

Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…

It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory,…

Free fermions are some of the best studied quantum systems. However, little is known about the complexity of learning free-fermion distributions. In this work we establish the hardness of this task in the particle number non-preserving…

We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…

Although neural networks are routinely and successfully trained in practice using simple gradient-based methods, most existing theoretical results are negative, showing that learning such networks is difficult, in a worst-case sense over…

We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…

Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

The model of learning with \emph{local membership queries} interpolates between the PAC model and the membership queries model by allowing the learner to query the label of any example that is similar to an example in the training set. This…

We investigate the complexity of evaluating queries in Relational Algebra (RA) over the relations extracted by regex formulas (i.e., regular expressions with capture variables) over text documents. Such queries, also known as the regular…

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…