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In this paper, we investigate the problem of predictive confidence in face and kinship verification. Most existing face and kinship verification methods focus on accuracy performance while ignoring confidence estimation for their prediction results. However, confidence estimation is essential for modeling reliability in such high-risk tasks. To address this issue, we first introduce a novel yet simple confidence measure for face and kinship verification, which allows the verification models to transform the similarity score into a confidence score for a given face pair. We further propose a confidence-calibrated approach called angular scaling calibration (ASC). ASC is easy to implement and can be directly applied to existing face and kinship verification models without model modifications, yielding accuracy-preserving and confidence-calibrated probabilistic verification models. To the best of our knowledge, our approach is the first general confidence-calibrated solution to face and kinship verification in a modern context. We conduct extensive experiments on four widely used face and kinship verification datasets, and the results demonstrate the effectiveness of our approach.

Compared to on-policy policy gradient techniques, off-policy model-free deep reinforcement learning (RL) that uses previously gathered data can improve sampling efficiency. However, off-policy learning becomes challenging when the discrepancy between the distributions of the policy of interest and the policies that collected the data increases. Although the well-studied importance sampling and off-policy policy gradient techniques were proposed to compensate for this discrepancy, they usually require a collection of long trajectories that increases the computational complexity and induce additional problems such as vanishing/exploding gradients or discarding many useful experiences. Moreover, their generalization to continuous action domains is strictly limited as they require action probabilities, which is unsuitable for deterministic policies. To overcome these limitations, we introduce a novel policy similarity measure to mitigate the effects of such discrepancy. Our method offers an adequate single-step off-policy correction without any probability estimates, and theoretical results show that it can achieve a contraction mapping with a fixed unique point, which allows "safe" off-policy learning. An extensive set of empirical results indicate that our algorithm substantially improves the state-of-the-art and attains higher returns in fewer steps than the competing methods by efficiently scheduling the learning rate in Q-learning and policy optimization.

This study presents a whole-body model predictive control (MPC) of robotic systems with rigid contacts, under a given contact sequence using online switching time optimization (STO). We treat robot dynamics with rigid contacts as a switched system and formulate an optimal control problem of switched systems to implement the MPC. We utilize an efficient solution algorithm for the MPC problem that optimizes the switching times and trajectory simultaneously. The present efficient algorithm, unlike inefficient existing methods, enables online optimization as well as switching times. The proposed MPC with online STO is compared over the conventional MPC with fixed switching times, through numerical simulations of dynamic jumping motions of a quadruped robot. In the simulation comparison, the proposed MPC successfully controls the dynamic jumping motions in twice as many cases as the conventional MPC, which indicates that the proposed method extends the ability of the whole-body MPC. We further conduct hardware experiments on the quadrupedal robot Unitree A1 and prove that the proposed method achieves dynamic motions on the real robot.

We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration, contact forces, and control input torques, as optimization variables and the inverse dynamics and acceleration constraints on the contact frames as equality constraints. We eliminate the update of the acceleration, contact forces, and their dual variables from the linear equation to be solved in each Newton-type iteration in an efficient manner. As a result, the computational cost per Newton-type iteration is almost identical to that of the conventional non-lifted Newton-type iteration that embeds contact dynamics in the state equation. We conducted numerical experiments on the whole-body optimal control of various quadrupedal gaits subject to the friction cone constraints considered in interior-point methods and demonstrated that the proposed method can significantly increase the convergence speed to more than twice that of the conventional non-lifted approach.

As it is known, universal codes, which estimate the entropy rate consistently, exist for any stationary ergodic source over a finite alphabet but not over a countably infinite one. We cast the problem of universal coding into the problem of universal densities with respect to a given reference measure on a countably generated measurable space, examples being the counting measure or the Lebesgue measure. We show that universal densities, which estimate the differential entropy rate consistently, exist if the reference measure is finite, which disproves that the assumption of a finite alphabet is necessary in general. To exhibit a universal density, we combine the prediction by partial matching (PPM) code with the non-parametric differential (NPD) entropy rate estimator, putting a prior both over all Markov orders and all quantization levels. The proof of universality applies Barron's asymptotic equipartition for densities and continuity of $f$-divergences for filtrations. As an application, we demonstrate that any universal density induces a strongly consistent Ces\`aro mean estimator of the conditional density given an infinite past, which solves the problem of universal prediction with the $0-1$ loss for a countable alphabet, by the way. We also show that there exists a strongly consistent entropy rate estimator with respect to the Lebesgue measure in the class of stationary ergodic Gaussian processes.

We study the rank of sub-matrices arising out of kernel functions, $F(\pmb{x},\pmb{y}): \mathbb{R}^d \times \mathbb{R}^d \mapsto \mathbb{R}$, where $\pmb{x},\pmb{y} \in \mathbb{R}^d$ with $F(\pmb{x},\pmb{y})$ is smooth everywhere except along the line $\pmb{x}=\pmb{y}$. Such kernel functions are frequently encountered in a wide range of applications such as $N$ body problems, Green's functions, integral equations, geostatistics, kriging, Gaussian processes, etc. One of the challenges in dealing with these kernel functions is that the corresponding matrix associated with these kernels is large and dense and thereby, the computational cost of matrix operations is high. In this article, we prove new theorems bounding the numerical rank of sub-matrices arising out of these kernel functions. Under reasonably mild assumptions, we prove that the rank of certain sub-matrices is rank-deficient in finite precision. This rank depends on the dimension of the ambient space and also on the type of interaction between the hyper-cubes containing the corresponding set of particles. This rank structure can be leveraged to reduce the computational cost of certain matrix operations such as matrix-vector products, solving linear systems, etc. We also present numerical results on the growth of rank of certain sub-matrices in $1$D, $2$D, $3$D and $4$D, which, not surprisingly, agrees with the theoretical results.

Fuzzing is an automated software testing technique broadly adopted by the industry. A popular variant is mutation-based fuzzing, which discovers a large number of bugs in practice. While the research community has studied mutation-based fuzzing for years now, the algorithms' interactions within the fuzzer are highly complex and can, together with the randomness in every instance of a fuzzer, lead to unpredictable effects. Most efforts to improve this fragile interaction focused on optimizing seed scheduling. However, real-world results like Google's FuzzBench highlight that these approaches do not consistently show improvements in practice. Another approach to improve the fuzzing process algorithmically is optimizing mutation scheduling. Unfortunately, existing mutation scheduling approaches also failed to convince because of missing real-world improvements or too many user-controlled parameters whose configuration requires expert knowledge about the target program. This leaves the challenging problem of cleverly processing test cases and achieving a measurable improvement unsolved. We present DARWIN, a novel mutation scheduler and the first to show fuzzing improvements in a realistic scenario without the need to introduce additional user-configurable parameters, opening this approach to the broad fuzzing community. DARWIN uses an Evolution Strategy to systematically optimize and adapt the probability distribution of the mutation operators during fuzzing. We implemented a prototype based on the popular general-purpose fuzzer AFL. DARWIN significantly outperforms the state-of-the-art mutation scheduler and the AFL baseline in our own coverage experiment, in FuzzBench, and by finding 15 out of 21 bugs the fastest in the MAGMA benchmark. Finally, DARWIN found 20 unique bugs (including one novel bug), 66% more than AFL, in widely-used real-world applications.

This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub "prompt-based learning". Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x), prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x' that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website //pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.