Related papers: Learning Complexity Dimensions for a Continuous-Ti…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
Continual learning (CL) studies how models acquire tasks sequentially while retaining previously learned knowledge. Despite substantial progress in benchmarking CL methods, comparative evaluations typically keep the fine-tuning regime…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
This work proposes and evaluates a novel approach to determine interesting categorical attributes for lists of entities. Once identified, such categories are of immense value to allow constraining (filtering) a current view of a user to…
We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which…
Temporal logic specifications play an important role in a wide range of software analysis tasks, such as model checking, automated synthesis, program comprehension, and runtime monitoring. Given a set of positive and negative examples,…
Dataset complexity assessment aims to predict classification performance on a dataset with complexity calculation before training a classifier, which can also be used for classifier selection and dataset reduction. The training process of…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…
For a given base class of sequence-to-next-token generators, we consider learning prompt-to-answer mappings obtained by iterating a fixed, time-invariant generator for multiple steps, thus generating a chain-of-thought, and then taking the…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…
In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
This paper proposes basic definitions of similarity and similarity indexes between heterogeneous linear systems and presents a similarity-based learning control strategy. By exploring geometric properties of admissible behaviors of linear…
Learning governing dynamics from data is a common goal across the sciences, yet it is only well-posed when the underlying mechanisms are identifiable. In practice, many data-driven methods implicitly assume identifiability; when this…