Related papers: Binary Decision Diagrams for Affine Approximation
Knowledge compilation transforms logical theories into circuit representations that support efficient reasoning. We study this problem for propositional groundings of FO2, the two-variable fragment of first-order logic over finite domains.…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a…
When using Bayesian networks for modelling the behavior of man-made machinery, it usually happens that a large part of the model is deterministic. For such Bayesian networks deterministic part of the model can be represented as a Boolean…
An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. OBDDs are also known as special cases of oblivious read-once branching programs in the field of complexity theory. Since OBDDs have…
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.…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
In this paper, we propose to train convolutional neural networks (CNNs) with both binarized weights and activations, leading to quantized models specifically} for mobile devices with limited power capacity and computation resources.…
This paper presents a general framework for constructing reduced models that approximate the Boltzmann equation with arbitrary orders of accuracy in terms of the Knudsen number $\mathit{Kn}$, applicable to general collision models in…
We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory…
In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation).…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
Binary neural network (BNN) is an extreme quantization version of convolutional neural networks (CNNs) with all features and weights mapped to just 1-bit. Although BNN saves a lot of memory and computation demand to make CNN applicable on…
Although traditionally binary visual representations are mainly designed to reduce computational and storage costs in the image retrieval research, this paper argues that binary visual representations can be applied to large scale…
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…
Recommender systems rely on Collaborative Filtering (CF) to predict user preferences by leveraging patterns in historical user-item interactions. While traditional CF methods primarily focus on learning compact vector embeddings for users…
We prove a new structural lemma for partial Boolean functions $f$, which we call the seed lemma for DNF. Using the lemma, we give the first subexponential algorithm for proper learning of DNF in Angluin's Equivalence Query (EQ) model. The…
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x…
We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a…
We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…