Related papers: L is different from NP

The open question, P=NP?, was presented by Cook (1971). In this paper, a proof that P is not equal to NP is presented. In addition, it is shown that P is not equal to the intersection of NP and co-NP. Finally, the exact inclusion…

We prove that for $1\le p,q\le\infty$ the mixed-norm spaces $L_q(L_p)$ are mutually non-isomorphic, with the only exception that $L_q(L_2)$ is isomorphic to $L_q(L_q)$ for all $1<q<\infty$.

In-context learning (ICL, also known as few-shot prompting) has been the standard method of adapting LLMs to downstream tasks, by learning from a few input-output examples. Nonetheless, all ICL-based approaches only learn from correct…

Large Language Models revolutionized NLP and showed dramatic performance improvements across several tasks. In this paper, we investigated the role of such language models in text classification and how they compare with other approaches…

We show that noncommutative $L_p$-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant $2^{1 \over p}$. Therefore, noncommutative $L_p$-spaces can be embedded into $B(H)$ $2^{1 \over p}$-completely…

Logs are one of the most critical data for service management. It contains rich runtime information for both services and users. Since size of logs are often enormous in size and have free handwritten constructions, a typical log-based…

Existing definitions of the relativizations of \NCOne, \L\ and \NL\ do not preserve the inclusions $\NCOne \subseteq \L$, $\NL\subseteq \ACOne$. We start by giving the first definitions that preserve them. Here for \L\ and \NL\ we define…

Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which…

We prove a comparison theorem between locally analytic group cohomology and Lie algebra cohomology for locally analytic representations of a Lie group over a nonarchimedean field of characteristic 0. The proof is similar to that of…

We claim to resolve the P=?NP problem via a formal argument for P=NP.

There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…

Most current long-context language models still rely on attention to handle both local interaction and long-range state, which leaves relatively little room to test alternative decompositions of sequence modeling. We propose LPC-SM, a…

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…

Learning-based systems are increasingly deployed across various domains, yet the complexity of traditional neural networks poses significant challenges for formal verification. Unlike conventional neural networks, learned Logic Gate…

Neural Processes (NPs) are popular methods in meta-learning that can estimate predictive uncertainty on target datapoints by conditioning on a context dataset. Previous state-of-the-art method Transformer Neural Processes (TNPs) achieve…

This expository note outlines why it is sometimes useful to consider the bigraded type A link homology theories as associated with the Lie algebras gl(N) instead of sl(N).

Weakly supervised text classification methods typically train a deep neural classifier based on pseudo-labels. The quality of pseudo-labels is crucial to final performance but they are inevitably noisy due to their heuristic nature, so…

Neurochaos Learning (NL) has shown promise in recent times over traditional deep learning due to its two key features: ability to learn from small sized training samples, and low compute requirements. In prior work, NL has been implemented…

In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…

Separation Logic is a non-classical logic used to verify pointer-intensive code. In this paper, however, we show that Separation Logic, along with its natural extensions, can also be used as a specification language for concurrent-system…