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A numerical approach is developed for detecting the equivalence of deep learning architectures. The method is based on generating Mixed Matrix Ensembles (MMEs) out of deep neural network weight matrices and {\it conjugate circular ensemble}…

A suitable similarity index for comparing learnt neural networks plays an important role in understanding the behaviour of the highly-nonlinear functions, and can provide insights on further theoretical analysis and empirical studies. We…

Quantifying similarity between population spike patterns is essential for understanding how neural dynamics encode information. Traditional approaches, which combine kernel smoothing, PCA, and CCA, have limitations: smoothing kernel…

We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…

Over the last years, word and sentence embeddings have established as text preprocessing for all kinds of NLP tasks and improved the performances significantly. Unfortunately, it has also been shown that these embeddings inherit various…

Convolutional Neural Networks (CNNs) exhibit a well-known texture bias, prioritizing local patterns over global shapes - a tendency inherent to their convolutional architecture. While this bias is beneficial for texture-rich natural images,…

What can representational similarity matrices (RSMs) tell us about a neural code? As the popularity of these summary statistics grows, so too does the need for a more complete characterization of their properties. Here, we show that…

Contrastive learning is a paradigm for learning representations from unlabelled data that has been highly successful for image and text data. Several recent works have examined contrastive losses to claim that contrastive models effectively…

We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…

Neuroscientists have recently shown that images that are difficult to find in visual search elicit similar patterns of firing across a population of recorded neurons. The $L^{1}$ distance between firing rate vectors associated with two…

Similarity measures based purely on word embeddings are comfortably competing with much more sophisticated deep learning and expert-engineered systems on unsupervised semantic textual similarity (STS) tasks. In contrast to commonly used…

The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…

Deep metric learning techniques have been used for visual representation in various supervised and unsupervised learning tasks through learning embeddings of samples with deep networks. However, classic approaches, which employ a fixed…

The ventral, dorsal, and lateral streams in high-level human visual cortex are implicated in distinct functional processes. Yet, deep neural networks (DNNs) trained on a single task model the entire visual system surprisingly well, hinting…

High-resolution functional imaging is providing increasingly rich measurements of brain activity in animals and humans. A major challenge is to leverage such data to gain insight into the brain's computational mechanisms. The first step is…

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…

Deep learning has become an essential part of computer vision, with deep neural networks (DNNs) excelling in predictive performance. However, they often fall short in other critical quality dimensions, such as robustness, calibration, or…

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…

Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image…

Machine learning is advancing towards a data-science approach, implying a necessity to a line of investigation to divulge the knowledge learnt by deep neuronal networks. Limiting the comparison among networks merely to a predefined…