Sandpile Prediction on Structured Undirected Graphs

We present algorithms that compute the terminal configurations for sandpile instances in $O(n \log n)$ time on trees and $O(n)$ time on paths, where $n$ is the number of vertices. The Abelian Sandpile model is a well-known model used in exploring self-organized criticality. Despite a large amount of work on other aspects of sandpiles, there have been limited results in efficiently computing the terminal state, known as the sandpile prediction problem. Our algorithm improves the previous best runtime of $O(n \log^5 n)$ on trees [Ramachandran-Schild SODA '17] and $O(n \log n)$ on paths [Moore-Nilsson '99]. To do so, we move beyond the simulation of individual events by directly computing the number of firings for each vertex. The computation is accelerated using splittable binary search trees. We also generalize our algorithm to adapt at most three sink vertices, which is the first prediction algorithm faster than mere simulation on a sandpile model with sinks. We provide a general reduction that transforms the prediction problem on an arbitrary graph into problems on its subgraphs separated by any vertex set $P$. The reduction gives a time complexity of $O(\log^{|P|} n \cdot T)$ where $T$ denotes the total time for solving on each subgraph. In addition, we give algorithms in $O(n)$ time on cliques and $O(n \log^2 n)$ time on pseudotrees.Comment: 66 pages, submitted to SODA2

Exponential Convergence of Sinkhorn Under Regularization Scheduling

In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we work on understanding the Sinkhorn algorithm under regularization scheduling, and thus modify it with a mechanism that adaptively doubles the regularization parameter $\eta$ periodically. We prove that such modified version of Sinkhorn has an exponential convergence rate as iteration complexity depending on $\log(1/\varepsilon)$ instead of $\varepsilon^{-O(1)}$ from previous analyses [Cut13][ANWR17] in the optimal transport problems with integral supply and demand. Furthermore, with cost and capacity scaling procedures, the general optimal transport problem can be solved with a logarithmic dependence on $1/\varepsilon$ as well.Comment: ACDA23, 13 page

Learning-Augmented B-Trees

We study learning-augmented binary search trees (BSTs) and B-Trees via Treaps with composite priorities. The result is a simple search tree where the depth of each item is determined by its predicted weight $w_x$. To achieve the result, each item $x$ has its composite priority $-\lfloor\log\log(1/w_x)\rfloor + U(0, 1)$ where $U(0, 1)$ is the uniform random variable. This generalizes the recent learning-augmented BSTs [Lin-Luo-Woodruff ICML`22], which only work for Zipfian distributions, to arbitrary inputs and predictions. It also gives the first B-Tree data structure that can provably take advantage of localities in the access sequence via online self-reorganization. The data structure is robust to prediction errors and handles insertions, deletions, as well as prediction updates.Comment: 25 page

Hardness of Graph-Structured Algebraic and Symbolic Problems

In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in $\mathbb{Z}_p$ to solving unit-weight low-degree graph Laplacians over $\mathbb{Z}_p$ with a polylogarithmic overhead on the number of non-zeros. Given the hardness of solving general linear systems in $\mathbb{Z}_p$ [Casacuberta-Kyng 2022], this result shows that it is unlikely that we can generalize Laplacian solvers over $\mathbb{R}$, or finite-element based methods over $\mathbb{R}$ in general, to a finite-field setting. We also reduce solving general linear systems over $\mathbb{Z}_p$ to solving linear systems whose coefficient matrices are walk matrices (matrices with all ones on the diagonal) and normalized Laplacians (Laplacians that are also walk matrices) over $\mathbb{Z}_p$. We often need to apply linear system solvers to random linear systems, in which case the worst case analysis above might be less relevant. For example, we often need to substitute variables in a symbolic matrix with random values. Here, a symbolic matrix is simply a matrix whose entries are in a polynomial ring $\mathbb{F}[x_1, \ldots, x_t]$. We formally define the reducibility between symbolic matrix classes, which are classified in terms of the degrees of the entries and the number of occurrences of the variables. We show that the determinant identity testing problem for symbolic matrices with polynomial degree $1$ and variable multiplicity at most $3$ is at least as hard as the same problem for general matrices over $\mathbb{R}$.Comment: 57 pages, submitted version to STOC2

Fast Adaptively Weighted Matrix Factorization for Recommendation with Implicit Feedback

Recommendation from implicit feedback is a highly challenging task due to the lack of the reliable observed negative data. A popular and effective approach for implicit recommendation is to treat unobserved data as negative but downweight their confidence. Naturally, how to assign confidence weights and how to handle the large number of the unobserved data are two key problems for implicit recommendation models. However, existing methods either pursuit fast learning by manually assigning simple confidence weights, which lacks flexibility and may create empirical bias in evaluating user's preference; or adaptively infer personalized confidence weights but suffer from low efficiency. To achieve both adaptive weights assignment and efficient model learning, we propose a fast adaptively weighted matrix factorization (FAWMF) based on variational auto-encoder. The personalized data confidence weights are adaptively assigned with a parameterized neural network (function) and the network can be inferred from the data. Further, to support fast and stable learning of FAWMF, a new specific batch-based learning algorithm fBGD has been developed, which trains on all feedback data but its complexity is linear to the number of observed data. Extensive experiments on real-world datasets demonstrate the superiority of the proposed FAWMF and its learning algorithm fBGD

Active Globally Explainable Learning for Medical Images via Class Association Embedding and Cyclic Adversarial Generation

Explainability poses a major challenge to artificial intelligence (AI) techniques. Current studies on explainable AI (XAI) lack the efficiency of extracting global knowledge about the learning task, thus suffer deficiencies such as imprecise saliency, context-aware absence and vague meaning. In this paper, we propose the class association embedding (CAE) approach to address these issues. We employ an encoder-decoder architecture to embed sample features and separate them into class-related and individual-related style vectors simultaneously. Recombining the individual-style code of a given sample with the class-style code of another leads to a synthetic sample with preserved individual characters but changed class assignment, following a cyclic adversarial learning strategy. Class association embedding distills the global class-related features of all instances into a unified domain with well separation between classes. The transition rules between different classes can be then extracted and further employed to individual instances. We then propose an active XAI framework which manipulates the class-style vector of a certain sample along guided paths towards the counter-classes, resulting in a series of counter-example synthetic samples with identical individual characters. Comparing these counterfactual samples with the original ones provides a global, intuitive illustration to the nature of the classification tasks. We adopt the framework on medical image classification tasks, which show that more precise saliency maps with powerful context-aware representation can be achieved compared with existing methods. Moreover, the disease pathology can be directly visualized via traversing the paths in the class-style space

Mixup-Augmented Meta-Learning for Sample-Efficient Fine-Tuning of Protein Simulators

Molecular dynamics simulations have emerged as a fundamental instrument for studying biomolecules. At the same time, it is desirable to perform simulations of a collection of particles under various conditions in which the molecules can fluctuate. In this paper, we explore and adapt the soft prompt-based learning method to molecular dynamics tasks. Our model can remarkably generalize to unseen and out-of-distribution scenarios with limited training data. While our work focuses on temperature as a test case, the versatility of our approach allows for efficient simulation through any continuous dynamic conditions, such as pressure and volumes. Our framework has two stages: 1) Pre-trains with data mixing technique, augments molecular structure data and temperature prompts, then applies a curriculum learning method by increasing the ratio of them smoothly. 2) Meta-learning-based fine-tuning framework improves sample-efficiency of fine-tuning process and gives the soft prompt-tuning better initialization points. Comprehensive experiments reveal that our framework excels in accuracy for in-domain data and demonstrates strong generalization capabilities for unseen and out-of-distribution samples

Piezoresistivity and piezopermittivity of cement-based sensors under quasi-static stress and changing moisture

Integrated cement-based sensors offer an economic alternative to extrinsic sensors for health monitoring applications in concrete structures due to their high strength to cost ratio, geometrical versatility, low shrinkage, and natural compatibility. Nonetheless, their performance under in-service conditions were in lack of investigations. While the piezoresistivity (change in resistance with stress) has been commonly used for mechanical sensing, the piezopermittivity (change in capacitive reactance with stress) is rarely characterized. Exploiting the high relative permittivity and electrical conductivity of carbon fibre reinforced cement-based sensors, this study investigates the piezoresistivity and piezopermittivity under changing stress and moisture using electrochemical impedance spectroscopy (EIS). Two types of sensors were evaluated: one containing 0.5 vol% of carbon fibres whose electrical conductivity was ionically dominant, and another with electronically dominant (1.2 vol% of carbon fibres) conductivity. Results highlighted that the piezopermittivity is “moisture content-dominant” whilst the piezoresistivity is “fibre content-dominant”. As the moisture content decreased, the sensitivity of piezopermittivity for both sensor types decreased, while the sensitivity of piezoresistivity decreased for the ionically dominant sensor but increased for the electronically dominant sensor. The piezoresistivity of the electronically dominant sensor was less sensitive than piezopermittivity at a water saturation of 80%. Conversely, the piezoresistivity of the ionically dominant sensor was more sensitive than piezopermittivity at the tested water saturations ≤ 80%. For the first time, this study presents the combined effects of moisture and fibre content on the pressure sensitive response of cement-based sensors through a dual-phase (i.e., piezoresistivity and piezopermittivity) EIS interpretation technique, providing valuable information to benefit further behaviour prediction and single-effect recognition in the field scenario where the sensors are subject to simultaneous environmental effects causing moisture variations such as temperature and humidity variations, freeze-thawing, and so on

Tirofiban for Stroke without Large or Medium-Sized Vessel Occlusion

The effects of the glycoprotein IIb/IIIa receptor inhibitor tirofiban in patients with acute ischemic stroke but who have no evidence of complete occlusion of large or medium-sized vessels have not been extensively studied. In a multicenter trial in China, we enrolled patients with ischemic stroke without occlusion of large or medium-sized vessels and with a National Institutes of Health Stroke Scale score of 5 or more and at least one moderately to severely weak limb. Eligible patients had any of four clinical presentations: ineligible for thrombolysis or thrombectomy and within 24 hours after the patient was last known to be well; progression of stroke symptoms 24 to 96 hours after onset; early neurologic deterioration after thrombolysis; or thrombolysis with no improvement at 4 to 24 hours. Patients were assigned to receive intravenous tirofiban (plus oral placebo) or oral aspirin (100 mg per day, plus intravenous placebo) for 2 days; all patients then received oral aspirin until day 90. The primary efficacy end point was an excellent outcome, defined as a score of 0 or 1 on the modified Rankin scale (range, 0 [no symptoms] to 6 [death]) at 90 days. Secondary end points included functional independence at 90 days and a quality-of-life score. The primary safety end points were death and symptomatic intracranial hemorrhage. A total of 606 patients were assigned to the tirofiban group and 571 to the aspirin group. Most patients had small infarctions that were presumed to be atherosclerotic. The percentage of patients with a score of 0 or 1 on the modified Rankin scale at 90 days was 29.1% with tirofiban and 22.2% with aspirin (adjusted risk ratio, 1.26; 95% confidence interval, 1.04 to 1.53, P = 0.02). Results for secondary end points were generally not consistent with the results of the primary analysis. Mortality was similar in the two groups. The incidence of symptomatic intracranial hemorrhage was 1.0% in the tirofiban group and 0% in the aspirin group. In this trial involving heterogeneous groups of patients with stroke of recent onset or progression of stroke symptoms and nonoccluded large and medium-sized cerebral vessels, intravenous tirofiban was associated with a greater likelihood of an excellent outcome than low-dose aspirin. Incidences of intracranial hemorrhages were low but slightly higher with tirofiban

Latent Diffusion Energy-based Model for Graph Generation

Generating graph-structured data is a challenging task that needs to capture complex relationship between nodes and edges with permutation-invariance property. This paper purposes to generate graphs using latent space energy-based models (EBM). We formulate the latent space EBM as an informative prior distribution, which is trained jointly with the graph generator model. And short-run Markov chain Monte Carlo (MCMC) is employed for the posterior inference and prior sampling process. To further capture the complex distribution of graph data, we provide another version that replaces the EBM prior with a sequence of EBMs, transforming the prior process with a diffusion process. Different graph datasets including generic graphs and molecular graphs are used to validate the method, demonstrating the effectiveness of the latent space EBM and the latent diffusion method