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As the scaling of semiconductor devices nears its limits, utilizing the back-side space of silicon has emerged as a new trend for future integrated circuits. With intense interest, several works have hacked existing backend tools to explore…

In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of $e$-computability and we use it to prove that Strassen's Conjecture holds in infinitely many new…

Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or…

In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…

Machine learning-based applications are increasingly prevalent in IoT devices. The power and storage constraints of these devices make it particularly challenging to run modern neural networks, limiting the number of new applications that…

We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…

We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…

Symmetric and sparse tensors arise naturally in many domains including linear algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors are equal to their transposes, so in the $n$-dimensional case we can save up to a…

Multi-task learning has shown to significantly enhance the performance of multiple related learning tasks in a variety of situations. We present the fused logistic regression, a sparse multi-task learning approach for binary classification.…

We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…

This paper presents a new approach to design verified compositions of Neural Network (NN) controllers for autonomous systems with tasks captured by Linear Temporal Logic (LTL) formulas. Particularly, the LTL formula requires the system to…

Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…

Despite significant investment in software infrastructure, machine learning systems, runtimes and compilers do not compose properly. We propose a new design aiming at providing unprecedented degrees of modularity, composability and…

Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…

We present a new approach for the design of a synthetic biological circuit whose behaviour is specified in terms of signal temporal logic (STL) formulae. We first show how to characterise with STL formulae the input/output behaviour of…

Motivated by the search for a deeper understanding of tensor rank, in view of its computational complexity applications, we investigate a possible path to determine the maximum symmetric rank in given degree and dimension. We work in terms…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

The prediction of phase diagrams in the search for new phases is a complex and computationally intensive task. Density functional theory provides, in many situations, the desired accuracy, but its throughput becomes prohibitively limited as…