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In this paper, we present a probabilistic adaptation of an Assume/Guarantee contract formalism. For the sake of generality, we assume that the extended state machines used in the contracts and implementations define sets of runs on a given…

Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can…

A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization…

Testing multiple hypotheses of conditional independence with provable error rate control is a fundamental problem with various applications. To infer conditional independence with family-wise error rate (FWER) control when only summary…

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…

Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by…

We propose a new method named the Conditional Randomization Rank Test (CRRT) for testing conditional independence of a response variable Y and a covariate variable X, conditional on the rest of the covariates Z. The new method generalizes…

When solving partial differential equations using boundary integral equation methods, accurate evaluation of singular and nearly singular integrals in layer potentials is crucial. A recent scheme for this is quadrature by expansion (QBX),…

Mitigating measurement errors in quantum systems without relying on quantum error correction is of critical importance for the practical development of quantum technology. Deep learning-based quantum measurement error mitigation has…

A major open problem in proof complexity is to demonstrate that random 3-CNFs with a linear number of clauses require super-polynomial size refutations in bounded-depth Frege systems. We take the first step towards addressing this question…

Invariant causal prediction provides a useful framework for identifying causal predictors of a response using heterogeneous data from multiple environments. One valuable property of the original invariant causal prediction method is that it…

The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…

We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…

A dynamic treatment regime effectively incorporates both accrued information and long-term effects of treatment from specially designed clinical trials. As these become more and more popular in conjunction with longitudinal data from…

Flow and diffusion models are typically pre-trained on limited available data (e.g., molecular samples), covering only a fraction of the valid design space (e.g., the full molecular space). As a consequence, they tend to generate samples…

Some reinforcement learning methods suffer from high sample complexity causing them to not be practical in real-world situations. $Q$-function reuse, a transfer learning method, is one way to reduce the sample complexity of learning,…

This paper introduces the sequential CRT, which is a variable selection procedure that combines the conditional randomization test (CRT) and Selective SeqStep+. Valid p-values are constructed via the flexible CRT, which are then ordered and…