相关论文: Anti-Structure Problems
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
We introduce a novel generalization of entropy and conditional entropy from which most definitions from the literature can be derived as particular cases. Within this general framework, we investigate the problem of designing…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
We consider the problem of finding a net that supports prescribed forces applied at prescribed points, yet avoids certain obstacles, with all the elements of the net under compression (strut net) or under tension (cable web). In the case of…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
We consider a directed acyclic network with multiple sources and multiple terminals where each terminal is interested in decoding the sum of independent sources generated at the source nodes. We describe a procedure whereby a simple…
Deep neural networks are vulnerable to adversarial examples - small input perturbations that result in incorrect predictions. We study this problem for models of source code, where we want the network to be robust to source-code…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
In this work, we tackle model efficiency by exploiting redundancy in the \textit{implicit structure} of the building blocks of convolutional neural networks. We start our analysis by introducing a general definition of Composite Kernel…
Stabilization schemes in wall-bounded flows often invoke fluid transpiration through porous boundaries. While these have been extensively validated for external flows, their efficacy in channels, particularly from the standpoint of…
This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…
We study the network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called…
Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely…
Incompatible quantum channels cannot be jointly and exactly realized, meaning that any approximate joint realization inevitably entails a tradeoff in implementation accuracy. While this notion of channel incompatibility unifies fundamental…
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity",…