RMM and DRMM enable efficient inference via message passing (e.g., using the max-sum/product

Directed acyclic graphs (DAGs) are central to science and engineering applications including causal inference, scheduling, and neural architecture search. In this work, we introduce the DAG Convolutional Network (DCN), a novel graph neural network (GNN) architecture designed specifically for convolutional learning from signals supported on DAGs. The DCN leverages causal graph filters to learn nodal representations that account for the partial ordering inherent to DAGs, a strong inductive bias does not present in conventional GNNs. Unlike prior art in machine learning over DAGs, DCN builds on formal convolutional operations that admit spectral-domain representations. We further propose the Parallel DCN (PDCN), a model that feeds input DAG signals to a parallel bank of causal graph-shift operators and processes these DAG-aware features using a shared multilayer perceptron. This way, PDCN decouples model complexity from graph size while maintaining satisfactory predictive performance. The architectures' permutation equivariance and expressive power properties are also established. Comprehensive numerical tests across several tasks, datasets, and experimental conditions demonstrate that (P)DCN compares favorably with state-of-the-art baselines in terms of accuracy, robustness, and computational efficiency. These results position (P)DCN as a viable framework for deep learning from DAG-structured data that is designed from first (graph) signal processing principles.

Class-incremental learning (CIL) for time series data faces critical challenges in balancing stability against catastrophic forgetting and plasticity for new knowledge acquisition, particularly under real-world constraints where historical data access is restricted. While pre-trained models (PTMs) have shown promise in CIL for vision and NLP domains, their potential in time series class-incremental learning (TSCIL) remains underexplored due to the scarcity of large-scale time series pre-trained models. Prompted by the recent emergence of large-scale pre-trained models (PTMs) for time series data, we present the first exploration of PTM-based Time Series Class-Incremental Learning (TSCIL). Our approach leverages frozen PTM backbones coupled with incrementally tuning the shared adapter, preserving generalization capabilities while mitigating feature drift through knowledge distillation. Furthermore, we introduce a Feature Drift Compensation Network (DCN), designed with a novel two-stage training strategy to precisely model feature space transformations across incremental tasks. This allows for accurate projection of old class prototypes into the new feature space. By employing DCN-corrected prototypes, we effectively enhance the unified classifier retraining, mitigating model feature drift and alleviating catastrophic forgetting. Extensive experiments on five real-world datasets demonstrate state-of-the-art performance, with our method yielding final accuracy gains of 1.4%-6.1% across all datasets compared to existing PTM-based approaches. Our work establishes a new paradigm for TSCIL, providing insights into stability-plasticity optimization for continual learning systems.

This work investigates an important phenomenon in centroid-based deep clustering (DC) algorithms: Performance quickly saturates after a period of rapid early gains. Practitioners commonly address early saturation with periodic reclustering, which we demonstrate to be insufficient to address performance plateaus. We call this phenomenon the "reclustering barrier" and empirically show when the reclustering barrier occurs, what its underlying mechanisms are, and how it is possible to Break the Reclustering Barrier with our algorithm BRB. BRB avoids early over-commitment to initial clusterings and enables continuous adaptation to reinitialized clustering targets while remaining conceptually simple. Applying our algorithm to widely-used centroid-based DC algorithms, we show that (1) BRB consistently improves performance across a wide range of clustering benchmarks, (2) BRB enables training from scratch, and (3) BRB performs competitively against state-of-the-art DC algorithms when combined with a contrastive loss. We release our code and pre-trained models at https://github.com/Probabilistic-and-Interactive-ML/breaking-the-reclustering-barrier .

We develop a novel convolutional architecture tailored for learning from data defined over directed acyclic graphs (DAGs). DAGs can be used to model causal relationships among variables, but their nilpotent adjacency matrices pose unique challenges towards developing DAG signal processing and machine learning tools. To address this limitation, we harness recent advances offering alternative definitions of causal shifts and convolutions for signals on DAGs. We develop a novel convolutional graph neural network that integrates learnable DAG filters to account for the partial ordering induced by the graph topology, thus providing valuable inductive bias to learn effective representations of DAG-supported data. We discuss the salient advantages and potential limitations of the proposed DAG convolutional network (DCN) and evaluate its performance on two learning tasks using synthetic data: network diffusion estimation and source identification. DCN compares favorably relative to several baselines, showcasing its promising potential.

We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate that max-sum inference in the DRMM yields an algorithm that exactly reproduces the operations in deep convolutional neural networks (DCNs), providing a first principles derivation. Our framework provides new insights into the successes and shortcomings of DCNs as well as a principled route to their improvement. DRMM training via the Expectation-Maximization (EM) algorithm is a powerful alternative to DCN back-propagation, and initial training results are promising. Classification based on the DRMM and other variants outperforms DCNs in supervised digit classification, training 2-3 faster while achieving similar accuracy. Moreover, the DRMM is applicable to semi-supervised and unsupervised learning tasks, achieving results that are state-of-the-art in several categories on the MNIST benchmark and comparable to state of the art on the CIFAR10 benchmark.

This paper investigates the initialization bias of the Fourier neural operator (FNO). A mean-field theory for FNO is established, analyzing the behavior of the random FNO from an "edge of chaos" perspective. We uncover that the forward and backward propagation behaviors exhibit characteristics unique to FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Building upon this observation, we also propose a FNO version of the He initialization scheme to mitigate the negative initialization bias leading to training instability. Experimental results demonstrate the effectiveness of our initialization scheme, enabling stable training of a 32-layer FNO without the need for additional techniques or significant performance degradation. The recent surge in interest towards solving partial differential equations (PDEs) has led to the use of neural network (NN)-based surrogate models.

We are not only observers but also actors of reality. Our capability to intervene and alter the course of some events in the space and time surrounding us is an essential component of how we build our model of the world. In this doctoral thesis we introduce a generic a-priori assessment of each possible intervention, in order to select the most cost-effective interventions only, and avoid unnecessary systematic experimentation on the real world. Based on this a-priori assessment, we propose an active learning algorithm that identifies the causal relations in any given causal model, using a least cost sequence of interventions. There are several novel aspects introduced by our algorithm. It is, in most case scenarios, able to discard many causal model candidates using relatively inexpensive interventions that only test one value of the intervened variables. Also, the number of interventions performed by the algorithm can be bounded by the number of causal model candidates. Hence, fewer initial candidates (or equivalently, more prior knowledge) lead to fewer interventions for causal discovery. Causality is intimately related to time, as causes appear to precede their effects. Cyclical causal processes are a very interesting case of causality in relation to time. In this doctoral thesis we introduce a formal analysis of time cyclical causal settings by defining a causal analog to the purely observational Dynamic Bayesian Networks, and provide a sound and complete algorithm for the identification of causal effects in the cyclic setting. We introduce the existence of two types of hidden confounder variables in this framework, which affect in substantially different ways the identification procedures, a distinction with no analog in either Dynamic Bayesian Networks or standard causal graphs.