Related papers: Data-Driven Inference of Representation Invariants

Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An…

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants…

In this work, we perform unsupervised learning of representations by maximizing mutual information between an input and the output of a deep neural network encoder. Importantly, we show that structure matters: incorporating knowledge about…

For every positive integer h, the representation function of order h associated to a subset A of the integers or, more generally, of any group or semigroup X, counts the number of ways an element of X can be written as the sum (or product,…

We describe techniques for synthesis and verification of recursive functional programs over unbounded domains. Our techniques build on top of an algorithm for satisfiability modulo recursive functions, a framework for deductive synthesis,…

Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model's representations. In…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Recent studies show that deep neural networks are vulnerable to adversarial examples which can be generated via certain types of transformations. Being robust to a desired family of adversarial attacks is then equivalent to being invariant…

We propose an automated verification technique for hypersafety properties, which express sets of valid interrelations between multiple finite runs of a program. The key observation is that constructing a proof for a small representative set…

The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn…

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of…

State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Generalizable implicit neural representation (INR) enables a single continuous function, i.e., a coordinate-based neural network, to represent multiple data instances by modulating its weights or intermediate features using latent codes.…

Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…

It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically…

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry…

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…