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Natural policy gradient (NPG) methods with entropy regularization achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy regularization remain elusive in the function approximation regime. In this paper, we establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation under softmax parameterization. In particular, we prove that entropy-regularized NPG with averaging satisfies the \emph{persistence of excitation} condition, and achieves a fast convergence rate of $\tilde{O}(1/T)$ up to a function approximation error in regularized Markov decision processes. This convergence result does not require any a priori assumptions on the policies. Furthermore, under mild regularity conditions on the concentrability coefficient and basis vectors, we prove that entropy-regularized NPG exhibits \emph{linear convergence} up to a function approximation error.

The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly accurate single-state predictors such as AlphaFold and ESMFold and fine-tune them under a custom flow matching framework to obtain sequence-conditoned generative models of protein structure called AlphaFlow and ESMFlow. When trained and evaluated on the PDB, our method provides a superior combination of precision and diversity compared to AlphaFold with MSA subsampling. When further trained on ensembles from all-atom MD, our method accurately captures conformational flexibility, positional distributions, and higher-order ensemble observables for unseen proteins. Moreover, our method can diversify a static PDB structure with faster wall-clock convergence to certain equilibrium properties than replicate MD trajectories, demonstrating its potential as a proxy for expensive physics-based simulations. Code is available at //github.com/bjing2016/alphaflow.

The revolutionary capabilities of large language models (LLMs) have paved the way for multimodal large language models (MLLMs) and fostered diverse applications across various specialized domains. In the remote sensing (RS) field, however, the diverse geographical landscapes and varied objects in RS imagery are not adequately considered in recent MLLM endeavors. To bridge this gap, we construct a large-scale RS image-text dataset, LHRS-Align, and an informative RS-specific instruction dataset, LHRS-Instruct, leveraging the extensive volunteered geographic information (VGI) and globally available RS images. Building on this foundation, we introduce LHRS-Bot, an MLLM tailored for RS image understanding through a novel multi-level vision-language alignment strategy and a curriculum learning method. Comprehensive experiments demonstrate that LHRS-Bot exhibits a profound understanding of RS images and the ability to perform nuanced reasoning within the RS domain.

Protein-protein interactions (PPIs) are crucial in regulating numerous cellular functions, including signal transduction, transportation, and immune defense. As the accuracy of multi-chain protein complex structure prediction improves, the challenge has shifted towards effectively navigating the vast complex universe to identify potential PPIs. Herein, we propose PPIretrieval, the first deep learning-based model for protein-protein interaction exploration, which leverages existing PPI data to effectively search for potential PPIs in an embedding space, capturing rich geometric and chemical information of protein surfaces. When provided with an unseen query protein with its associated binding site, PPIretrieval effectively identifies a potential binding partner along with its corresponding binding site in an embedding space, facilitating the formation of protein-protein complexes.

The partial Gromov-Wasserstein (PGW) problem facilitates the comparison of measures with unequal masses residing in potentially distinct metric spaces, thereby enabling unbalanced and partial matching across these spaces. In this paper, we demonstrate that the PGW problem can be transformed into a variant of the Gromov-Wasserstein problem, akin to the conversion of the partial optimal transport problem into an optimal transport problem. This transformation leads to two new solvers, mathematically and computationally equivalent, based on the Frank-Wolfe algorithm, that provide efficient solutions to the PGW problem. We further establish that the PGW problem constitutes a metric for metric measure spaces. Finally, we validate the effectiveness of our proposed solvers in terms of computation time and performance on shape-matching and positive-unlabeled learning problems, comparing them against existing baselines.

We study an extension of the cardinality-constrained knapsack problem wherein each item has a concave piecewise linear utility structure (CCKP), which is motivated by applications such as resource management problems in monitoring and surveillance tasks. Our main contributions are combinatorial algorithms for the offline CCKP and an online version of the CCKP. For the offline problem, we present a fully polynomial-time approximation scheme and show that it can be cast as the maximization of a submodular function with cardinality constraints; the latter property allows us to derive a greedy $(1 - \frac{1}{e})$-approximation algorithm. For the online CCKP in the random order model, we derive a $\frac{10.427}{\alpha}$-competitive algorithm based on $\alpha$-approximation algorithms for the offline CCKP; moreover, we derive stronger guarantees for the cases wherein the cardinality capacity is very small or relatively large. Finally, we investigate the empirical performance of the proposed algorithms in numerical experiments.

The quaternion biconjugate gradient (QBiCG) method, as a novel variant of quaternion Lanczos-type methods for solving the non-Hermitian quaternion linear systems, does not yield a minimization property. This means that the method possesses a rather irregular convergence behavior, which leads to numerical instability. In this paper, we propose a new structure-preserving quaternion quasi-minimal residual method, based on the quaternion biconjugate orthonormalization procedure with coupled two-term recurrences, which overcomes the drawback of QBiCG. The computational cost and storage required by the proposed method are much less than the traditional QMR iterations for the real representation of quaternion linear systems. Some convergence properties of which are also established. Finally, we report the numerical results to show the robustness and effectiveness of the proposed method compared with QBiCG.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

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.

Relying entirely on an attention mechanism, the Transformer introduced by Vaswani et al. (2017) achieves state-of-the-art results for machine translation. In contrast to recurrent and convolutional neural networks, it does not explicitly model relative or absolute position information in its structure. Instead, it requires adding representations of absolute positions to its inputs. In this work we present an alternative approach, extending the self-attention mechanism to efficiently consider representations of the relative positions, or distances between sequence elements. On the WMT 2014 English-to-German and English-to-French translation tasks, this approach yields improvements of 1.3 BLEU and 0.3 BLEU over absolute position representations, respectively. Notably, we observe that combining relative and absolute position representations yields no further improvement in translation quality. We describe an efficient implementation of our method and cast it as an instance of relation-aware self-attention mechanisms that can generalize to arbitrary graph-labeled inputs.