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This paper presents a neural vocoder based on a denoising diffusion probabilistic model (DDPM) incorporating explicit periodic signals as auxiliary conditioning signals. Recently, DDPM-based neural vocoders have gained prominence as non-autoregressive models that can generate high-quality waveforms. The neural vocoders based on DDPM have the advantage of training with a simple time-domain loss. In practical applications, such as singing voice synthesis, there is a demand for neural vocoders to generate high-fidelity speech waveforms with flexible pitch control. However, conventional DDPM-based neural vocoders struggle to generate speech waveforms under such conditions. Our proposed model aims to accurately capture the periodic structure of speech waveforms by incorporating explicit periodic signals. Experimental results show that our model improves sound quality and provides better pitch control than conventional DDPM-based neural vocoders.

Thanks to advances in deep learning techniques, Human Pose Estimation (HPE) has achieved significant progress in natural scenarios. However, these models perform poorly in artificial scenarios such as painting and sculpture due to the domain gap, constraining the development of virtual reality and augmented reality. With the growth of model size, retraining the whole model on both natural and artificial data is computationally expensive and inefficient. Our research aims to bridge the domain gap between natural and artificial scenarios with efficient tuning strategies. Leveraging the potential of language models, we enhance the adaptability of traditional pose estimation models across diverse scenarios with a novel framework called VLPose. VLPose leverages the synergy between language and vision to extend the generalization and robustness of pose estimation models beyond the traditional domains. Our approach has demonstrated improvements of 2.26% and 3.74% on HumanArt and MSCOCO, respectively, compared to state-of-the-art tuning strategies.

We propose two novel extensions of the Wyner common information optimization problem. Each relaxes one fundamental constraints in Wyner's formulation. The \textit{Variational Wyner Common Information} relaxes the matching constraint to the known distribution while imposing conditional independence to the feasible solution set. We derive a tight surrogate upper bound of the obtained unconstrained Lagrangian via the theory of variational inference, which can be minimized efficiently. Our solver caters to problems where conditional independence holds with significantly reduced computation complexity; On the other hand, the \textit{Bipartite Wyner Common Information} relaxes the conditional independence constraint whereas the matching condition is enforced on the feasible set. By leveraging the difference-of-convex structure of the formulated optimization problem, we show that our solver is resilient to conditional dependent sources. Both solvers are provably convergent (local stationary points), and empirically, they obtain more accurate solutions to Wyner's formulation with substantially less runtime. Moreover, them can be extended to unknown distribution settings by parameterizing the common randomness as a member of the exponential family of distributions. Our approaches apply to multi-modal clustering problems, where multiple modalities of observations come from the same cluster. Empirically, our solvers outperform the state-of-the-art multi-modal clustering algorithms with significantly improved performance.

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in time polynomial in $d$, $k$, and $n$) find a potentially dense estimate for the regression vector that achieves non-trivial prediction error on the $n$ samples. Information-theoretically this can be achieved using $\Theta(k \log (d/k))$ samples. Yet, despite its prominence in the literature, there is no polynomial-time algorithm known to achieve the same guarantees using less than $\Theta(d)$ samples without additional restrictions on the model. Similarly, existing hardness results are either restricted to the proper setting, in which the estimate must be sparse as well, or only apply to specific algorithms. We give evidence that efficient algorithms for this task require at least (roughly) $\Omega(k^2)$ samples. In particular, we show that an improper learning algorithm for sparse linear regression can be used to solve sparse PCA problems (with a negative spike) in their Wishart form, in regimes in which efficient algorithms are widely believed to require at least $\Omega(k^2)$ samples. We complement our reduction with low-degree and statistical query lower bounds for the sparse PCA problems from which we reduce. Our hardness results apply to the (correlated) random design setting in which the covariates are drawn i.i.d. from a mean-zero Gaussian distribution with unknown covariance.

Deep learning models are being adopted and applied on various critical decision-making tasks, yet they are trained to provide point predictions without providing degrees of confidence. The trustworthiness of deep learning models can be increased if paired with uncertainty estimations. Conformal Prediction has emerged as a promising method to pair machine learning models with prediction intervals, allowing for a view of the model's uncertainty. However, popular uncertainty estimation methods for conformal prediction fail to provide heteroskedastic intervals that are equally accurate for all samples. In this paper, we propose a method to estimate the uncertainty of each sample by calculating the variance obtained from a Deep Regression Forest. We show that the deep regression forest variance improves the efficiency and coverage of normalized inductive conformal prediction on a drug response prediction task.

Graph contrastive learning (GCL) has emerged as a state-of-the-art strategy for learning representations of diverse graphs including social and biomedical networks. GCL widely uses stochastic graph topology augmentation, such as uniform node dropping, to generate augmented graphs. However, such stochastic augmentations may severely damage the intrinsic properties of a graph and deteriorate the following representation learning process. We argue that incorporating an awareness of cohesive subgraphs during the graph augmentation and learning processes has the potential to enhance GCL performance. To this end, we propose a novel unified framework called CTAug, to seamlessly integrate cohesion awareness into various existing GCL mechanisms. In particular, CTAug comprises two specialized modules: topology augmentation enhancement and graph learning enhancement. The former module generates augmented graphs that carefully preserve cohesion properties, while the latter module bolsters the graph encoder's ability to discern subgraph patterns. Theoretical analysis shows that CTAug can strictly improve existing GCL mechanisms. Empirical experiments verify that CTAug can achieve state-of-the-art performance for graph representation learning, especially for graphs with high degrees. The code is available at //doi.org/10.5281/zenodo.10594093, or //github.com/wuyucheng2002/CTAug.

Knowledge Distillation (KD) for object detection aims to train a compact detector by transferring knowledge from a teacher model. Since the teacher model perceives data in a way different from humans, existing KD methods only distill knowledge that is consistent with labels annotated by human expert while neglecting knowledge that is not consistent with human perception, which results in insufficient distillation and sub-optimal performance. In this paper, we propose inconsistent knowledge distillation (IKD), which aims to distill knowledge inherent in the teacher model's counter-intuitive perceptions. We start by considering the teacher model's counter-intuitive perceptions of frequency and non-robust features. Unlike previous works that exploit fine-grained features or introduce additional regularizations, we extract inconsistent knowledge by providing diverse input using data augmentation. Specifically, we propose a sample-specific data augmentation to transfer the teacher model's ability in capturing distinct frequency components and suggest an adversarial feature augmentation to extract the teacher model's perceptions of non-robust features in the data. Extensive experiments demonstrate the effectiveness of our method which outperforms state-of-the-art KD baselines on one-stage, two-stage and anchor-free object detectors (at most +1.0 mAP). Our codes will be made available at \url{//github.com/JWLiang007/IKD.git}.

Fact checking aims to predict claim veracity by reasoning over multiple evidence pieces. It usually involves evidence retrieval and veracity reasoning. In this paper, we focus on the latter, reasoning over unstructured text and structured table information. Previous works have primarily relied on fine-tuning pretrained language models or training homogeneous-graph-based models. Despite their effectiveness, we argue that they fail to explore the rich semantic information underlying the evidence with different structures. To address this, we propose a novel word-level Heterogeneous-graph-based model for Fact Checking over unstructured and structured information, namely HeterFC. Our approach leverages a heterogeneous evidence graph, with words as nodes and thoughtfully designed edges representing different evidence properties. We perform information propagation via a relational graph neural network, facilitating interactions between claims and evidence. An attention-based method is utilized to integrate information, combined with a language model for generating predictions. We introduce a multitask loss function to account for potential inaccuracies in evidence retrieval. Comprehensive experiments on the large fact checking dataset FEVEROUS demonstrate the effectiveness of HeterFC. Code will be released at: //github.com/Deno-V/HeterFC.

We study polynomial systems with prescribed monomial supports in the Cox rings of toric varieties built from complete polyhedral fans. We present combinatorial formulas for the dimensions of their associated subvarieties under genericity assumptions on the coefficients of the polynomials. Using these formulas, we identify at which degrees generic systems in polytopal algebras form regular sequences. Our motivation comes from sparse elimination theory, where knowing the expected dimension of these subvarieties leads to specialized algorithms and to large speed-ups for solving sparse polynomial systems. As a special case, we classify the degrees at which regular sequences defined by weighted homogeneous polynomials can be found, answering an open question in the Gr\"obner bases literature. We also show that deciding whether a sparse system is generically a regular sequence in a polytopal algebra is hard from the point of view of theoretical computational complexity.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.