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Circuit analysis of any certain model behavior is a central task in mechanistic interpretability. We introduce our circuit discovery pipeline with Sparse Autoencoders (SAEs) and a variant called Transcoders. With these two modules inserted…

Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…

Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…

Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…

Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…

Having sufficient grid-forming sources is one of the necessary conditions to guarantee the stability in a power system hosting a very large share of inverter-based generation. The grid-forming function has been historically fulfilled by…

Given a synchronous system, we study the question whether the behaviour of that system can be exhibited by a (non-trivially) distributed and hence asynchronous implementation. In this paper we show, by counterexample, that synchronous…

Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can…

Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…

Causal inference provides an analytical framework to identify and quantify cause-and-effect relationships among a network of interacting agents. This paper offers a novel framework for analyzing cascading failures in power transmission…

Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…

Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…

We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep…

The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…

Current fluctuations play an important role in non-equilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations…

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…

Two problems are addressed for the path of certain stochastic processes: a) do they define currents? b) are these currents of a classical type? A general answer to question a) is given for processes like semimartingales or with Lyons-Zheng…

We introduce a random circuit family and show they are robust against current classical simulation techniques, specifically tensor network contraction and Pauli propagation. We also show that local variables do not concentrate, ensuring…

Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…