An elementary data analysis task is to count the number of unique elements occurring in a dataset.

What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We argue that a "good" extrapolant should follow certain kinds of rules, and here we study a particularly appealing criterion for rule-following in list functions: that the function should behave predictably even when certain elements are removed. In functional programming, a standard way to express such removal operations is by using a filter function. Accordingly, our paper introduces a new semantic class of functions -- the filter equivariant functions. We show that this class contains interesting examples, prove some basic theorems about it, and relate it to the well-known class of map equivariant functions. We also present a geometric account of filter equivariants, showing how they correspond naturally to certain simplicial structures. Our highlight result is the amalgamation algorithm, which constructs any filter-equivariant function's output by first studying how it behaves on sublists of the input, in a way that extrapolates perfectly.

The Artificial Intelligence field seldom address the development of a fundamental building piece: a framework, methodology or algorithm to automatically build hierarchies of abstractions. This is a key requirement in order to build intelligent behaviour, as recent neuroscience studies clearly expose. In this paper we present a primitive-based framework to automatically generate hierarchies of constructive archetypes, as a theory of how to generate hierarchies of abstractions. We assume the existence of a primitive with very specific characteristics, and we develop our framework over it. We prove the effectiveness of our framework through mathematical definitions and proofs. Finally, we give a few insights about potential uses of our framework and the expected results.

Ragnarock is a virtual reality (VR) rhythm game in which you play a Viking captain competing in a longship race. With two hammers, the task is to crush the incoming runes in sync with epic Viking music. The runes are defined by a beat map which the player can manually create. The creation of beat maps takes hours. This work aims to automate the process of beat map creation, also known as the task of learning to choreograph. The assignment is broken down into three parts: determining the timing of the beats (action placement), determining where in space the runes connected with the chosen beats should be placed (action selection) and web-application creation. For the first task of action placement, extraction of predominant local pulse (PLP) information from music recordings is used. This approach allows to learn where and how many beats are supposed to be placed. For the second task of action selection, Recurrent Neural Networks (RNN) are used, specifically Gated recurrent unit (GRU) to learn sequences of beats, and their patterns to be able to recreate those rules and receive completely new levels. Then the last task was to build a solution for non-technical players, the task was to combine the results of the first and the second parts into a web application for easy use. For this task the frontend was built using JavaScript and React and the backend - python and FastAPI.

Despite its importance for federated learning, continuous learning and many other applications, on-device training remains an open problem for EdgeAI. The problem stems from the large number of operations (e.g., floating point multiplications and additions) and memory consumption required during training by the back-propagation algorithm. Consequently, in this paper, we propose a new gradient filtering approach which enables on-device CNN model training. More precisely, our approach creates a special structure with fewer unique elements in the gradient map, thus significantly reducing the computational complexity and memory consumption of back propagation during training. Extensive experiments on image classification and semantic segmentation with multiple CNN models (e.g., MobileNet, DeepLabV3, UPerNet) and devices (e.g., Raspberry Pi and Jetson Nano) demonstrate the effectiveness and wide applicability of our approach. For example, compared to SOTA, we achieve up to 19$\times$ speedup and 77.1% memory savings on ImageNet classification with only 0.1% accuracy loss. Finally, our method is easy to implement and deploy; over 20$\times$ speedup and 90% energy savings have been observed compared to highly optimized baselines in MKLDNN and CUDNN on NVIDIA Jetson Nano. Consequently, our approach opens up a new direction of research with a huge potential for on-device training.

Robustly determining the optimal number of clusters in a data set is an essential factor in a wide range of applications. Cluster enumeration becomes challenging when the true underlying structure in the observed data is corrupted by heavy-tailed noise and outliers. Recently, Bayesian cluster enumeration criteria have been derived by formulating cluster enumeration as maximization of the posterior probability of candidate models. This article generalizes robust Bayesian cluster enumeration so that it can be used with any arbitrary Real Elliptically Symmetric (RES) distributed mixture model. Our framework also covers the case of M-estimators that allow for mixture models, which are decoupled from a specific probability distribution. Examples of Huber's and Tukey's M-estimators are discussed. We derive a robust criterion for data sets with finite sample size, and also provide an asymptotic approximation to reduce the computational cost at large sample sizes. The algorithms are applied to simulated and real-world data sets, including radar-based person identification, and show a significant robustness improvement in comparison to existing methods.

We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe an approach that yields sample-efficient differentially private testers for these problems. Our theoretical results show that there exist private identity and closeness testers that are nearly as sample-efficient as their non-private counterparts. We perform an experimental evaluation of our algorithms on synthetic data. Our experiments illustrate that our private testers achieve small type I and type II errors with sample size sublinear in the domain size of the underlying distributions.