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Let $T$ be the theory of an o-minimal field and $T_0$ a common reduct of $T$ and $T_{an}$. I adapt Mourgues' and Ressayre's constructions to deduce structure results for $T_0$-reducts of $T$-$\lambda$-spherical completion of models of…

The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using…

This paper presents a way of doing large scale audio understanding without traditional state of the art neural architectures. Ever since the introduction of deep learning for understanding audio signals in the past decade, convolutional…

This work presents Orient Anything V2, an enhanced foundation model for unified understanding of object 3D orientation and rotation from single or paired images. Building upon Orient Anything V1, which defines orientation via a single…

Current numerical abstract interpretation relies on fixed, hand-crafted, instruction-specific transformers tailored to each domain, causing three key limitations: transformers cannot be reused across domains; precise compositional reasoning…

ConvNets, through their architecture, only enforce invariance to translation. In this paper, we introduce a new class of deep convolutional architectures called Non-Parametric Transformation Networks (NPTNs) which can learn \textit{general}…

In this paper, we address the minimum-area rectangular and square annulus problem, which asks a rectangular or square annulus of minimum area, either in a fixed orientation or over all orientations, that encloses a set $P$ of $n$ input…

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the…

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This…

Serialization formats designed for document interchange impose structural overhead that becomes prohibitive when large language models consume operational data at scale. A modest dataset of 1,000 IoT sensor readings serialized as JSON…

Existing open-set recognition (OSR) studies typically assume that each image contains only one class label, with the unknown test set (negative) having a disjoint label space from the known test set (positive), a scenario referred to as…

The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to…

This paper introduces alternators, a novel family of non-Markovian dynamical models for sequences. An alternator features two neural networks: the observation trajectory network (OTN) and the feature trajectory network (FTN). The OTN and…

This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.

The increasing deployment of low-cost IoT sensor platforms in industry boosts the demand for anomaly detection solutions that fulfill two key requirements: minimal configuration effort and easy transferability across equipment. Recent…

The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to…

A polygon is derived that contains the numerical range of a bounded linear operator on a complex Hilbert space, using only norms. In its most general form, the polygon is an octagon, symmetric with respect to the origin, and tangent to the…

We show that global constraints on finite domains like all-different can be reformulated into answer set programs on which we achieve arc, bound or range consistency. These reformulations offer a number of other advantages beyond providing…