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The recent surge in 3D data acquisition has spurred the development of geometric deep learning models for point cloud processing, boosted by the remarkable success of transformers in natural language processing. While point cloud transformers (PTs) have achieved impressive results recently, their quadratic scaling with respect to the point cloud size poses a significant scalability challenge for real-world applications. To address this issue, we propose the Adaptive Point Cloud Transformer (AdaPT), a standard PT model augmented by an adaptive token selection mechanism. AdaPT dynamically reduces the number of tokens during inference, enabling efficient processing of large point clouds. Furthermore, we introduce a budget mechanism to flexibly adjust the computational cost of the model at inference time without the need for retraining or fine-tuning separate models. Our extensive experimental evaluation on point cloud classification tasks demonstrates that AdaPT significantly reduces computational complexity while maintaining competitive accuracy compared to standard PTs. The code for AdaPT is made publicly available.

We establish an entropic, quantum central limit theorem and quantum inverse sumset theorem in discrete-variable quantum systems describing qudits or qubits. Both results are enabled by using our recently-discovered quantum convolution. We show that the exponential rate of convergence of the entropic central limit theorem is bounded by the magic gap. We also establish an ``quantum, entropic inverse sumset theorem,'' by introducing a quantum doubling constant. Furthermore, we introduce a ``quantum Ruzsa divergence'', and we pose a conjecture called ``convolutional strong subaddivity,'' which leads to the triangle inequality for the quantum Ruzsa divergence. A byproduct of this work is a magic measure to quantify the nonstabilizer nature of a state, based on the quantum Ruzsa divergence.

We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.

This paper presents a transient forward harmonic adjoint sensitivity analysis (TFHA), which is a combination of a transient forward circuit analysis with a harmonic balance based adjoint sensitivity analysis. TFHA provides sensitivities of quantities of interest from time-periodic problems w.r.t. many design parameters, as used in the design process of power-electronics devices. The TFHA shows advantages in applications where the harmonic balance based adjoint sensitivity analysis or finite difference approaches for sensitivity analysis perform poorly. In contrast to existing methods, the TFHA can be used in combination with arbitrary forward solvers, i.e. general transient solvers.

The fractional discrete nonlinear Schr\"odinger equation (fDNLS) is studied on a periodic lattice from the analytic and dynamic perspective by varying the mesh size $h>0$ and the nonlocal L\'evy index $\alpha \in (0,2]$. We show that the discrete system converges to the fractional NLS as $h \rightarrow 0$ below the energy space by directly estimating the difference between the discrete and continuum solutions in $L^2(\mathbb{T})$ using the periodic Strichartz estimates. The sharp convergence rate via the finite-difference method is shown to be $O(h^{\frac{\alpha}{2+\alpha}})$ in the energy space. On the other hand for a fixed $h > 0$, the linear stability analysis on a family of continuous wave (CW) solutions reveals a rich dynamical structure of CW waves due to the interplay between nonlinearity, nonlocal dispersion, and discreteness. The gain spectrum is derived to understand the role of $h$ and $\alpha$ in triggering higher mode excitations. The transition from the quadratic dependence of maximum gain on the amplitude of CW solutions to the linear dependence, due to the lattice structure, is shown analytically and numerically.

Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.

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.

We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.

The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.