Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep Galerkin method, which uses deep neural networks to solve differential equations. This primer aims to provide technical and practical insights into the Deep Galerkin method and its implementation. We demonstrate how to solve the one-dimensional heat equation step-by-step. We also show how to apply the Deep Galerkin method to solve systems of ordinary differential equations and integral equations, such as the Fredholm of the second kind. Additionally, we provide code snippets within the text and the complete source code on Github. The examples are designed so that one can run them on a simple computer without needing a GPU.
We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in optimization across various experiments, from small-scale ``grokking'' to large-scale tasks like image classification with ConvNets, image generation with UNets, speech recognition with LSTMs, and language modeling with Transformers. We also demonstrate that weight decay enhances this bias beyond its role as a norm regularizer, even in practical systems. Moreover, we show that these spectral dynamics distinguish memorizing networks from generalizing ones, offering a novel perspective on this longstanding conundrum. Additionally, we leverage spectral dynamics to explore the emergence of well-performing sparse subnetworks (lottery tickets) and the structure of the loss surface through linear mode connectivity. Our findings suggest that spectral dynamics provide a coherent framework to better understand the behavior of neural networks across diverse settings.
In high-energy physics, accurately estimating the kinematic parameters (position and momentum) of anti-neutrons ($\bar{n}$) is essential for exploring the fundamental governing principles. However, this process is particularly challenging when using an electromagnetic calorimeter (EMC) as the energy detector, due to their limited accuracy and efficiency in interacting with $\bar{n}$. To address this issue, we propose Vision Calorimeter (ViC), a data-driven framework which migrates visual object detection techniques to high-energy particle images. To accommodate the unique characteristics of particle images, we introduce the heat-conduction operator (HCO) into both the backbone and the head of the conventional object detector and conduct significant structural improvements. HCO enjoys the advantage of both radial prior and global attention, as it is inspired by physical heat conduction which naturally aligns with the pattern of particle incidence. Implemented via the Discrete Cosine Transform (DCT), HCO extracts frequency-domain features, bridging the distribution gap between the particle images and the natural images on which visual object detectors are pre-trained. Experimental results demonstrate that ViC significantly outperforms traditional approaches, reducing the incident position prediction error by 46.16% (from 17.31$^{\circ}$ to 9.32$^{\circ}$) and providing the first baseline result with an incident momentum regression error of 21.48%. This study underscores ViC's great potential as a general-purpose particle parameter estimator in high-energy physics. Code is available at https://github.com/yuhongtian17/ViC.
Hierarchical federated learning (HFL) is a promising distributed deep learning model training paradigm, but it has crucial security concerns arising from adversarial attacks. This research investigates and assesses the security of HFL using a novel methodology by focusing on its resilience against adversarial attacks inference-time and training-time. Through a series of extensive experiments across diverse datasets and attack scenarios, we uncover that HFL demonstrates robustness against untargeted training-time attacks due to its hierarchical structure. However, targeted attacks, particularly backdoor attacks, exploit this architecture, especially when malicious clients are positioned in the overlapping coverage areas of edge servers. Consequently, HFL shows a dual nature in its resilience, showcasing its capability to recover from attacks thanks to its hierarchical aggregation that strengthens its suitability for adversarial training, thereby reinforcing its resistance against inference-time attacks. These insights underscore the necessity for balanced security strategies in HFL systems, leveraging their inherent strengths while effectively mitigating vulnerabilities.
Photovoltaic (PV) energy grows rapidly and is crucial for the decarbonization of electric systems. However, centralized registries recording the technical characteristifs of rooftop PV systems are often missing, making it difficult to accurately monitor this growth. The lack of monitoring could threaten the integration of PV energy into the grid. To avoid this situation, the remote sensing of rooftop PV systems using deep learning emerged as a promising solution. However, existing techniques are not reliable enough to be used by public authorities or transmission system operators (TSOs) to construct up-to-date statistics on the rooftop PV fleet. The lack of reliability comes from the fact that deep learning models are sensitive to distribution shifts. This work proposes a comprehensive evaluation of the effects of distribution shifts on the classification accuracy of deep learning models trained to detect rooftop PV panels on overhead imagery. We construct a benchmark to isolate the sources of distribution shift and introduce a novel methodology that leverages explainable artificial intelligence (XAI) and decomposition of the input image and model's decision in terms of scales to understand how distribution shifts affect deep learning models. Finally, based on our analysis, we introduce a data augmentation technique meant to improve the robustness of deep learning classifiers to varying acquisition conditions. We show that our proposed approach outperforms competing methods. We discuss some practical recommendations for mapping PV systems using overhead imagery and deep learning models.
As global warming soars, the need to assess the environmental impact of research is becoming increasingly urgent. Despite this, few recommender systems research papers address their environmental impact. In this study, we estimate the environmental impact of recommender systems research by reproducing typical experimental pipelines. Our analysis spans 79 full papers from the 2013 and 2023 ACM RecSys conferences, comparing traditional "good old-fashioned AI" algorithms with modern deep learning algorithms. We designed and reproduced representative experimental pipelines for both years, measuring energy consumption with a hardware energy meter and converting it to CO2 equivalents. Our results show that papers using deep learning algorithms emit approximately 42 times more CO2 equivalents than papers using traditional methods. On average, a single deep learning-based paper generates 3,297 kilograms of CO2 equivalents - more than the carbon emissions of one person flying from New York City to Melbourne or the amount of CO2 one tree sequesters over 300 years.
Text has become the predominant form of communication on social media, embedding a wealth of emotional nuances. Consequently, the extraction of emotional information from text is of paramount importance. Despite previous research making some progress, existing text sentiment analysis models still face challenges in integrating diverse semantic information and lack interpretability. To address these issues, we propose a quantum-inspired deep learning architecture that combines fundamental principles of quantum mechanics (QM principles) with deep learning models for text sentiment analysis. Specifically, we analyze the commonalities between text representation and QM principles to design a quantum-inspired text representation method and further develop a quantum-inspired text embedding layer. Additionally, we design a feature extraction layer based on long short-term memory (LSTM) networks and self-attention mechanisms (SAMs). Finally, we calculate the text density matrix using the quantum complex numbers principle and apply 2D-convolution neural networks (CNNs) for feature condensation and dimensionality reduction. Through a series of visualization, comparative, and ablation experiments, we demonstrate that our model not only shows significant advantages in accuracy and efficiency compared to previous related models but also achieves a certain level of interpretability by integrating QM principles. Our code is available at QISA.
The intersection of artificial intelligence and bioinformatics has enabled significant advancements in drug discovery, particularly through the application of machine learning models. In this study, we present a combined approach using genetic algorithms and deep learning models to address two critical aspects of drug discovery: the generation of novel tyrosine kinase inhibitors and the prediction of their bioactivity. The generative model leverages genetic algorithms to create new small molecules with optimized ADMET (absorption, distribution, metabolism, excretion, and toxicity) and drug-likeness properties. Concurrently, a deep learning model is employed to predict the bioactivity of these generated molecules against tyrosine kinases, a key enzyme family involved in various cellular processes and cancer progression. By integrating these advanced computational methods, we demonstrate a powerful framework for accelerating the generation and identification of potential tyrosine kinase inhibitors, contributing to more efficient and effective early-stage drug discovery processes.
While adversarial robustness in computer vision is a mature research field, fewer researchers have tackled the evasion attacks against tabular deep learning, and even fewer investigated robustification mechanisms and reliable defenses. We hypothesize that this lag in the research on tabular adversarial attacks is in part due to the lack of standardized benchmarks. To fill this gap, we propose TabularBench, the first comprehensive benchmark of robustness of tabular deep learning classification models. We evaluated adversarial robustness with CAA, an ensemble of gradient and search attacks which was recently demonstrated as the most effective attack against a tabular model. In addition to our open benchmark (https://github.com/serval-uni-lu/tabularbench) where we welcome submissions of new models and defenses, we implement 7 robustification mechanisms inspired by state-of-the-art defenses in computer vision and propose the largest benchmark of robust tabular deep learning over 200 models across five critical scenarios in finance, healthcare and security. We curated real datasets for each use case, augmented with hundreds of thousands of realistic synthetic inputs, and trained and assessed our models with and without data augmentations. We open-source our library that provides API access to all our pre-trained robust tabular models, and the largest datasets of real and synthetic tabular inputs. Finally, we analyze the impact of various defenses on the robustness and provide actionable insights to design new defenses and robustification mechanisms.
We use a space-time discretization based on physics informed deep learning (PIDL) to approximate solutions of a class of rate-dependent strain gradient plasticity models. The differential equation governing the plastic flow, the so-called microforce balance for this class of yield-free plasticity models, is very stiff, often leading to numerical corruption and a consequent lack of accuracy or convergence by finite element (FE) methods. Indeed, setting up the discretized framework, especially with an elaborate meshing around the propagating plastic bands whose locations are often unknown a-priori, also scales up the computational effort significantly. Taking inspiration from physics informed neural networks, we modify the loss function of a PIDL model in several novel ways to account for the balance laws, either through energetics or via the resulting PDEs once a variational scheme is applied, and the constitutive equations. The initial and the boundary conditions may either be imposed strictly by encoding them within the PIDL architecture, or enforced weakly as a part of the loss function. The flexibility in the implementation of a PIDL technique often makes for its ready interface with powerful optimization schemes, and this in turn provides for many possibilities in posing the problem. We have used freely available open-source libraries that perform fast, parallel computations on GPUs. Using numerical illustrations, we demonstrate how PIDL methods could address the computational challenges posed by strain gradient plasticity models. Also, PIDL methods offer abundant potentialities, vis-\'a-vis a somewhat straitjacketed and poorer approximant of FE methods, in customizing the formulation as per the problem objective.
Different activation functions work best for different deep learning models. To exploit this, we leverage recent advancements in gradient-based search techniques for neural architectures to efficiently identify high-performing activation functions for a given application. We propose a fine-grained search cell that combines basic mathematical operations to model activation functions, allowing for the exploration of novel activations. Our approach enables the identification of specialized activations, leading to improved performance in every model we tried, from image classification to language models. Moreover, the identified activations exhibit strong transferability to larger models of the same type, as well as new datasets. Importantly, our automated process for creating customized activation functions is orders of magnitude more efficient than previous approaches. It can easily be applied on top of arbitrary deep learning pipelines and thus offers a promising practical avenue for enhancing deep learning architectures.
The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging this dominance. This paper investigates the use of autoregressive state-space models for tabular data and compares their performance against established benchmark models. Additionally, we explore various adaptations of these models, including different pooling strategies, feature interaction mechanisms, and bi-directional processing techniques to understand their effectiveness for tabular data. Our findings indicate that interpreting features as a sequence and processing them and their interactions through structured state-space layers can lead to significant performance improvement. This research underscores the versatility of autoregressive models in tabular data analysis, positioning them as a promising alternative that could substantially enhance deep learning capabilities in this traditionally challenging area. The source code is available at https://github.com/basf/mamba-tabular.
Evaluating the behavioral boundaries of deep learning (DL) systems is crucial for understanding their reliability across diverse, unseen inputs. Existing solutions fall short as they rely on untargeted random, model- or latent-based perturbations, due to difficulties in generating controlled input variations. In this work, we introduce Mimicry, a novel black-box test generator for fine-grained, targeted exploration of DL system boundaries. Mimicry performs boundary testing by leveraging the probabilistic nature of DL outputs to identify promising directions for exploration. It uses style-based GANs to disentangle input representations into content and style components, enabling controlled feature mixing to approximate the decision boundary. We evaluated Mimicry's effectiveness in generating boundary inputs for five widely used DL image classification systems of increasing complexity, comparing it to two baseline approaches. Our results show that Mimicry consistently identifies inputs closer to the decision boundary. It generates semantically meaningful boundary test cases that reveal new functional (mis)behaviors, while the baselines produce mainly corrupted or invalid inputs. Thanks to its enhanced control over latent space manipulations, Mimicry remains effective as dataset complexity increases, maintaining competitive diversity and higher validity rates, confirmed by human assessors.
Classical optimization and learning-based methods are the two reigning paradigms in deformable image registration. While optimization-based methods boast generalizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature. In this paper, we make an explicit correspondence between the mutual information of the distribution of per-pixel intensity and labels, and the performance of classical registration methods. This strong correlation hints to the fact that architectural designs in learning-based methods is unlikely to affect this correlation, and therefore, the performance of learning-based methods. This hypothesis is thoroughly validated with state-of-the-art classical and learning-based methods. However, learning-based methods with weak supervision can perform high-fidelity intensity and label registration, which is not possible with classical methods. Next, we show that this high-fidelity feature learning does not translate to invariance to domain shift, and learning-based methods are sensitive to such changes in the data distribution. Finally, we propose a general recipe to choose the best paradigm for a given registration problem, based on these observations.
Full-complexity Earth system models (ESMs) are computationally very expensive, limiting their use in exploring the climate outcomes of multiple emission pathways. More efficient emulators that approximate ESMs can directly map emissions onto climate outcomes, and benchmarks are being used to evaluate their accuracy on standardized tasks and datasets. We investigate a popular benchmark in data-driven climate emulation, ClimateBench, on which deep learning-based emulators are currently achieving the best performance. We compare these deep learning emulators with a linear regression-based emulator, akin to pattern scaling, and show that it outperforms the incumbent 100M-parameter deep learning foundation model, ClimaX, on 3 out of 4 regionally-resolved climate variables, notably surface temperature and precipitation. While emulating surface temperature is expected to be predominantly linear, this result is surprising for emulating precipitation. Precipitation is a much more noisy variable, and we show that deep learning emulators can overfit to internal variability noise at low frequencies, degrading their performance in comparison to a linear emulator. We address the issue of overfitting by increasing the number of climate simulations per emission pathway (from 3 to 50) and updating the benchmark targets with the respective ensemble averages from the MPI-ESM1.2-LR model. Using the new targets, we show that linear pattern scaling continues to be more accurate on temperature, but can be outperformed by a deep learning-based technique for emulating precipitation. We publish our code and data at github.com/blutjens/climate-emulator.
Run to run variability in parallel programs caused by floating-point non-associativity has been known to significantly affect reproducibility in iterative algorithms, due to accumulating errors. Non-reproducibility can critically affect the efficiency and effectiveness of correctness testing for stochastic programs. Recently, the sensitivity of deep learning training and inference pipelines to floating-point non-associativity has been found to sometimes be extreme. It can prevent certification for commercial applications, accurate assessment of robustness and sensitivity, and bug detection. New approaches in scientific computing applications have coupled deep learning models with high-performance computing, leading to an aggravation of debugging and testing challenges. Here we perform an investigation of the statistical properties of floating-point non-associativity within modern parallel programming models, and analyze performance and productivity impacts of replacing atomic operations with deterministic alternatives on GPUs. We examine the recently-added deterministic options in PyTorch within the context of GPU deployment for deep learning, uncovering and quantifying the impacts of input parameters triggering run to run variability and reporting on the reliability and completeness of the documentation. Finally, we evaluate the strategy of exploiting automatic determinism that could be provided by deterministic hardware, using the Groq accelerator for inference portions of the deep learning pipeline. We demonstrate the benefits that a hardware-based strategy can provide within reproducibility and correctness efforts.
Visual analytics is essential for studying large time series due to its ability to reveal trends, anomalies, and insights. DeepVATS is a tool that merges Deep Learning (Deep) with Visual Analytics (VA) for the analysis of large time series data (TS). It has three interconnected modules. The Deep Learning module, developed in R, manages the load of datasets and Deep Learning models from and to the Storage module. This module also supports models training and the acquisition of the embeddings from the latent space of the trained model. The Storage module operates using the Weights and Biases system. Subsequently, these embeddings can be analyzed in the Visual Analytics module. This module, based on an R Shiny application, allows the adjustment of the parameters related to the projection and clustering of the embeddings space. Once these parameters are set, interactive plots representing both the embeddings, and the time series are shown. This paper introduces the tool and examines its scalability through log analytics. The execution time evolution is examined while the length of the time series is varied. This is achieved by resampling a large data series into smaller subsets and logging the main execution and rendering times for later analysis of scalability.
Due to domain shift, deep learning image classifiers perform poorly when applied to a domain different from the training one. For instance, a classifier trained on chest X-ray (CXR) images from one hospital may not generalize to images from another hospital due to variations in scanner settings or patient characteristics. In this paper, we introduce our CROCODILE framework, showing how tools from causality can foster a model's robustness to domain shift via feature disentanglement, contrastive learning losses, and the injection of prior knowledge. This way, the model relies less on spurious correlations, learns the mechanism bringing from images to prediction better, and outperforms baselines on out-of-distribution (OOD) data. We apply our method to multi-label lung disease classification from CXRs, utilizing over 750000 images from four datasets. Our bias-mitigation method improves domain generalization and fairness, broadening the applicability and reliability of deep learning models for a safer medical image analysis. Find our code at: https://github.com/gianlucarloni/crocodile.
Ultrasound imaging is challenging to interpret due to non-uniform intensities, low contrast, and inherent artifacts, necessitating extensive training for non-specialists. Advanced representation with clear tissue structure separation could greatly assist clinicians in mapping underlying anatomy and distinguishing between tissue layers. Decomposing an image into semantically meaningful segments is mainly achieved using supervised segmentation algorithms. Unsupervised methods are beneficial, as acquiring large labeled datasets is difficult and costly, but despite their advantages, they still need to be explored in ultrasound. This paper proposes a novel unsupervised deep learning strategy tailored to ultrasound to obtain easily interpretable tissue separations. We integrate key concepts from unsupervised deep spectral methods, which combine spectral graph theory with deep learning methods. We utilize self-supervised transformer features for spectral clustering to generate meaningful segments based on ultrasound-specific metrics and shape and positional priors, ensuring semantic consistency across the dataset. We evaluate our unsupervised deep learning strategy on three ultrasound datasets, showcasing qualitative results across anatomical contexts without label requirements. We also conduct a comparative analysis against other clustering algorithms to demonstrate superior segmentation performance, boundary preservation, and label consistency.
The added value of machine learning for weather and climate applications is measurable through performance metrics, but explaining it remains challenging, particularly for large deep learning models. Inspired by climate model hierarchies, we propose that a full hierarchy of Pareto-optimal models, defined within an appropriately determined error-complexity plane, can guide model development and help understand the models' added value. We demonstrate the use of Pareto fronts in atmospheric physics through three sample applications, with hierarchies ranging from semi-empirical models with minimal parameters to deep learning algorithms. First, in cloud cover parameterization, we find that neural networks identify nonlinear relationships between cloud cover and its thermodynamic environment, and assimilate previously neglected features such as vertical gradients in relative humidity that improve the representation of low cloud cover. This added value is condensed into a ten-parameter equation that rivals deep learning models. Second, we establish a machine learning model hierarchy for emulating shortwave radiative transfer, distilling the importance of bidirectional vertical connectivity for accurately representing absorption and scattering, especially for multiple cloud layers. Third, we emphasize the importance of convective organization information when modeling the relationship between tropical precipitation and its surrounding environment. We discuss the added value of temporal memory when high-resolution spatial information is unavailable, with implications for precipitation parameterization. Therefore, by comparing data-driven models directly with existing schemes using Pareto optimality, we promote process understanding by hierarchically unveiling system complexity, with the hope of improving the trustworthiness of machine learning models in atmospheric applications.