Related papers: Covering Relations in the Poset of Combinatorial N…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
We investigate coding schemes that map source symbols into multisets of an alphabet set. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over…
A capsule is a collection of neurons which represents different variants of a pattern in the network. The routing scheme ensures only certain capsules which resemble lower counterparts in the higher layer should be activated. However, the…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
Compositional explanations are a family of methods that aim to describe the spatial alignment between neurons' receptive field activations and concepts through logical rules, typically computed via a search over all possible concept…
Covering arrays are combinatorial objects that have been successfully applied in the design of test suites for testing systems such as software, circuits and networks, where failures can be caused by the interaction between their…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
We present a functional form (that we refer to as a Unified Neural Scaling Law (UNSL)) that accurately models and extrapolates the scaling behaviors of deep neural networks as multiple dimensions all vary simultaneously (i.e. how the…
Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…
Comparing the internal representations of neural networks is a central goal in both neuroscience and machine learning. Standard alignment metrics operate on raw neural activations, implicitly assuming that similar representations produce…
Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…
We study a combinatorial notion where given a set of lattice points one takes the set of all sums of subsets of a fixed size, and we ask if the given set comes from a convex lattice polytope whether the resulting set also comes from a…
Partially inspired by features of computation in visual cortex, deep neural networks compute hierarchical representations of their inputs. While these networks have been highly successful in machine learning, it remains unclear to what…
In natural scenes, objects generally appear together with other objects. Yet, theoretical studies of neural population coding typically focus on the encoding of single objects in isolation. Experimental studies suggest that neural responses…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…
Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…