Related papers: Abstract Interpretation with Higher-Dimensional El…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We propose a new synthesis algorithm that can efficiently search programs with local variables (e.g., those introduced by lambdas). Prior bottom-up synthesis algorithms are not able to evaluate programs with free local variables, and…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
Large language models can consult information that fixed static analyzers cannot, such as documentation, current security advisories, version-specific metadata, and informal API contracts. This makes LLMs a compelling option for program…
While program comprehension tools often use static program analysis techniques to obtain useful information, they usually work only with sufficiently scalable techniques with limited precision. A possible improvement of this approach is to…
We introduce a new method, combination of random testing and abstract interpretation, for the analysis of programs featuring both probabilistic and non-probabilistic nondeterminism. After introducing "ordinary" testing, we show how to…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…
We extend abstract interpretation for the purpose of verifying hybrid systems. Abstraction has been playing an important role in many verification methodologies for hybrid systems, but some special care is needed for abstraction of…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
We propose a new static program analysis called program behavior analysis. The analysis aims to calculate possible symbolic expressions for every variable at each program point. We design a new lattice, transfer function, and widening…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
Many music theoretical constructs (such as scale types, modes, cadences, and chord types) are defined in terms of pitch intervals---relative distances between pitches. Therefore, when computer models are employed in music tasks, it can be…