Related papers: Composition limits and separating examples for som…
Despite a multitude of empirical studies, little consensus exists on whether neural networks are able to generalise compositionally, a controversy that, in part, stems from a lack of agreement about what it means for a neural model to be…
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction…
Several recent works [DHLNSY25, CPPS25a, CPPS25b] have studied a model of property testing of Boolean functions under a \emph{relative-error} criterion. In this model, the distance from a target function $f: \{0,1\}^n \to \{0,1\}$ that is…
The validation of biclustering algorithms remains a challenging task, even though a number of measures have been proposed for evaluating the quality of these algorithms. Although no criterion is universally accepted as the overall best, a…
Polynomial representations of Boolean functions over various rings such as $\mathbb{Z}$ and $\mathbb{Z}_m$ have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of fields including…
This paper proposes a novel method that can replace compression-based dissimilarity measure (CDM) in composer estimation task. The main features of the proposed method are clarity and scalability. First, since the proposed method is…
We describe a $\tilde{O}(d^{5/6})$-query monotonicity tester for Boolean functions $f:[n]^d \to \{0,1\}$ on the $n$-hypergrid. This is the first $o(d)$ monotonicity tester with query complexity independent of $n$. Motivated by this…
Control systems often must satisfy strict safety requirements over an extended operating lifetime. Control Barrier Functions (CBFs) are a promising recent approach to constructing simple and safe control policies. This paper proposes a…
We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…
Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous…
Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
The two-point correlation function (2pcf) is the key statistic in structure formation; it measures the clustering of galaxies or other density field tracers. Estimators of the 2pcf, including the standard Landy-Szalay (LS) estimator,…
Bisimulation metric is a robust behavioural semantics for probabilistic processes. Given any SOS specification of probabilistic processes, we provide a method to compute for each operator of the language its respective metric…
The automated synthesis of correct-by-construction Boolean functions from logical specifications is known as the Boolean Functional Synthesis (BFS) problem. BFS has many application areas that range from software engineering to circuit…
We prove a lower bound of $\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This…
In this work, we consider a new type of Fourier-like representation of Boolean function $f\colon\{+1,-1\}^n\to\{+1,-1\}$ \[ f(x) = \cos\left(\pi\sum_{S\subseteq[n]}\phi_S \prod_{i\in S} x_i\right). \] This representation, which we call the…
In this paper, we consider the relationship between the Mahler measure of a polynomial and its separation. In 1964, Mahler proved that if $f(x) \in \mathbb{Z}[x]$ is separable of degree $n$, then $\operatorname{sep}(f) \gg_n M(f)^{-(n-1)}$.…
In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…
We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ and sampling oracle access to an unknown distribution…