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For many machine learning applications, a common input representation is a spectrogram. The underlying representation for a spectrogram is a short time Fourier transform (STFT) which gives complex values. The spectrogram uses the magnitude…

The generalizability of PBE solvers is the key to the empirical synthesis performance. Despite the importance of generalizability, related studies on PBE solvers are still limited. In theory, few existing solvers provide theoretical…

The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…

Software synthesis - the process of generating complete, general-purpose programs from specifications - has become a hot research topic in the past few years. For decades the problem was thought to be insurmountable: the search space of…

Agentic AI systems can now generate code with remarkable fluency, but a fundamental question remains: \emph{does the generated code actually do what the user intended?} The gap between informal natural language requirements and precise…

Batch Normalization (BN) has been used extensively in deep learning to achieve faster training process and better resulting models. However, whether BN works strongly depends on how the batches are constructed during training and it may not…

Solving systems of Boolean equations is a fundamental task in symbolic computation and algebraic cryptanalysis, with wide-ranging applications in cryptography, coding theory, and formal verification. Among existing approaches, the Boolean…

In this paper, we consider the problem of synthesizing a controller in the presence of uncertainty such that the resulting closed-loop system satisfies certain hard constraints while optimizing certain (soft) performance objectives. We…

In recent years, various flow-based generative models have been proposed to generate high-fidelity waveforms in real-time. However, these models require either a well-trained teacher network or a number of flow steps making them…

Learning precise Boolean logic via gradient descent remains challenging: neural networks typically converge to "fuzzy" approximations that degrade under quantization. We introduce Hierarchical Spectral Composition, a differentiable…

The prediction of chemical properties using Machine Learning (ML) techniques calls for a set of appropriate descriptors that accurately describe atomic and, on a larger scale, molecular environments. A mapping of conformational information…

Certifying the safety of nonlinear systems, through the lens of set invariance and control barrier functions (CBFs), offers a powerful method for controller synthesis, provided a CBF can be constructed. This paper draws connections between…

The control synthesis of a dynamic system subject to a signal temporal logic (STL) specification is commonly formulated as a mixed-integer linear/convex programming (MILP/MICP) problem. Solving such a problem is computationally expensive…

Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs…

Reactive synthesis is the process of using temporal logic specifications in LTL to generate correct controllers, but its use has been restricted to Boolean specifications. Recently, a Boolean abstraction technique allows to translate LTL T…

Stochastic Boolean Function Evaluation (SBFE) is the problem of determining the value of a given Boolean function $f$ on an unknown input $x$, when each bit of $x_i$ of $x$ can only be determined by paying a given associated cost $c_i$.…

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by…

We aim at providing a foundation of a theory of "good" SAT representations F of boolean functions f. We argue that the hierarchy UC_k of unit-refutation complete clause-sets of level k, introduced by the authors, provides the most basic…

Deep neural networks, (DNNs, a.k.a. NNs), have been widely used in various tasks and have been proven to be successful. However, the accompanied expensive computing and storage costs make the deployments in resource-constrained devices a…

In robotics, control barrier function (CBF)-based safety filters are commonly used to enforce state constraints. A critical challenge arises when the relative degree of the CBF varies across the state space. This variability can create…