Marco Baity-Jesi

Chaopeng Shen, Alison P. Appling, Pierre Gentine et al.

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme -- differentiable modeling -- is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). "Differentiable" refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages.

Emanuele Francazi, Marco Baity-Jesi, Aurelien Lucchi

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalance such as oversampling.

Emanuele Francazi, Aurelien Lucchi, Marco Baity-Jesi

Understanding and controlling biasing effects in neural networks is crucial for ensuring accurate and fair model performance. In the context of classification problems, we provide a theoretical analysis demonstrating that the structure of a deep neural network (DNN) can condition the model to assign all predictions to the same class, even before the beginning of training, and in the absence of explicit biases. We prove that, besides dataset properties, the presence of this phenomenon, which we call \textit{Initial Guessing Bias} (IGB), is influenced by model choices including dataset preprocessing methods, and architectural decisions, such as activation functions, max-pooling layers, and network depth. Our analysis of IGB provides information for architecture selection and model initialization. We also highlight theoretical consequences, such as the breakdown of node-permutation symmetry, the violation of self-averaging and the non-trivial effects that depth has on the phenomenon.

Emanuele Francazi, Francesco Pinto, Aurelien Lucchi et al.

Normalization layers were introduced to stabilize and accelerate training, yet their influence is critical already at initialization, where they shape signal propagation and output statistics before parameters adapt to data. In practice, both which normalization to use and where to place it are often chosen heuristically, despite the fact that these decisions can qualitatively alter a model's behavior. We provide a theoretical characterization of how normalization choice and placement (Pre-Norm vs. Post-Norm) determine the distribution of class predictions at initialization, ranging from unbiased (Neutral) to highly concentrated (Prejudiced) regimes. We show that these architectural decisions induce systematic shifts in the initial prediction regime, thereby modulating subsequent learning dynamics. By linking normalization design directly to prediction statistics at initialization, our results offer principled guidance for more controlled and interpretable network design, including clarifying how widely used choices such as BatchNorm vs. LayerNorm and Pre-Norm vs. Post-Norm shape behavior from the outset of training.

Alberto Bassi, Marco Baity-Jesi, Aurelien Lucchi et al.

Understanding the statistical properties of deep neural networks (DNNs) at initialization is crucial for elucidating both their trainability and the intrinsic architectural biases they encode prior to data exposure. Mean-field (MF) analyses have demonstrated that the parameter distribution in randomly initialized networks dictates whether gradients vanish or explode. Recent work has shown that untrained DNNs exhibit an initial-guessing bias (IGB), in which large regions of the input space are assigned to a single class. In this work, we provide a theoretical proof linking IGB to MF analyses, establishing that a network predisposition toward specific classes is intrinsically tied to the conditions for efficient learning. This connection leads to a counterintuitive conclusion: the initialization that optimizes trainability is systematically biased rather than neutral. We validate our theory through experiments across multiple architectures and datasets.

Cheng Chen, Sreenath Kyathanahally, Marta Reyes et al.

Modern plankton high-throughput monitoring relies on deep learning classifiers for species recognition in water ecosystems. Despite satisfactory nominal performances, a significant challenge arises from Dataset Shift, which causes performances to drop during deployment. In our study, we integrate the ZooLake dataset with manually-annotated images from 10 independent days of deployment, serving as test cells to benchmark Out-Of-Dataset (OOD) performances. Our analysis reveals instances where classifiers, initially performing well in In-Dataset conditions, encounter notable failures in practical scenarios. For example, a MobileNet with a 92% nominal test accuracy shows a 77% OOD accuracy. We systematically investigate conditions leading to OOD performance drops and propose a preemptive assessment method to identify potential pitfalls when classifying new data, and pinpoint features in OOD images that adversely impact classification. We present a three-step pipeline: (i) identifying OOD degradation compared to nominal test performance, (ii) conducting a diagnostic analysis of degradation causes, and (iii) providing solutions. We find that ensembles of BEiT vision transformers, with targeted augmentations addressing OOD robustness, geometric ensembling, and rotation-based test-time augmentation, constitute the most robust model, which we call BEsT model. It achieves an 83% OOD accuracy, with errors concentrated on container classes. Moreover, it exhibits lower sensitivity to dataset shift, and reproduces well the plankton abundances. Our proposed pipeline is applicable to generic plankton classifiers, contingent on the availability of suitable test cells. By identifying critical shortcomings and offering practical procedures to fortify models against dataset shift, our study contributes to the development of more reliable plankton classification technologies.

Jimeng Wu, Simone D'Ambrosi, Lorenz Ammann et al.

We applied machine learning methods to predict chemical hazards focusing on fish acute toxicity across taxa. We analyzed the relevance of taxonomy and experimental setup, showing that taking them into account can lead to considerable improvements in the classification performance. We quantified the gain obtained throught the introduction of taxonomic and experimental information, compared to classification based on chemical information alone. We used our approach with standard machine learning models (K-nearest neighbors, random forests and deep neural networks), as well as the recently proposed Read-Across Structure Activity Relationship (RASAR) models, which were very successful in predicting chemical hazards to mammals based on chemical similarity. We were able to obtain accuracies of over 93% on datasets where, due to noise in the data, the maximum achievable accuracy was expected to be below 96%. The best performances were obtained by random forests and RASAR models. We analyzed metrics to compare our results with animal test reproducibility, and despite most of our models "outperform animal test reproducibility" as measured through recently proposed metrics, we showed that the comparison between machine learning performance and animal test reproducibility should be addressed with particular care. While we focused on fish mortality, our approach, provided that the right data is available, is valid for any combination of chemicals, effects and taxa.

Mario Geiger, Stefano Spigler, Stéphane d'Ascoli et al.

Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding under which conditions neural networks do not get stuck in poor minima of the loss, and how the landscape of that loss evolves as depth is increased remains a challenge. Here we predict, and test empirically, an analogy between this landscape and the energy landscape of repulsive ellipses. We argue that in FC networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. In the vicinity of this transition, properties of the curvature of the minima of the loss are critical. This transition shares direct similarities with the jamming transition by which particles form a disordered solid as the density is increased, which also occurs in certain classes of computational optimization and learning problems such as the perceptron. Our analysis gives a simple explanation as to why poor minima of the loss cannot be encountered in the overparametrized regime, and puts forward the surprising result that the ability of fully connected networks to fit random data is independent of their depth. Our observations suggests that this independence also holds for real data. We also study a quantity $Δ$ which characterizes how well ($Δ<0$) or badly ($Δ>0$) a datum is learned. At the critical point it is power-law distributed, $P_+(Δ)\simΔ^θ$ for $Δ>0$ and $P_-(Δ)\sim(-Δ)^{-γ}$ for $Δ<0$, with $θ\approx0.3$ and $γ\approx0.2$. This observation suggests that near the transition the loss landscape has a hierarchical structure and that the learning dynamics is prone to avalanche-like dynamics, with abrupt changes in the set of patterns that are learned.