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Studies in circadian biology often use trigonometric regression to model phenomena over time. Ideally, protocols in these studies would collect samples at evenly distributed and equally spaced time points over a 24 hour period. This sample collection protocol is known as an equispaced design, which is considered the optimal experimental design for trigonometric regression under multiple statistical criteria. However, implementing equispaced designs in studies involving individuals is logistically challenging, and failure to employ an equispaced design could cause a loss of statistical power when performing hypothesis tests with an estimated model. This paper is motivated by the potential loss of statistical power during hypothesis testing, and considers a weighted trigonometric regression as a remedy. Specifically, the weights for this regression are the normalized reciprocals of estimates derived from a kernel density estimator for sample collection time, which inflates the weight of samples collected at underrepresented time points. A search procedure is also introduced to identify the concentration hyperparameter for kernel density estimation that maximizes the Hessian of weighted squared loss, which relates to both maximizing the $D$-optimality criterion from experimental design literature and minimizing the generalized variance. Simulation studies consistently demonstrate that this weighted regression mitigates variability in inferences produced by an estimated model. Illustrations with three real circadian biology data sets further indicate that this weighted regression consistently yields larger test statistics than its unweighted counterpart for first-order trigonometric regression, or cosinor regression, which is prevalent in circadian biology studies.

We present a bag of tricks framework for few-shot class-incremental learning (FSCIL), which is a challenging form of continual learning that involves continuous adaptation to new tasks with limited samples. FSCIL requires both stability and adaptability, i.e., preserving proficiency in previously learned tasks while learning new ones. Our proposed bag of tricks brings together eight key and highly influential techniques that improve stability, adaptability, and overall performance under a unified framework for FSCIL. We organize these tricks into three categories: stability tricks, adaptability tricks, and training tricks. Stability tricks aim to mitigate the forgetting of previously learned classes by enhancing the separation between the embeddings of learned classes and minimizing interference when learning new ones. On the other hand, adaptability tricks focus on the effective learning of new classes. Finally, training tricks improve the overall performance without compromising stability or adaptability. We perform extensive experiments on three benchmark datasets, CIFAR-100, CUB-200, and miniIMageNet, to evaluate the impact of our proposed framework. Our detailed analysis shows that our approach substantially improves both stability and adaptability, establishing a new state-of-the-art by outperforming prior works in the area. We believe our method provides a go-to solution and establishes a robust baseline for future research in this area.

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.

Sample efficient learning of manipulation skills poses a major challenge in robotics. While recent approaches demonstrate impressive advances in the type of task that can be addressed and the sensing modalities that can be incorporated, they still require large amounts of training data. Especially with regard to learning actions on robots in the real world, this poses a major problem due to the high costs associated with both demonstrations and real-world robot interactions. To address this challenge, we introduce BOpt-GMM, a hybrid approach that combines imitation learning with own experience collection. We first learn a skill model as a dynamical system encoded in a Gaussian Mixture Model from a few demonstrations. We then improve this model with Bayesian optimization building on a small number of autonomous skill executions in a sparse reward setting. We demonstrate the sample efficiency of our approach on multiple complex manipulation skills in both simulations and real-world experiments. Furthermore, we make the code and pre-trained models publicly available at //bopt-gmm. cs.uni-freiburg.de.

Robot Imitation Learning (IL) is a widely used method for training robots to perform manipulation tasks that involve mimicking human demonstrations to acquire skills. However, its practicality has been limited due to its requirement that users be trained in operating real robot arms to provide demonstrations. This paper presents an innovative solution: an Augmented Reality (AR)-assisted framework for demonstration collection, empowering non-roboticist users to produce demonstrations for robot IL using devices like the HoloLens 2. Our framework facilitates scalable and diverse demonstration collection for real-world tasks. We validate our approach with experiments on three classical robotics tasks: reach, push, and pick-and-place. The real robot performs each task successfully while replaying demonstrations collected via AR.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

We study the problem of incorporating prior knowledge into a deep Transformer-based model,i.e.,Bidirectional Encoder Representations from Transformers (BERT), to enhance its performance on semantic textual matching tasks. By probing and analyzing what BERT has already known when solving this task, we obtain better understanding of what task-specific knowledge BERT needs the most and where it is most needed. The analysis further motivates us to take a different approach than most existing works. Instead of using prior knowledge to create a new training task for fine-tuning BERT, we directly inject knowledge into BERT's multi-head attention mechanism. This leads us to a simple yet effective approach that enjoys fast training stage as it saves the model from training on additional data or tasks other than the main task. Extensive experiments demonstrate that the proposed knowledge-enhanced BERT is able to consistently improve semantic textual matching performance over the original BERT model, and the performance benefit is most salient when training data is scarce.