Related papers: Differential Invariants
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such…
Automated code generation allows for a separation between the development of a model, expressed via a domain specific language, and lower level implementation details. Algorithmic differentiation can be applied symbolically at the level of…
Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
Data driven algorithm design is an important aspect of modern data science and algorithm design. Rather than using off the shelf algorithms that only have worst case performance guarantees, practitioners often optimize over large families…
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…
The reliability and proper function of data-driven applications hinge on the data's continued conformance to the applications' initial design. When data deviates from this initial profile, system behavior becomes unpredictable. Data…
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.
The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems…
A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property.…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with…
We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each…