We outline a geometrical correspondence between capacity and effective free energy minima of discrete memoryless channels. This correspondence informs the behavior of a timescale that is important in effective statistical physics.
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Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.
Transformers have achieved state-of-the-art results across multiple NLP tasks. However, the self-attention mechanism complexity scales quadratically with the sequence length, creating an obstacle for tasks involving long sequences, like in the speech domain. In this paper, we discuss the usefulness of self-attention for Direct Speech Translation. First, we analyze the layer-wise token contributions in the self-attention of the encoder, unveiling local diagonal patterns. To prove that some attention weights are avoidable, we propose to substitute the standard self-attention with a local efficient one, setting the amount of context used based on the results of the analysis. With this approach, our model matches the baseline performance, and improves the efficiency by skipping the computation of those weights that standard attention discards.
Ball 3D localization in team sports has various applications including automatic offside detection in soccer, or shot release localization in basketball. Today, this task is either resolved by using expensive multi-views setups, or by restricting the analysis to ballistic trajectories. In this work, we propose to address the task on a single image from a calibrated monocular camera by estimating ball diameter in pixels and use the knowledge of real ball diameter in meters. This approach is suitable for any game situation where the ball is (even partly) visible. To achieve this, we use a small neural network trained on image patches around candidates generated by a conventional ball detector. Besides predicting ball diameter, our network outputs the confidence of having a ball in the image patch. Validations on 3 basketball datasets reveals that our model gives remarkable predictions on ball 3D localization. In addition, through its confidence output, our model improves the detection rate by filtering the candidates produced by the detector. The contributions of this work are (i) the first model to address 3D ball localization on a single image, (ii) an effective method for ball 3D annotation from single calibrated images, (iii) a high quality 3D ball evaluation dataset annotated from a single viewpoint. In addition, the code to reproduce this research is be made freely available at //github.com/gabriel-vanzandycke/deepsport.
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are known informally as $\mathsf{C}$-sets. In this paper, we describe and implement an extension of $\mathsf{C}$-sets having data attributes with fixed types, such as graphs with labeled vertices or real-valued edge weights. We call such structures "acsets," short for "attributed $\mathsf{C}$-sets." Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames. They also encompass more elaborate graph-like objects such as wiring diagrams and Petri nets with rate constants. We develop the mathematical theory of acsets and then describe a generic implementation in the Julia programming language, which uses advanced language features to achieve performance comparable with specialized data structures.
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic.
The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.
Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature is becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, Chignolin and Bovine Pancreatic Trypsin Inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.
Transformers have dominated the field of natural language processing, and recently impacted the computer vision area. In the field of medical image analysis, Transformers have also been successfully applied to full-stack clinical applications, including image synthesis/reconstruction, registration, segmentation, detection, and diagnosis. Our paper presents both a position paper and a primer, promoting awareness and application of Transformers in the field of medical image analysis. Specifically, we first overview the core concepts of the attention mechanism built into Transformers and other basic components. Second, we give a new taxonomy of various Transformer architectures tailored for medical image applications and discuss their limitations. Within this review, we investigate key challenges revolving around the use of Transformers in different learning paradigms, improving the model efficiency, and their coupling with other techniques. We hope this review can give a comprehensive picture of Transformers to the readers in the field of medical image analysis.
The U-Net was presented in 2015. With its straight-forward and successful architecture it quickly evolved to a commonly used benchmark in medical image segmentation. The adaptation of the U-Net to novel problems, however, comprises several degrees of freedom regarding the exact architecture, preprocessing, training and inference. These choices are not independent of each other and substantially impact the overall performance. The present paper introduces the nnU-Net ('no-new-Net'), which refers to a robust and self-adapting framework on the basis of 2D and 3D vanilla U-Nets. We argue the strong case for taking away superfluous bells and whistles of many proposed network designs and instead focus on the remaining aspects that make out the performance and generalizability of a method. We evaluate the nnU-Net in the context of the Medical Segmentation Decathlon challenge, which measures segmentation performance in ten disciplines comprising distinct entities, image modalities, image geometries and dataset sizes, with no manual adjustments between datasets allowed. At the time of manuscript submission, nnU-Net achieves the highest mean dice scores across all classes and seven phase 1 tasks (except class 1 in BrainTumour) in the online leaderboard of the challenge.
In this paper, we focus on three problems in deep learning based medical image segmentation. Firstly, U-net, as a popular model for medical image segmentation, is difficult to train when convolutional layers increase even though a deeper network usually has a better generalization ability because of more learnable parameters. Secondly, the exponential ReLU (ELU), as an alternative of ReLU, is not much different from ReLU when the network of interest gets deep. Thirdly, the Dice loss, as one of the pervasive loss functions for medical image segmentation, is not effective when the prediction is close to ground truth and will cause oscillation during training. To address the aforementioned three problems, we propose and validate a deeper network that can fit medical image datasets that are usually small in the sample size. Meanwhile, we propose a new loss function to accelerate the learning process and a combination of different activation functions to improve the network performance. Our experimental results suggest that our network is comparable or superior to state-of-the-art methods.
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