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We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete…
We consider end-to-end learning approaches for inverse problems of gravimetry. Due to ill-posedness of the inverse gravimetry, the reliability of learning approaches is questionable. To deal with this problem, we propose the strategy of…
Active learning is a paradigm of machine learning which aims at reducing the amount of labeled data needed to train a classifier. Its overall principle is to sequentially select the most informative data points, which amounts to determining…
This research addresses a fundamental question in AI: whether large language models truly understand concepts or simply recognize patterns. The authors propose bidirectional reasoning,the ability to apply transformations in both directions…
Ma-Minda class (of starlike functions) consists of all normalized analytic functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is contained in the some starlike region in the right-half plane. We obtain the best possible…
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
Let ${\mathcal A}$ be the class of functions $f$ that are analytic in the unit disk ${\mathbb D}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$. Let $0<\lambda\le1$ and \[ {\mathcal U}(\lambda) = \left\{ f\in{\mathcal A}: \left…
Non-injective functions are not globally invertible. However, they can often be restricted to locally injective subdomains where the inversion is well-defined. In many settings a preferred solution can be selected even when multiple valid…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…
Learning near-optimal behaviour from an expert's demonstrations typically relies on the assumption that the learner knows the features that the true reward function depends on. In this paper, we study the problem of learning from…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
Reflectional symmetry is ubiquitous in nature. While extrinsic reflectional symmetry can be easily parametrized and detected, intrinsic symmetry is much harder due to the high solution space. Previous works usually solve this problem by…
Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization…
Inverse Reinforcement Learning (IRL) techniques deal with the problem of deducing a reward function that explains the behavior of an expert agent who is assumed to act optimally in an underlying unknown task. In several problems of…
In this paper, we discuss the inverse problem of determining a semisimple group algebra from the knowledge of rings of the type sum_{t=1}^s M_{n_t}(Ft), where j is an arbitrary integer and F_t is finite field for each t, and show that it is…
We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification,…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Many relevant tasks require an agent to reach a certain state, or to manipulate objects into a desired configuration. For example, we might want a robot to align and assemble a gear onto an axle or insert and turn a key in a lock. These…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…