Related papers: Dp-rank and forbidden configurations
In human cognition, the expansion of perceived between-category distances and compression of within-category distances is known as categorical perception (CP). There are several hypotheses about the causes of CP (e.g., language, learning,…
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only…
This work concerns results on conditions guaranteeing that certain banded $M$-matrices have banded inverses. As a first goal, a graph theoretic characterization for an off-diagonal entry of the inverse of an $M$-matrix to be positive, is…
A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination…
In today's technology environment, information is abundant, dynamic, and heterogeneous in nature. Automated filtering and prioritization of information is based on the distinction between whether the information adds substantial value…
Deep learning has demonstrated the power of detailed modeling of complex high-order (multivariate) interactions in data. For some learning tasks there is power in learning models that are not only Deep but also Broad. By Broad, we mean…
There has been growing interest in generalization performance of large multilayer neural networks that can be trained to achieve zero training error, while generalizing well on test data. This regime is known as 'second descent' and it…
In this paper, we study VC-density over indiscernible sequences (denoted VC_ind-density). We answer an open question in [1], showing that VC_ind-density is always integer valued. We also show that VC_ind-density and dp-rank coincide in the…
In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Gaussian MIMO channel under total transmit and multiple interference power constraints (TPC and IPCs) is considered. A closed-form solution for its optimal transmit covariance matrix is obtained in the general case (up to dual variables). A…
Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
The Willems' fundamental lemma, which characterizes linear time-invariant (LTI) systems using input and output trajectories, has found many successful applications. Combining this with receding horizon control leads to a popular…
Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification,…
Metaquerying is a datamining technology by which hidden dependencies among several database relations can be discovered. This tool has already been successfully applied to several real-world applications. Recent papers provide only…
Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…
The ongoing experimental efforts in the high energy and high precision communities keep providing evidence for CPT, a fundamental symmetry holding in any local Lorentz invariant theory. We suggest possible interconnections between different…
In recent years, pattern analysis plays an important role in data mining and recognition, and many variants have been proposed to handle complicated scenarios. In the literature, it has been quite familiar with high dimensionality of data…
We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a…