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This paper introduces an iterative algorithm for training additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient descent, applied to the coefficients of a truncated basis expansion of the component functions. We show that the resulting estimator satisfies an oracle inequality that allows for model mis-specification. In the well-specified setting, by choosing the learning rate carefully across three distinct stages of training, we demonstrate that its risk is minimax optimal in terms of the dependence on the dimensionality of the data and the size of the training sample. We further illustrate the computational benefits by comparing the approach with traditional backfitting on two real-world datasets.

Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid sources, we propose an approach which targets the maximum entropy distribution, i.e., prioritizes retaining as much uncertainty as possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein distance to measure the discrepancy between the dataset and simulations - and thus suitable for simulators with intractable likelihoods. We benchmark our method on several tasks, and show that it can recover source distributions with substantially higher entropy without sacrificing the fidelity of the simulations. Finally, to demonstrate the utility of our approach, we infer source distributions for parameters of the Hodgkin-Huxley neuron model from experimental datasets with thousands of measurements. In summary, we propose a principled framework for inferring unique source distributions of scientific simulator parameters while retaining as much uncertainty as possible.

Large language models (LLMs) predominantly employ decoder-only transformer architectures, necessitating the retention of keys/values information for historical tokens to provide contextual information and avoid redundant computation. However, the substantial size and parameter volume of these LLMs require massive GPU memory. This memory demand increases with the length of the input text, leading to an urgent need for more efficient methods of information storage and processing. This study introduces the Anchor-based LLM (AnLLM), which utilizes an innovative anchor-based self-attention network (AnSAN) and also an anchor-based inference strategy. This approach enables LLMs to compress sequence information into an anchor token, reducing the keys/values cache and enhancing inference efficiency. Experiments show that the AnLLM maintains comparable accuracy with up to 99% keys/values cache reduction and up to 3.5 times faster inference. Despite a minor compromise in accuracy, the AnLLM significantly improves computational efficiency and resource utilization, demonstrating the potential of the anchor-based attention approach in the context of LLMs for real-time inference in practical applications.

Recently, a human evaluation study of Referring Expression Generation (REG) models had an unexpected conclusion: on \textsc{webnlg}, Referring Expressions (REs) generated by the state-of-the-art neural models were not only indistinguishable from the REs in \textsc{webnlg} but also from the REs generated by a simple rule-based system. Here, we argue that this limitation could stem from the use of a purely ratings-based human evaluation (which is a common practice in Natural Language Generation). To investigate these issues, we propose an intrinsic task-based evaluation for REG models, in which, in addition to rating the quality of REs, participants were asked to accomplish two meta-level tasks. One of these tasks concerns the referential success of each RE; the other task asks participants to suggest a better alternative for each RE. The outcomes suggest that, in comparison to previous evaluations, the new evaluation protocol assesses the performance of each REG model more comprehensively and makes the participants' ratings more reliable and discriminable.

In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD) fail at this task. A popular alternative is the CUR decomposition. In an SVD-like manner, the CUR decomposition approximates a matrix $A \in \mathbb{R}^{m \times n}$ as $A \approx CUR$, where $C$ and $R$ are matrices whose columns and rows are selected from the original matrix \cite{goreinov1997theory}, \cite{mahoney2009cur}. The difficulty in constructing a CUR decomposition is in determining which columns and rows to select when forming $C$ and $R$. Current column/row selection algorithms, particularly those that rely on an SVD, become infeasible as the size of the data becomes large \cite{dong2021simpler}. We address this problem by reducing the column/row selection problem to a collection of smaller sub-problems. The basic idea is to first partition the rows/columns of a matrix, and then apply an existing selection algorithm on each piece; for illustration purposes we use the Discrete Empirical Interpolation Method (\textsf{DEIM}) \cite{sorensen2016deim}. For the first task, we consider two existing algorithms that construct a Voronoi Tessellation (VT) of the rows and columns of a given matrix. We then extend these methods to automatically adapt to the data. The result is four data-driven row/column selection methods that are well-suited for parallelization, and compatible with nearly any existing column/row selection strategy. Theory and numerical examples show the design to be competitive with the original \textsf{DEIM} routine.

Medical image segmentation is essential in diagnostics, treatment planning, and healthcare, with deep learning offering promising advancements. Notably, Convolutional Neural Network (CNN) excel in capturing local image features, whereas Vision Transformer (ViT) adeptly model long-range dependencies through multi-head self-attention mechanisms. Despite their strengths, both CNN and ViT face challenges in efficiently processing long-range dependencies within medical images, often requiring substantial computational resources. This issue, combined with the high cost and limited availability of expert annotations, poses significant obstacles to achieving precise segmentation. To address these challenges, this paper introduces the Semi-Mamba-UNet, which integrates a visual mamba-based UNet architecture with a conventional UNet into a semi-supervised learning (SSL) framework. This innovative SSL approach leverages dual networks to jointly generate pseudo labels and cross supervise each other, drawing inspiration from consistency regularization techniques. Furthermore, we introduce a self-supervised pixel-level contrastive learning strategy, employing a projector pair to further enhance feature learning capabilities. Our comprehensive evaluation on a publicly available MRI cardiac segmentation dataset, comparing against various SSL frameworks with different UNet-based segmentation networks, highlights the superior performance of Semi-Mamba-UNet. The source code has been made publicly accessible.

The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is no constraint on the mutual coherence, so when this regressor is used to estimate sparse parameter vectors of a system, it may yield a large estimation error. This paper aims to tackle this issue for fixed denominator models, which include Laguerre, Kautz, and generalized orthonormal basis function expansion models, for example. The paper proposes an optimal input design method where the achieved Fisher information matrix is fitted to the desired Fisher matrix, together with a coordinate transformation designed to make the regressors in the transformed coordinates have low mutual coherence. The method can be used together with any sparse estimation method and in a numerical study we show its potential for alleviating the problem of model order selection when used in conjunction with, for example, classical methods such as AIC and BIC.

Most existing knowledge graphs suffer from incompleteness, which can be alleviated by inferring missing links based on known facts. One popular way to accomplish this is to generate low-dimensional embeddings of entities and relations, and use these to make inferences. ConvE, a recently proposed approach, applies convolutional filters on 2D reshapings of entity and relation embeddings in order to capture rich interactions between their components. However, the number of interactions that ConvE can capture is limited. In this paper, we analyze how increasing the number of these interactions affects link prediction performance, and utilize our observations to propose InteractE. InteractE is based on three key ideas -- feature permutation, a novel feature reshaping, and circular convolution. Through extensive experiments, we find that InteractE outperforms state-of-the-art convolutional link prediction baselines on FB15k-237. Further, InteractE achieves an MRR score that is 9%, 7.5%, and 23% better than ConvE on the FB15k-237, WN18RR and YAGO3-10 datasets respectively. The results validate our central hypothesis -- that increasing feature interaction is beneficial to link prediction performance. We make the source code of InteractE available to encourage reproducible research.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.