Francesca Dominici

Claudio Battiloro, Pietro Greiner, Dario Rancati et al.

As learning systems increasingly shape everyday decisions, Algorithmic Collective Action (ACA), i.e., users coordinating changes to shared data to steer model behavior, offers a complement to regulator-side policy and corporate model design. Real-world collective actions have traditionally been decentralized and fragmented into multiple collectives, despite sharing overarching objectives, with each collective differing in size, strategy, and actionable goals. However, most of the ACA literature focuses on single collective settings. To address this, we propose the first comprehensive statistical framework for ACA with multiple collectives acting on the same system. In particular, we focus on collective action in classification, studying how multiple collectives can influence a classifier's behavior. We provide quantitative statistical bounds on the success of the collectives, considering the role and the interplay of the collectives' sizes and the alignment of their goals. We make such bounds computable by each collective with only partial knowledge of other collectives' sizes and strategies. Finally, we numerically illustrate our framework on simulations inspired by interventions for climate adaptation in smart cities, demonstrating the usefulness of our bounds.

Kartik Tandon, Julian Gould, Tanishq Bhatia et al.

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified learning theory for these settings has been lacking. To start addressing this gap, we introduce a novel convolutional learning framework for possibly infinite-dimensional signals supported on a manifold. Namely, we use the connection Laplacian associated with a Hilbert bundle as a convolutional operator, and we derive filters and neural networks, dubbed as \textit{HilbNets}. We make HilbNets and, more generally, the convolution operation, implementable via a two-stage sampling procedure. First, we show that sampling the manifold induces a Hilbert Cellular Sheaf, a generalized graph structure with Hilbert feature spaces and edge-wise coupling rules, and we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin \& Niyogi \cite{BELKIN20081289} convergence result for the graph Laplacian to the manifold Laplacian, a theoretical cornerstone of geometric learning methods. Second, we discretize the signals and prove that the discretized (implementable) HilbNets converge to the underlying continuous architectures and are transferable across different samplings of the same bundle, providing consistency for learning. Finally, we validate our framework on synthetic and real-world tasks. Overall, our results broaden the scope of geometric learning as a whole by lifting classical Laplacian-based frameworks to settings where the signal at each point lives in its own Hilbert space.

Manuel Lecha, Andrea Cavallo, Francesca Dominici et al.

Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these relationships. In this paper, we first introduce a novel notion of higher-order directionality and we then design Directed Simplicial Neural Networks (Dir-SNNs) based on it. Dir-SNNs are message-passing networks operating on directed simplicial complexes able to leverage directed and possibly asymmetric interactions among the simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We theoretically and empirically prove that Dir-SNNs are more expressive than their directed graph counterpart in distinguishing isomorphic directed graphs. Experiments on a synthetic source localization task demonstrate that Dir-SNNs outperform undirected SNNs when the underlying complex is directed, and perform comparably when the underlying complex is undirected.

Claudio Battiloro, Ege Karaismailoğlu, Mauricio Tec et al.

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue. TDL enables the principled modeling of arbitrary multi-way, hierarchical higher-order interactions by operating on combinatorial topological spaces, such as simplicial or cell complexes, instead of graphs. However, little is known about how to leverage geometric features such as positions and velocities for TDL. This paper introduces E(n)-Equivariant Topological Neural Networks (ETNNs), which are E(n)-equivariant message-passing networks operating on combinatorial complexes, formal objects unifying graphs, hypergraphs, simplicial, path, and cell complexes. ETNNs incorporate geometric node features while respecting rotation, reflection, and translation equivariance. Moreover, being TDL models, ETNNs are natively ready for settings with heterogeneous interactions. We provide a theoretical analysis to show the improved expressiveness of ETNNs over architectures for geometric graphs. We also show how E(n)-equivariant variants of TDL models can be directly derived from our framework. The broad applicability of ETNNs is demonstrated through two tasks of vastly different scales: i) molecular property prediction on the QM9 benchmark and ii) land-use regression for hyper-local estimation of air pollution with multi-resolution irregular geospatial data. The results indicate that ETNNs are an effective tool for learning from diverse types of richly structured data, as they match or surpass SotA equivariant TDL models with a significantly smaller computational burden, thus highlighting the benefits of a principled geometric inductive bias. Our implementation of ETNNs can be found at https://github.com/NSAPH-Projects/topological-equivariant-networks.

Manuel Lecha, Andrea Cavallo, Francesca Dominici et al.

Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces. However, existing TDL models are restricted to undirected settings and fail to capture the higher-order directed patterns prevalent in many complex systems, e.g., brain networks, where such interactions are both abundant and functionally significant. To fill this gap, we introduce Semi-Simplicial Neural Networks (SSNs), a principled class of TDL models that operate on semi-simplicial sets -- combinatorial structures that encode directed higher-order motifs and their directional relationships. To enhance scalability, we propose Routing-SSNs, which dynamically select the most informative relations in a learnable manner. We prove that SSNs are strictly more expressive than standard graph and TDL models. We then introduce a new principled framework for brain dynamics representation learning, grounded in the ability of SSNs to provably recover topological descriptors shown to successfully characterize brain activity. Empirically, SSNs achieve state-of-the-art performance on brain dynamics classification tasks, outperforming the second-best model by up to 27%, and message passing GNNs by up to 50% in accuracy. Our results highlight the potential of principled topological models for learning from structured brain data, establishing a unique real-world case study for TDL. We also test SSNs on standard node classification and edge regression tasks, showing competitive performance. We will make the code and data publicly available.

Julian Kleutgens, Claudio Battiloro, Lingkai Kong et al.

Discrete diffusion models (DMs) have achieved strong performance in language and other discrete domains, offering a compelling alternative to autoregressive modeling. Yet this performance typically depends on large training datasets, challenging the performance of DMs in small-data regimes -- common under real-world constraints. Aimed at this challenge, recent work in continuous DMs suggests that transfer learning via classifier ratio-based guidance can adapt a pretrained DM to a related target distribution, often outperforming alternatives such as full-weight fine-tuning on the target data. By contrast, transfer learning for discrete DMs remains unexplored. We address this gap by exploring practical analogues of ratio-based transfer learning for discrete DMs. Our theoretical analysis shows that a direct extension of existing ratio-based guidance is computationally prohibitive, scaling with vocabulary size. To overcome this limitation, we introduce a scheduling mechanism that yields a practical algorithm, Guided Transfer Learning for discrete diffusion models (GTL). GTL enables sampling from a target distribution without modifying the pretrained denoiser and reduces the cost to linear scaling in vocabulary size, which in turn supports longer sequence generation. We evaluate GTL on sequential data, including synthetic Markov chains and language modeling tasks, and provide a detailed empirical analysis of its behavior. The results highlight a clear trade-off: when target datasets are large, weight fine-tuning is often preferable, whereas GTL becomes increasingly effective as target data shrinks. Finally, we experimentally demonstrate a key failure mode of GTL: when the source and target distributions overlap poorly, the ratio-based classifier required for guidance becomes unreliable, limiting transfer performance.

Ellen M. Considine, Rachel C. Nethery, Gregory A. Wellenius et al.

A key strategy in societal adaptation to climate change is using alert systems to prompt preventative action and reduce the adverse health impacts of extreme heat events. This paper implements and evaluates reinforcement learning (RL) as a tool to optimize the effectiveness of such systems. Our contributions are threefold. First, we introduce a new publicly available RL environment enabling the evaluation of the effectiveness of heat alert policies to reduce heat-related hospitalizations. The rewards model is trained from a comprehensive dataset of historical weather, Medicare health records, and socioeconomic/geographic features. We use scalable Bayesian techniques tailored to the low-signal effects and spatial heterogeneity present in the data. The transition model uses real historical weather patterns enriched by a data augmentation mechanism based on climate region similarity. Second, we use this environment to evaluate standard RL algorithms in the context of heat alert issuance. Our analysis shows that policy constraints are needed to improve RL's initially poor performance. Third, a post-hoc contrastive analysis provides insight into scenarios where our modified heat alert-RL policies yield significant gains/losses over the current National Weather Service alert policy in the United States.