相关论文: Polymorphism Is Rotation: Operational Mechanistic …

Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how…

In many imaging modalities, objects of interest can occur in a variety of locations and poses (i.e. are subject to translations and rotations in 2d or 3d), but the location and pose of an object does not change its semantics (i.e. the…

The importance of subtyping to enable a wider range of well-typed programs is undeniable. However, the interaction between subtyping, recursion, and polymorphism is not completely understood yet. In this work, we explore subtyping in a…

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…

In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We…

A widely cited result by Dong et al. (2021) showed that Transformers built from self-attention alone, without skip connections or feed-forward layers, suffer from rapid rank collapse: all token representations converge to a single…

A Parallel Self-Organizing Map (Parallel-SOM) is proposed to modify Kohonen's SOM in parallel computing environment. In this model, two separate layers of neurons are connected together. The number of neurons in both layers and connections…

Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning. This study introduces a novel approach by applying the principles of gauge symmetries, a key…

This paper presents two types of extended diffeomorphism designs to compensate for spatial placement differences between robot workspaces. Teleoperation of multiple robots is attracting attention to expand the utilization of the robot…

We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to…

Model multiplicity is a well-known but poorly understood phenomenon that undermines the generalisation guarantees of machine learning models. It appears when two models with similar training-time performance differ in their predictions and…

We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between…

Current sparse autoencoder (SAE) approaches to neural network interpretability assume that activations can be decomposed through linear superposition into sparse, interpretable features. Despite high reconstruction fidelity, SAEs…

Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…

This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies…

Some autoregressive models exhibit in-context learning capabilities: being able to learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. The origins of this…

Large-scale self-supervised pre-training has paved the way for one foundation model to handle many different vision tasks. Most pre-training methodologies train a single model of a certain size at one time. Nevertheless, various computation…

The matrix of a permutation is a partial case of Markov transition matrices. In the same way, a measure preserving bijection of a space A with finite measure is a partial case of Markov transition operators. A Markov transition operator…

From a multi-model compression perspective, model merging enables memory-efficient serving of multiple models fine-tuned from the same base, but suffers from degraded performance due to interference among their task-specific parameter…

Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios…