Related papers: Learning circuits with few negations

Feasible interpolation is a general technique for proving proof complexity lower bounds. The monotone version of the technique converts, in its basic variant, lower bounds for monotone Boolean circuits separating two NP-sets to proof…

Using logic gates is the traditional way of designing logic circuits. However, most of the minimization algorithms concern a limited set of gates (complete sets), like sum of products, exclusive-or sum of products, NAND gates, NOR gates…

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…

Understanding the inductive bias of neural networks is critical to explaining their ability to generalise. Here, for one of the simplest neural networks -- a single-layer perceptron with n input neurons, one output neuron, and no threshold…

A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…

This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free…

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…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

The circuits framework in mechanistic interpretability aims to identify causally important sparse subgraphs of model components, typically evaluated by measuring necessity and sufficiency. We measure circuit reuse, the proportion of…

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…

We address whether neural models for Natural Language Inference (NLI) can learn the compositional interactions between lexical entailment and negation, using four methods: the behavioral evaluation methods of (1) challenge test sets and (2)…

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…

We investigate monotone circuits with local oracles [K., 2016], i.e., circuits containing additional inputs $y_i = y_i(\vec{x})$ that can perform unstructured computations on the input string $\vec{x}$. Let $\mu \in [0,1]$ be the locality…

We present a framework for studying circuit complexity that is inspired by techniques that are used for analyzing the complexity of CSPs. We prove that the circuit complexity of a Boolean function $f$ is characterized by the partial…

We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus…

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…

We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space of all truth table properties. We…

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…

In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…

A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…