Related papers: On the relation between structured $d$-DNNFs and S…
Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current…
We introduce a novel category of set functions called Extended Deep Submodular functions (EDSFs), which are neural network-representable. EDSFs serve as an extension of Deep Submodular Functions (DSFs), inheriting crucial properties from…
A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge…
We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded $F_{1}$-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive…
The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as…
The conclusions provided by deep neural networks (DNNs) must be carefully scrutinized to determine whether they are universal or architecture dependent. The term DAG-DNN refers to a graphical representation of a DNN in which the…
Advances in word representations have shown tremendous improvements in downstream NLP tasks, but lack semantic interpretability. In this paper, we introduce Definition Frames (DF), a matrix distributed representation extracted from…
In discrete optimization, representing an objective function as an $s$-$t$ cut function of a network is a basic technique to design an efficient minimization algorithm. A network representable function can be minimized by computing a…
Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…
For neural models to garner widespread public trust and ensure fairness, we must have human-intelligible explanations for their predictions. Recently, an increasing number of works focus on explaining the predictions of neural models in…
Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to…
The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n, there is a definable type p in X, definable over a code for…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
Expressive text encoders such as RNNs and Transformer Networks have been at the center of NLP models in recent work. Most of the effort has focused on sentence-level tasks, capturing the dependencies between words in a single sentence, or…
Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision…
Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…
Recurrent and deep neural networks (RNNs/DNNs) are cornerstone architectures in machine learning. Remarkably, RNNs differ from DNNs only by weight sharing, as can be shown through unrolling in time. How does this structural similarity fit…
Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way. For networks, previously proposed systems are developed. Perceptron networks in disjunctive…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
Deep Neural Networks (DNNs) are universal function approximators providing state-of- the-art solutions on wide range of applications. Common perceptual tasks such as speech recognition, image classification, and object tracking are now…