Section B provides details of the datasets, baseline implementation andexperiment setup.

FromTheorem 2,thevariational gap is strictly positive as long as the rotation part of the score network remainstobenonzero.

Quantification of brain atrophy currently requires visual rating scales which are time consuming and automated brain image analysis is warranted. We validated our automated deep learning (DL) tool measuring the Global Cerebral Atrophy (GCA) score against trained human raters, and associations with age and cognitive impairment, in representative older (>65 years) patients. CT-brain scans were obtained from patients in acute medicine (ORCHARD-EPR), acute stroke (OCS studies) and a legacy sample. Scans were divided in a 60/20/20 ratio for training, optimisation and testing. CT-images were assessed by two trained raters (rater-1=864 scans, rater-2=20 scans). Agreement between DL tool-predicted GCA scores (range 0-39) and the visual ratings was evaluated using mean absolute error (MAE) and Cohen's weighted kappa. Among 864 scans (ORCHARD-EPR=578, OCS=200, legacy scans=86), MAE between the DL tool and rater-1 GCA scores was 3.2 overall, 3.1 for ORCHARD-EPR, 3.3 for OCS and 2.6 for the legacy scans and half had DL-predicted GCA error between -2 and 2. Inter-rater agreement was Kappa=0.45 between the DL-tool and rater-1, and 0.41 between the tool and rater- 2 whereas it was lower at 0.28 for rater-1 and rater-2. There was no difference in GCA scores from the DL-tool and the two raters (one-way ANOVA, p=0.35) or in mean GCA scores between the DL-tool and rater-1 (paired t-test, t=-0.43, p=0.66), the tool and rater-2 (t=1.35, p=0.18) or between rater-1 and rater-2 (t=0.99, p=0.32). DL-tool GCA scores correlated with age and cognitive scores (both p<0.001). Our DL CT-brain analysis tool measured GCA score accurately and without user input in real-world scans acquired from older patients. Our tool will enable extraction of standardised quantitative measures of atrophy at scale for use in health data research and will act as proof-of-concept towards a point-of-care clinically approved tool.

Graph contrastive learning (GCL) has been widely used as an effective self-supervised learning method for graph representation learning. However, how to apply adequate and stable graph augmentation to generating proper views for contrastive learning remains an essential problem. Dropping edges is a primary augmentation in GCL while adding edges is not a common method due to its unstable performance. To our best knowledge, there is no theoretical analysis to study why dropping edges usually outperforms adding edges. To answer this question, we introduce a new metric, namely Error Passing Rate (EPR), to quantify how a graph fits the network. Inspired by the theoretical conclusions and the idea of positive-incentive noise, we propose a novel GCL algorithm, Error-PAssing-based Graph Contrastive Learning (EPAGCL), which uses both edge adding and edge dropping as its augmentations. To be specific, we generate views by adding and dropping edges based on the weights derived from EPR. Extensive experiments on various real-world datasets are conducted to validate the correctness of our theoretical analysis and the effectiveness of our proposed algorithm. Our code is available at: https://github.com/hyzhang98/EPAGCL.

Active systems comprise a class of nonequilibrium dynamics in which individual components autonomously dissipate energy. Efforts towards understanding the role played by activity have centered on computation of the entropy production rate (EPR), which quantifies the breakdown of time reversal symmetry. A fundamental difficulty in this program is that high dimensionality of the phase space renders traditional computational techniques infeasible for estimating the EPR. Here, we overcome this challenge with a novel deep learning approach that estimates probability currents directly from stochastic system trajectories. We derive a new physical connection between the probability current and two local definitions of the EPR for inertial systems, which we apply to characterize the departure from equilibrium in a canonical model of flocking. Our results highlight that entropy is produced and consumed on the spatial interface of a flock as the interplay between alignment and fluctuation dynamically creates and annihilates order. By enabling the direct visualization of when and where a given system is out of equilibrium, we anticipate that our methodology will advance the understanding of a broad class of complex nonequilibrium dynamics.

Electronic patient records (EPRs) produce a wealth of data but contain significant missing information. Understanding and handling this missing data is an important part of clinical data analysis and if left unaddressed could result in bias in analysis and distortion in critical conclusions. Missing data may be linked to health care professional practice patterns and imputation of missing data can increase the validity of clinical decisions. This study focuses on statistical approaches for understanding and interpreting the missing data and machine learning based clinical data imputation using a single centre's paediatric emergency data and the data from UK's largest clinical audit for traumatic injury database (TARN). In the study of 56,961 data points related to initial vital signs and observations taken on children presenting to an Emergency Department, we have shown that missing data are likely to be non-random and how these are linked to health care professional practice patterns. We have then examined 79 TARN fields with missing values for 5,791 trauma cases. Singular Value Decomposition (SVD) and k-Nearest Neighbour (kNN) based missing data imputation methods are used and imputation results against the original dataset are compared and statistically tested. We have concluded that the 1NN imputer is the best imputation which indicates a usual pattern of clinical decision making: find the most similar patients and take their attributes as imputation.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

In-context learning is a new learning paradigm where a language model conditions on a few input-output pairs (demonstrations) and a test input, and directly outputs the prediction. It has been shown highly dependent on the provided demonstrations and thus promotes the research of demonstration retrieval: given a test input, relevant examples are retrieved from the training set to serve as informative demonstrations for in-context learning. While previous works focus on training task-specific retrievers for several tasks separately, these methods are often hard to transfer and scale on various tasks, and separately trained retrievers incur a lot of parameter storage and deployment cost. In this paper, we propose Unified Demonstration Retriever (\textbf{UDR}), a single model to retrieve demonstrations for a wide range of tasks. To train UDR, we cast various tasks' training signals into a unified list-wise ranking formulation by language model's feedback. Then we propose a multi-task list-wise ranking training framework, with an iterative mining strategy to find high-quality candidates, which can help UDR fully incorporate various tasks' signals. Experiments on 30+ tasks across 13 task families and multiple data domains show that UDR significantly outperforms baselines. Further analyses show the effectiveness of each proposed component and UDR's strong ability in various scenarios including different LMs (1.3B - 175B), unseen datasets, varying demonstration quantities, etc.

Artificial learning systems aspire to mimic human intelligence by continually learning from a stream of tasks without forgetting past knowledge. One way to enable such learning is to store past experiences in the form of input examples in episodic memory and replay them when learning new tasks. However, performance of such method suffers as the size of the memory becomes smaller. In this paper, we propose a new approach for experience replay, where we select the past experiences by looking at the saliency maps which provide visual explanations for the model's decision. Guided by these saliency maps, we pack the memory with only the parts or patches of the input images important for the model's prediction. While learning a new task, we replay these memory patches with appropriate zero-padding to remind the model about its past decisions. We evaluate our algorithm on CIFAR-100, miniImageNet and CUB datasets and report better performance than the state-of-the-art approaches. With qualitative and quantitative analyses we show that our method captures richer summaries of past experiences without any memory increase, and hence performs well with small episodic memory.

Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates of the parameters of interest. Under a linear model assumption, we formulate a multifidelity approximation as a modified stochastic bandit, and analyze the loss for a class of policies that uniformly explore each model before exploiting. Utilizing the estimated conditional mean-squared error, we propose a consistent algorithm, adaptive Explore-Then-Commit (AETC), and establish a corresponding trajectory-wise optimality result. These results are then extended to the case of vector-valued responses, where we demonstrate that the algorithm is efficient without the need to worry about estimating high-dimensional parameters. The main advantage of our approach is that we require neither hierarchical model structure nor \textit{a priori} knowledge of statistical information (e.g., correlations) about or between models. Instead, the AETC algorithm requires only knowledge of which model is a trusted high-fidelity model, along with (relative) computational cost estimates of querying each model. Numerical experiments are provided at the end to support our theoretical findings.