Summary and Contributions: The paper proposes a novel approach to learning a multiclass classifier under structural constraints motivated from fairness applications. The performance of a candidate classifier h -- a general mapping of the feature space on a probability simplex -- is measured through the so-called confusion matrix'' C[h] whose vectorization stacks the vector of expected sufficient statistics extracted from a datapoint (X,Y) and the classifier output \hat Y . The goal is then to solve a convex program, where a smooth and convex los is minimized over the set of achievable confusion matrices, corresponding to the fixed (and unknown to the learner) population distribution, under a number of (convex) functional constraints. This setup has been earlier considered by Narasimkhan (2018). The authors advocate the following approach: the problem is cast as convex program with smooth objective, and with constraint set given as the intersection of the two sets (of confusion matrices): - the feasible'' set \F corresponding to the functional constraints; - the achievable'' set \C corresponding to all possible confusion matrices for the data-generating distribution.

Generative AI is revolutionizing engineering design practices by enabling rapid prototyping and manipulation of designs. One example of design manipulation involves taking two reference design images and using them as prompts to generate a design image that combines aspects of both. Real engineering designs have physical constraints and functional requirements in addition to aesthetic design considerations. Internet-scale foundation models commonly used for image generation, however, are unable to take these physical constraints and functional requirements into consideration as part of the generation process. We consider the problem of generating a design inspired by two input designs, and propose a zero-shot framework toward enforcing physical, functional requirements over the generation process by leveraging a pretrained diffusion model as the backbone. As a case study, we consider the example of rotational symmetry in generation of wheel designs. Automotive wheels are required to be rotationally symmetric for physical stability. We formulate the requirement of rotational symmetry by the use of a symmetrizer, and we use this symmetrizer to guide the diffusion process towards symmetric wheel generations. Our experimental results find that the proposed approach makes generated interpolations with higher realism than methods in related work, as evaluated by Fr\'echet inception distance (FID). We also find that our approach generates designs that more closely satisfy physical and functional requirements than generating without the symmetry guidance.

This work presents a framework for a robot with a multi-fingered hand to freely utilize daily tools, including functional parts like buttons and triggers. An approach heatmap is generated by selecting a functional finger, indicating optimal palm positions on the object's surface that enable the functional finger to contact the tool's functional part. Once the palm position is identified through the heatmap, achieving the functional grasp becomes a straightforward process where the fingers stably grasp the object with low-dimensional inputs using the eigengrasp. As our approach does not need human demonstrations, it can easily adapt to various sizes and designs, extending its applicability to different objects. In our approach, we use directional manipulability to obtain the approach heatmap. In addition, we add two kinds of energy functions, i.e., palm energy and functional energy functions, to realize the eigengrasp. Using this method, each robotic gripper can autonomously identify its optimal workspace for functional grasping, extending its applicability to non-anthropomorphic robotic hands. We show that several daily tools like spray, drill, and remotes can be efficiently used by not only an anthropomorphic Shadow hand but also a non-anthropomorphic Barrett hand.

We consider the problem of minimizing a convex, nonsmooth function subject to a closed convex constraint domain. The methods that we propose are reforms of subgradient methods based on Metel--Takeda's paper [Optimization Letters 15.4 (2021): 1491-1504] and Boyd's works [Lecture notes of EE364b, Stanford University, Spring 2013-14, pp. 1-39]. While the former has complexity $\mathcal{O}(\varepsilon^{-2r})$ for all $r> 1$, the complexity of the latter is $\mathcal{O}(\varepsilon^{-2})$. We perform some comparisons between these two methods using several test examples.

This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into predictive models. We consider the probabilistic learning of a random vector that is made up of either a quantity of interest (unsupervised case) or the couple of the quantity of interest and a control parameter (supervised case). A training set of independent realizations of this random vector is assumed to be given and to be generated with a prior probability measure that is unknown. A target set of realizations of the QoI is available for the two considered cases. The framework is the one of non-Gaussian problems in high dimension. A functional approach is developed on the basis of a weak formulation of the Fourier transform of probability measures (characteristic functions). The construction makes it possible to take into account the target set of realizations of the QoI in the Kullback-Leibler minimum principle. The proposed approach allows for estimating the posterior probability measure of the QoI (unsupervised case) or of the posterior joint probability measure of the QoI with the control parameter (supervised case). The existence and the uniqueness of the posterior probability measure is analyzed for the two cases. The numerical aspects are detailed in order to facilitate the implementation of the proposed method. The presented application in high dimension demonstrates the efficiency and the robustness of the proposed algorithm.

COVID-19 has impacted nations differently based on their policy implementations. The effective policy requires taking into account public information and adaptability to new knowledge. Epidemiological models built to understand COVID-19 seldom provide the policymaker with the capability for adaptive pandemic control (APC). Among the core challenges to be overcome include (a) inability to handle a high degree of non-homogeneity in different contributing features across the pandemic timeline, (b) lack of an approach that enables adaptive incorporation of public health expert knowledge, and (c) transparent models that enable understanding of the decision-making process in suggesting policy. In this work, we take the early steps to address these challenges using Knowledge Infused Policy Gradient (KIPG) methods. Prior work on knowledge infusion does not handle soft and hard imposition of varying forms of knowledge in disease information and guidelines to necessarily comply with. Furthermore, the models do not attend to non-homogeneity in feature counts, manifesting as partial observability in informing the policy. Additionally, interpretable structures are extracted post-learning instead of learning an interpretable model required for APC. To this end, we introduce a mathematical framework for KIPG methods that can (a) induce relevant feature counts over multi-relational features of the world, (b) handle latent non-homogeneous counts as hidden variables that are linear combinations of kernelized aggregates over the features, and (b) infuse knowledge as functional constraints in a principled manner. The study establishes a theory for imposing hard and soft constraints and simulates it through experiments. In comparison with knowledge-intensive baselines, we show quick sample efficient adaptation to new knowledge and interpretability in the learned policy, especially in a pandemic context.

The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints : conditional independencies, AS READ through the d - separation criterion, AND functional constraints, FOR which no general criterion IS available.This paper offers a systematic way OF identifying functional constraints AND, thus, facilitates the task OF testing causal models AS well AS inferring such models FROM data.

We propose computer-assisted techniques for helping with pedagogy in Algebra. In particular, given a proof problem p (of the form “Left-hand-side-term = Right-hand-side-term”), we show how to automatically generate problems that are similar to p. We believe that such a tool can be used by teachers in making examinations where they need to test students on problems similar to what they taught in class, and by students in generating practice problems tailored to their specific needs. Our first insight is that we can generalize p syntactically to a query Q that implicitly represents a set of problems [[Q]] (which includes p). Our second insight is that we can explore the space of problems [[Q]] automatically, use classical results from polynomial identity testing to generate only those problems in [[Q]] that are correct, and then use pruning techniques to generate only unique and interesting problems. Our third insight is that with a small amount of manual tuning on the query Q, the user can interactively guide the computer to generate problems of interest to her. We present the technical details of the above mentioned steps, and also describe a tool where these steps have been implemented. We also present an empirical evaluation on a wide variety of problems from various sub-fields of algebra including polynomials, trigonometry, calculus, determinants etc. Our tool is able to generate a rich corpus of similar problems from each given problem; while some of these similar problems were already present in the textbook, several were new!

The hardness of finite domain Constraint Satisfaction Problems (CSPs) is an important research topic in Constraint Programming (CP) community. In this paper, we study the association rule mining techniques together with rule deduction and propose a cascaded approach to extract interesting patterns of hard CSPs with functional constraints. Specifically, we generate random CSPs, collect controlling parameters and hardness characteristics by solving all the CSP instances. Afterwards, we apply association rule mining with rule deduction on the collected data set and further extract interesting patterns of the hardness of the randomly generated CSPs. As far as we know, this problem is investigated with data mining techniques for the first time.

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other nonfunctional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints. To appear in Theory and Practice of Logic Programming (TPLP).