Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes it impractical for real-world systems. In this letter, we propose a novel ML decoding architecture for polar codes based on the Grover adaptive search, a quantum exhaustive search algorithm. Unlike conventional studies, our approach, enabled by a newly formulated objective function, uniquely supports Gray-coded multi-level modulation without expanding the search space size compared to the classical ML decoding. Simulation results demonstrate that our proposed quantum decoding achieves ML performance while providing a pure quadratic speedup in query complexity.
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Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original geometric space, leading to high computational costs when the number of sample points is large. We present the Latent Neural Operator (LNO) solving PDEs in the latent space. In particular, we first propose Physics-Cross-Attention (PhCA) transforming representation from the geometric space to the latent space, then learn the operator in the latent space, and finally recover the real-world geometric space via the inverse PhCA map. Our model retains flexibility that can decode values in any position not limited to locations defined in the training set, and therefore can naturally perform interpolation and extrapolation tasks particularly useful for inverse problems. Moreover, the proposed LNO improves both prediction accuracy and computational efficiency. Experiments show that LNO reduces the GPU memory by 50%, speeds up training 1.8 times, and reaches state-of-the-art accuracy on four out of six benchmarks for forward problems and a benchmark for inverse problem. Code is available at //github.com/L-I-M-I-T/LatentNeuralOperator.
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a subset of variables with a pre-specified size that maximizes the variance-regularized kernel MMD statistic. We focus on three commonly used types of kernels: linear, quadratic, and Gaussian. From a computational perspective, we derive mixed-integer programming formulations and propose exact and approximation algorithms with performance guarantees to solve these formulations. From a statistical viewpoint, we derive the rate of testing power of our framework under appropriate conditions. These results show that the sample size requirements for the three kernels depend crucially on the number of selected variables, rather than the data dimension. Experimental results on synthetic and real datasets demonstrate the superior performance of our method, compared to other variable selection frameworks, particularly in high-dimensional settings.
Previous research has shown that constraining the gradient of loss function with respect to model-predicted probabilities can enhance the model robustness against noisy labels. These methods typically specify a fixed optimal threshold for gradient clipping through validation data to obtain the desired robustness against noise. However, this common practice overlooks the dynamic distribution of gradients from both clean and noisy-labeled samples at different stages of training, significantly limiting the model capability to adapt to the variable nature of gradients throughout the training process. To address this issue, we propose a simple yet effective approach called Optimized Gradient Clipping (OGC), which dynamically adjusts the clipping threshold based on the ratio of noise gradients to clean gradients after clipping, estimated by modeling the distributions of clean and noisy samples. This approach allows us to modify the clipping threshold at each training step, effectively controlling the influence of noise gradients. Additionally, we provide statistical analysis to certify the noise-tolerance ability of OGC. Our extensive experiments across various types of label noise, including symmetric, asymmetric, instance-dependent, and real-world noise, demonstrate the effectiveness of our approach.
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its convergence follows from the convergence of the Sinkhorn--Knopp algorithm for the matrix scaling problem, and Altschuler et al. show that its worst-case time complexity is in near-linear time. Very recently, sequentially composed optimal transports were proposed by Watanabe and Isobe as a hierarchical extension of optimal transports. In this paper, we present an efficient approximation algorithm, namely Sinkhorn algorithm for sequentially composed optimal transports, for its entropic regularization. Furthermore, we present a theoretical analysis of the Sinkhorn algorithm, namely (i) its exponential convergence to the optimal solution with respect to the Hilbert pseudometric, and (ii) a worst-case complexity analysis for the case of one sequential composition.
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the $\epsilon$-contamination model, where an adversary can inspect and replace up to an $\epsilon$-fraction of the samples, a fundamental open problem is determining the optimal rates for robust stochastic convex optimization (SCO) under such contamination. We develop novel algorithms that achieve minimax-optimal excess risk (up to logarithmic factors) under the $\epsilon$-contamination model. Our approach improves over existing algorithms, which are not only suboptimal but also require stringent assumptions, including Lipschitz continuity and smoothness of individual sample functions. By contrast, our optimal algorithms do not require these restrictive assumptions, and can handle nonsmooth but Lipschitz population loss functions. We complement our algorithmic developments with a tight lower bound for robust SCO.
Inductive reasoning - the process of inferring general rules from a small number of observations - is a fundamental aspect of human intelligence. Recent works suggest that large language models (LLMs) can engage in inductive reasoning by sampling multiple hypotheses about the rules and selecting the one that best explains the observations. However, due to the IID sampling, semantically redundant hypotheses are frequently generated, leading to significant wastage of compute. In this paper, we 1) demonstrate that increasing the temperature to enhance the diversity is limited due to text degeneration issue, and 2) propose a novel method to improve the diversity while maintaining text quality. We first analyze the effect of increasing the temperature parameter, which is regarded as the LLM's diversity control, on IID hypotheses. Our analysis shows that as temperature rises, diversity and accuracy of hypotheses increase up to a certain point, but this trend saturates due to text degeneration. To generate hypotheses that are more semantically diverse and of higher quality, we propose a novel approach inspired by human inductive reasoning, which we call Mixture of Concepts (MoC). When applied to several inductive reasoning benchmarks, MoC demonstrated significant performance improvements compared to standard IID sampling and other approaches.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
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