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Early detection of surgical complications allows for timely therapy and proactive risk mitigation. Machine learning (ML) can be leveraged to identify and predict patient risks for postoperative complications. We developed and validated the effectiveness of predicting postoperative complications using a novel surgical Variational Autoencoder (surgVAE) that uncovers intrinsic patterns via cross-task and cross-cohort presentation learning. This retrospective cohort study used data from the electronic health records of adult surgical patients over four years (2018 - 2021). Six key postoperative complications for cardiac surgery were assessed: acute kidney injury, atrial fibrillation, cardiac arrest, deep vein thrombosis or pulmonary embolism, blood transfusion, and other intraoperative cardiac events. We compared prediction performances of surgVAE against widely-used ML models and advanced representation learning and generative models under 5-fold cross-validation. 89,246 surgeries (49% male, median (IQR) age: 57 (45-69)) were included, with 6,502 in the targeted cardiac surgery cohort (61% male, median (IQR) age: 60 (53-70)). surgVAE demonstrated superior performance over existing ML solutions across all postoperative complications of cardiac surgery patients, achieving macro-averaged AUPRC of 0.409 and macro-averaged AUROC of 0.831, which were 3.4% and 3.7% higher, respectively, than the best alternative method (by AUPRC scores). Model interpretation using Integrated Gradients highlighted key risk factors based on preoperative variable importance. surgVAE showed excellent discriminatory performance for predicting postoperative complications and addressing the challenges of data complexity, small cohort sizes, and low-frequency positive events. surgVAE enables data-driven predictions of patient risks and prognosis while enhancing the interpretability of patient risk profiles.

Multimedia recommendation, which incorporates various modalities (e.g., images, texts, etc.) into user or item representation to improve recommendation quality, and self-supervised learning carries multimedia recommendation to a plateau of performance, because of its superior performance in aligning different modalities. However, more and more research finds that aligning all modal representations is suboptimal because it damages the unique attributes of each modal. These studies use subtraction and orthogonal constraints in geometric space to learn unique parts. However, our rigorous analysis reveals the flaws in this approach, such as that subtraction does not necessarily yield the desired modal-unique and that orthogonal constraints are ineffective in user and item high-dimensional representation spaces. To make up for the previous weaknesses, we propose Separate Learning (SEA) for multimedia recommendation, which mainly includes mutual information view of modal-unique and -generic learning. Specifically, we first use GNN to learn the representations of users and items in different modalities and split each modal representation into generic and unique parts. We employ contrastive log-ratio upper bound to minimize the mutual information between the general and unique parts within the same modality, to distance their representations, thus learning modal-unique features. Then, we design Solosimloss to maximize the lower bound of mutual information, to align the general parts of different modalities, thus learning more high-quality modal-generic features. Finally, extensive experiments on three datasets demonstrate the effectiveness and generalization of our proposed framework. The code is available at SEA and the full training record of the main experiment.

The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to be optimized. Unfortunately, whether the $\mathcal{O}(N\log_2 N)$ time complexity of the fast Fourier transform (FFT) can be outperformed remains an unresolved question in the theory of computation. However, in many applications of the DFT -- such as compressive sensing, image processing, and wideband spectral analysis -- only a small fraction of the output signal needs to be computed because the signal is sparse. This motivates the development of algorithms that compute specific DFT coefficients more efficiently than the FFT algorithm. In this article, we show that the number of points of some DFT coefficients can be dramatically reduced by means of elementary mathematical properties. We present an algorithm that compacts the square index coefficients (SICs) of DFT (i.e., $X_{k\sqrt{N}}$, $k=0,1,\cdots, \sqrt{N}-1$, for a square number $N$) from $N$ to $\sqrt{N}$ points at the expense of $N-1$ complex sums and no multiplication. Based on this, any regular DFT algorithm can be straightforwardly applied to compute the SICs with a reduced number of complex multiplications. If $N$ is a power of two, one can combine our algorithm with the FFT to calculate all SICs in $\mathcal{O}(\sqrt{N}\log_2\sqrt{N})$ time complexity.

When rows of an $n \times d$ matrix $A$ are given in a stream, we study algorithms for approximating the top eigenvector of the matrix ${A}^TA$ (equivalently, the top right singular vector of $A$). We consider worst case inputs $A$ but assume that the rows are presented to the streaming algorithm in a uniformly random order. We show that when the gap parameter $R = \sigma_1(A)^2/\sigma_2(A)^2 = \Omega(1)$, then there is a randomized algorithm that uses $O(h \cdot d \cdot \operatorname{polylog}(d))$ bits of space and outputs a unit vector $v$ that has a correlation $1 - O(1/\sqrt{R})$ with the top eigenvector $v_1$. Here $h$ denotes the number of \emph{heavy rows} in the matrix, defined as the rows with Euclidean norm at least $\|{A}\|_F/\sqrt{d \cdot \operatorname{polylog}(d)}$. We also provide a lower bound showing that any algorithm using $O(hd/R)$ bits of space can obtain at most $1 - \Omega(1/R^2)$ correlation with the top eigenvector. Thus, parameterizing the space complexity in terms of the number of heavy rows is necessary for high accuracy solutions. Our results improve upon the $R = \Omega(\log n \cdot \log d)$ requirement in a recent work of Price and Xun (FOCS 2024). We note that the algorithm of Price and Xun works for arbitrary order streams whereas our algorithm requires a stronger assumption that the rows are presented in a uniformly random order. We additionally show that the gap requirements in their analysis can be brought down to $R = \Omega(\log^2 d)$ for arbitrary order streams and $R = \Omega(\log d)$ for random order streams. The requirement of $R = \Omega(\log d)$ for random order streams is nearly tight for their analysis as we obtain a simple instance with $R = \Omega(\log d/\log\log d)$ for which their algorithm, with any fixed learning rate, cannot output a vector approximating the top eigenvector $v_1$.

We consider the dunking problem: a solid body at uniform temperature $T_{\text i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and spatially uniform time-independent heat transfer coefficient. We permit heterogeneous material composition: spatially dependent density, specific heat, and thermal conductivity. Mathematically, the problem is described by a heat equation with Robin boundary conditions. The crucial parameter is the Biot number -- a nondimensional heat transfer (Robin) coefficient; we consider the limit of small Biot number. We introduce first-order and second-order asymptotic approximations (in Biot number) for several quantities of interest, notably the spatial domain average temperature as a function of time; the first-order approximation is simply the standard engineering `lumped' model. We then provide asymptotic error estimates for the first-order and second-order approximations for small Biot number, and also, for the first-order approximation, alternative strict bounds valid for all Biot number. Companion numerical solutions of the heat equation confirm the effectiveness of the error estimates for small Biot number. The second-order approximation and the first-order and second-order error estimates depend on several functional outputs associated to an elliptic partial differential equation; the latter is derived from Biot-sensitivity analysis of the heat equation eigenproblem in the limit of small Biot number. Most important is $\phi$, the only functional output required for the first-order error estimates; $\phi$ admits a simple physical interpretation in terms of conduction length scale. We investigate the domain and property dependence of $\phi$: most notably, we characterize spatial domains for which the standard lumped-model error criterion -- Biot number (based on volume-to-area length scale) small -- is deficient.

We create two German-only decoder models, LL\"aMmlein 120M and 1B, transparently from scratch and publish them, along with the training data, for the German NLP research community to use. The model training involved several key steps, including extensive data preprocessing, the creation of a custom German tokenizer, the training itself, as well as the evaluation of the final models on various benchmarks. Throughout the training process, multiple checkpoints were saved and analyzed using the SuperGLEBer benchmark to monitor the models' learning dynamics. Compared to state-of-the-art models on the SuperGLEBer benchmark, both LL\"aMmlein models performed competitively, consistently matching or surpassing models with similar parameter sizes. The results show that the models' quality scales with size as expected, but performance improvements on some tasks plateaued early, offering valuable insights into resource allocation for future model development.

Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by showing that an aperiodic monotile exists in sufficiently high dimension $n$ [Ann. Math. 200(2024), 301-363]. In another paper [to appear in J. Eur. Math. Soc.], they also show that if the dimension $n$ is part of the input, then the translational tiling for subsets of $\mathbb{Z}^n$ with one tile is undecidable. These two results are very strong pieces of evidence for the conjecture that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable, for some fixed $n$. This paper gives another supportive result for this conjecture by showing that translational tiling of the $4$-dimensional space with a set of three connected tiles is undecidable.

While existing work in robust deep learning has focused on small pixel-level $\ell_p$ norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations -- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.

Event detection (ED), a sub-task of event extraction, involves identifying triggers and categorizing event mentions. Existing methods primarily rely upon supervised learning and require large-scale labeled event datasets which are unfortunately not readily available in many real-life applications. In this paper, we consider and reformulate the ED task with limited labeled data as a Few-Shot Learning problem. We propose a Dynamic-Memory-Based Prototypical Network (DMB-PN), which exploits Dynamic Memory Network (DMN) to not only learn better prototypes for event types, but also produce more robust sentence encodings for event mentions. Differing from vanilla prototypical networks simply computing event prototypes by averaging, which only consume event mentions once, our model is more robust and is capable of distilling contextual information from event mentions for multiple times due to the multi-hop mechanism of DMNs. The experiments show that DMB-PN not only deals with sample scarcity better than a series of baseline models but also performs more robustly when the variety of event types is relatively large and the instance quantity is extremely small.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.