Related papers: Further Collapses in TFNP
Long-horizon execution in Large Language Models (LLMs) remains unstable even when high-level strategies are provided. Evaluating on controlled algorithmic puzzles, we demonstrate that while decomposition is essential for stability, extreme…
Deep classifier neural networks enter the terminal phase of training (TPT) when training error reaches zero and tend to exhibit intriguing Neural Collapse (NC) properties. Neural collapse essentially represents a state at which the…
Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular…
The classes PPA-$p$ have attracted attention lately, because they are the main candidates for capturing the complexity of Necklace Splitting with $p$ thieves, for prime $p$. However, these classes were not known to have complete problems of…
The second-order cone linear complementarity problem (SOCLCP) is a generalization of the classical linear complementarity problem. It has been known that SOCLCP, with the globally uniquely solvable property, is essentially equivalent to a…
"Period collapse" refers to any situation where the period of the Ehrhart function of a polytope is less than the denominator of that polytope. We study several interesting situations where this occurs, primarily involving triangles. For…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
Neural collapse is a phenomenon observed during the terminal phase of neural network training, characterized by the convergence of network activations, class means, and linear classifier weights to a simplex equiangular tight frame (ETF), a…
In recent years, learning for neural networks can be viewed as optimization in the space of probability measures. To obtain the exponential convergence to the optimizer, the regularizing term based on Shannon entropy plays an important…
Recent years have witnessed the huge success of deep neural networks (DNNs) in various tasks of computer vision and text processing. Interestingly, these DNNs with massive number of parameters share similar structural properties on their…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to…
We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and…
Out-of-distribution (OOD) detection plays a crucial role in ensuring the security of neural networks. Existing works have leveraged the fact that In-distribution (ID) samples form a subspace in the feature space, achieving state-of-the-art…
Forbidden Patterns Problems (FPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs). However, we show that when the input is connected and belongs to a class which has low tree-depth decomposition (e.g. structure of…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
This paper introduces the Furthest Hyperplane Problem (FHP), which is an unsupervised counterpart of Support Vector Machines. Given a set of n points in Rd, the objective is to produce the hyperplane (passing through the origin) which…
We introduce Hausdorff (complexity) classes, which provide canonical characterizations of the intermediate levels of the iterated exponential hierarchies, including the Polynomial Hierarchy, the (Weak) Exponential Hierarchy, and…
This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…
Consider the following two fundamental open problems in complexity theory: (a) Does a hard-on-average language in NP imply the existence of one-way functions?, or (b) Does a hard-on-average language in NP imply a hard-on-average problem in…