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Existing out-of-distribution (OOD) methods have shown great success on balanced datasets but become ineffective in long-tailed recognition (LTR) scenarios where 1) OOD samples are often wrongly classified into head classes and/or 2) tail-class samples are treated as OOD samples. To address these issues, current studies fit a prior distribution of auxiliary/pseudo OOD data to the long-tailed in-distribution (ID) data. However, it is difficult to obtain such an accurate prior distribution given the unknowingness of real OOD samples and heavy class imbalance in LTR. A straightforward solution to avoid the requirement of this prior is to learn an outlier class to encapsulate the OOD samples. The main challenge is then to tackle the aforementioned confusion between OOD samples and head/tail-class samples when learning the outlier class. To this end, we introduce a novel calibrated outlier class learning (COCL) approach, in which 1) a debiased large margin learning method is introduced in the outlier class learning to distinguish OOD samples from both head and tail classes in the representation space and 2) an outlier-class-aware logit calibration method is defined to enhance the long-tailed classification confidence. Extensive empirical results on three popular benchmarks CIFAR10-LT, CIFAR100-LT, and ImageNet-LT demonstrate that COCL substantially outperforms state-of-the-art OOD detection methods in LTR while being able to improve the classification accuracy on ID data. Code is available at //github.com/mala-lab/COCL.

Open-loop stable limit cycles are foundational to the dynamics of legged robots. They impart a self-stabilizing character to the robot's gait, thus alleviating the need for compute-heavy feedback-based gait correction. This paper proposes a general approach to rapidly generate limit cycles with explicit stability constraints for a given dynamical system. In particular, we pose the problem of open-loop limit cycle stability as a single-stage constrained-optimization problem (COP), and use Direct Collocation to transcribe it into a nonlinear program (NLP) with closed-form expressions for constraints, objectives, and their gradients. The COP formulations of stability are developed based (1) on the spectral radius of a discrete return map, and (2) on the spectral radius of the system's monodromy matrix, where the spectral radius is bounded using different constraint-satisfaction formulations of the eigenvalue problem. We compare the performance and solution qualities of each approach, but specifically highlight the Schur decomposition of the monodromy matrix as a formulation which boasts wider applicability through weaker assumptions and attractive numerical convergence properties. Moreover, we present results from our experiments on a spring-loaded inverted pendulum model of a robot, where our method generated actuation trajectories for open-loop stable hopping in under 2 seconds (on the Intel Core i7-6700K), and produced energy-minimizing actuation trajectories even under tight stability constraints.

Many real world data, particularly in the natural sciences and computer vision, lie on known Riemannian manifolds such as spheres, tori or the group of rotation matrices. The predominant approaches to learning a distribution on such a manifold require solving a differential equation in order to sample from the model and evaluate densities. The resulting sampling times are slowed down by a high number of function evaluations. In this work, we propose an alternative approach which only requires a single function evaluation followed by a projection to the manifold. Training is achieved by an adaptation of the recently proposed free-form flow framework to Riemannian manifolds. The central idea is to estimate the gradient of the negative log-likelihood via a trace evaluated in the tangent space. We evaluate our method on various manifolds, and find significantly faster inference at competitive performance compared to previous work. We make our code public at //github.com/vislearn/FFF.

We devise a version of Linear Temporal Logic (LTL) on a denotational domain of streams. We investigate this logic in terms of domain theory, (point-free) topology and geometric logic. This yields the first steps toward an extension of the "Domain Theory in Logical Form" paradigm to temporal liveness properties. We show that the negation-free formulae of LTL induce sober subspaces of streams, but that this is in general not the case in presence of negation. We propose a direct, inductive, translation of negation-free LTL to geometric logic. This translation reflects the approximations used to compute the usual fixpoint representations of LTL modalities. As a motivating example, we handle a natural input-output specification for the usual filter function on streams.

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost over ambiguity sets, i.e., sets of distributions that are sufficiently compatible with the observed data. In this paper, the ambiguity sets capture the set of probability distributions whose convolution with the noise distribution remains within a ball centered at the empirical noisy distribution of data samples parameterized by the total variation distance. Using the prescribed ambiguity set, the solutions of the distributionally-robust optimizations converge to the solutions of the original stochastic programs when the numbers of the data samples grow to infinity. Therefore, the proposed distributionally-robust optimization problems are asymptotically consistent. This is proved under the assumption that the distribution of the noise is uniformly diagonally dominant. More importantly, the distributionally-robust optimization problems can be cast as tractable convex optimization problems and are therefore amenable to large-scale stochastic problems.

The prevalence of the powerful multilingual models, such as Whisper, has significantly advanced the researches on speech recognition. However, these models often struggle with handling the code-switching setting, which is essential in multilingual speech recognition. Recent studies have attempted to address this setting by separating the modules for different languages to ensure distinct latent representations for languages. Some other methods considered the switching mechanism based on language identification. In this study, a new attention-guided adaptation is proposed to conduct parameter-efficient learning for bilingual ASR. This method selects those attention heads in a model which closely express language identities and then guided those heads to be correctly attended with their corresponding languages. The experiments on the Mandarin-English code-switching speech corpus show that the proposed approach achieves a 14.2% mixed error rate, surpassing state-of-the-art method, where only 5.6% additional parameters over Whisper are trained.

Chain-of-thought (CoT) reasoning has exhibited impressive performance in language models for solving complex tasks and answering questions. However, many real-world questions require multi-modal information, such as text and images. Previous research on multi-modal CoT has primarily focused on extracting fixed image features from off-the-shelf vision models and then fusing them with text using attention mechanisms. This approach has limitations because these vision models were not designed for complex reasoning tasks and do not align well with language thoughts. To overcome this limitation, we introduce a novel approach for multi-modal CoT reasoning that utilizes latent space learning via diffusion processes to generate effective image features that align with language thoughts. Our method fuses image features and text representations at a deep level and improves the complex reasoning ability of multi-modal CoT. We demonstrate the efficacy of our proposed method on multi-modal ScienceQA and machine translation benchmarks, achieving state-of-the-art performance on ScienceQA. Overall, our approach offers a more robust and effective solution for multi-modal reasoning in language models, enhancing their ability to tackle complex real-world problems.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Pre-trained deep neural network language models such as ELMo, GPT, BERT and XLNet have recently achieved state-of-the-art performance on a variety of language understanding tasks. However, their size makes them impractical for a number of scenarios, especially on mobile and edge devices. In particular, the input word embedding matrix accounts for a significant proportion of the model's memory footprint, due to the large input vocabulary and embedding dimensions. Knowledge distillation techniques have had success at compressing large neural network models, but they are ineffective at yielding student models with vocabularies different from the original teacher models. We introduce a novel knowledge distillation technique for training a student model with a significantly smaller vocabulary as well as lower embedding and hidden state dimensions. Specifically, we employ a dual-training mechanism that trains the teacher and student models simultaneously to obtain optimal word embeddings for the student vocabulary. We combine this approach with learning shared projection matrices that transfer layer-wise knowledge from the teacher model to the student model. Our method is able to compress the BERT_BASE model by more than 60x, with only a minor drop in downstream task metrics, resulting in a language model with a footprint of under 7MB. Experimental results also demonstrate higher compression efficiency and accuracy when compared with other state-of-the-art compression techniques.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.