Related papers: Pac-learning Recursive Logic Programs: Negative Re…

We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the…

This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in…

We prove an exponential separation for the sample complexity between the standard PAC-learning model and a version of the Equivalence-Query-learning model. We then show that this separation has interesting implications for adversarial…

Recursive loops in a logic program present a challenging problem to the PLP framework. On the one hand, they loop forever so that the PLP backward-chaining inferences would never stop. On the other hand, they generate cyclic influences,…

This survey paper gives an overview of various known results on learning classes of Boolean functions in Valiant's Probably Approximately Correct (PAC) learning model and its commonly studied variants.

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…

Compared with traditional deep learning techniques, continual learning enables deep neural networks to learn continually and adaptively. Deep neural networks have to learn new tasks and overcome forgetting the knowledge obtained from the…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…

Despite the empirical success of the deep Q network (DQN) reinforcement learning algorithm and its variants, DQN is still not well understood and it does not guarantee convergence. In this work, we show that DQN can indeed diverge and cease…

The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations of gradient-based methods for learning the parity bit of the…

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)…

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine…

A classical result in learning theory shows the equivalence of PAC learnability of binary hypothesis classes and the finiteness of VC dimension. Extending this to the multiclass setting was an open problem, which was settled in a recent…

We show that, in a precise sense, a broad class of feedforward neural networks learn (have finite sample complexity) in the PAC model: every fixed finite feedforward architecture whose layers are definable in an o-minimal structure has…

Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning…

In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially…

Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable…

An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally…

Recent continual learning approaches have primarily focused on mitigating catastrophic forgetting. Nevertheless, two critical areas have remained relatively unexplored: 1) evaluating the robustness of proposed methods and 2) ensuring the…