James Bagrow

Milo Z. Trujillo, Laurent Hébert-Dufresne, James Bagrow

GitHub has become the central online platform for much of open source, hosting most open source code repositories. With this popularity, the public digital traces of GitHub are now a valuable means to study teamwork and collaboration. In many ways, however, GitHub is a convenience sample, and may not be representative of open source development off the platform. Here we develop a novel, extensive sample of public open source project repositories outside of centralized platforms. We characterized these projects along a number of dimensions, and compare to a time-matched sample of corresponding GitHub projects. Our sample projects tend to have more collaborators, are maintained for longer periods, and tend to be more focused on academic and scientific problems.

James Bagrow

Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit pathologically high-curvature oscillations, making them difficult to interpret, and standard regularization penalties do not prevent this. Here we derive a basis-agnostic curvature penalty and show that penalized models can maintain accuracy while achieving substantially smoother activations. Accounting for how function composition shapes curvature, we prove an upper bound on the full model's curvature relative to the curvature penalty, and use this to motivate richer forms of penalties. Scientific machine learning is increasingly bottlenecked by the trade-off between accuracy and interpretability. Results such as ours that improve interpretability without sacrificing accuracy will further strengthen KANs as a practical tool for both prediction and insight.

James Bagrow, Josh Bongard

Efforts to improve Kolmogorov-Arnold networks (KANs) with architectural enhancements have been stymied by the complexity those enhancements bring, undermining the interpretability that makes KANs attractive in the first place. Here we study overprovisioned architectures combined with sparsification to learn compact, interpretable KANs without sacrificing accuracy. Crucially, we focus on differentiable sparsification, turning architecture search into an end-to-end optimization problem. Across function approximation benchmarks, dynamical systems forecasting, and real-world prediction tasks, we demonstrate competitive or superior accuracy while discovering substantially smaller models. Overprovisioning and sparsification are synergistic, with the combination outperforming either alone. The result is a principled path toward models that are both more expressive and more interpretable, addressing a key tension in scientific machine learning.

James Bagrow, Josh Bongard

Kolmogorov-Arnold Networks (KANs) offer a promising path toward interpretable machine learning: their learnable activations can be studied individually, while collectively fitting complex data accurately. In practice, however, trained activations often lack symbolic fidelity, learning pathological decompositions with no meaningful correspondence to interpretable forms. We propose Softly Symbolified Kolmogorov-Arnold Networks (S2KAN), which integrate symbolic primitives directly into training. Each activation draws from a dictionary of symbolic and dense terms, with learnable gates that sparsify the representation. Crucially, this sparsification is differentiable, enabling end-to-end optimization, and is guided by a principled Minimum Description Length objective. When symbolic terms suffice, S2KAN discovers interpretable forms; when they do not, it gracefully degrades to dense splines. We demonstrate competitive or superior accuracy with substantially smaller models across symbolic benchmarks, dynamical systems forecasting, and real-world prediction tasks, and observe evidence of emergent self-sparsification even without regularization pressure.

James Bagrow, Josh Bongard

Kolmogorov-Arnold Networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be difficult to optimize and interpret. Here we introduce multi-exit KANs, where each layer includes its own prediction branch, enabling the network to make accurate predictions at multiple depths simultaneously. This architecture provides deep supervision that improves training while discovering the right level of model complexity for each task. Multi-exit KANs consistently outperform standard, single-exit versions on synthetic functions, dynamical systems, and real-world datasets. Remarkably, the best predictions often come from earlier, simpler exits, revealing that these networks naturally identify smaller, more parsimonious and interpretable models without sacrificing accuracy. To automate this discovery, we develop a differentiable "learning-to-exit" algorithm that balances contributions from exits during training. Our approach offers scientists a practical way to achieve both high performance and interpretability, addressing a fundamental challenge in machine learning for scientific discovery.

Atoosa Parsa, James Bagrow, Corey S. O'Hern et al.

Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design sound-focusing/scrambling devices, acoustic filters, and analog computational units. At high amplitude vibrations or low confinement pressures, the effect of nonlinear particle contacts becomes increasingly noticeable, and the interplay of nonlinearity, disorder, and discreteness in the system gives rise to remarkable properties, particularly useful in designing structures with exotic properties. In this paper, we build upon the data-driven methods in dynamical system analysis and show that the Koopman spectral theory can be applied to granular crystals, enabling their phase space analysis beyond the linearizable regime and without recourse to any approximations considered in the previous works. We show that a deep neural network can map the dynamics to a latent space where the essential nonlinearity of the granular system unfolds into a high-dimensional linear space. As a proof of concept, we use data from numerical simulations of a two-particle system and evaluate the accuracy of the trajectory predictions under various initial conditions. By incorporating data from experimental measurements, our proposed framework can directly capture the underlying dynamics without imposing any assumptions about the physics model. Spectral analysis of the trained surrogate system can help bridge the gap between the simulation results and the physical realization of granular crystals and facilitate the inverse design of materials with desired behaviors.

Abigail Hotaling, James Bagrow

Allocation strategies improve the efficiency of crowdsourcing by decreasing the work needed to complete individual tasks accurately. However, these algorithms introduce bias by preferentially allocating workers onto easy tasks, leading to sets of completed tasks that are no longer representative of all tasks. This bias challenges inference of problem-wide properties such as typical task difficulty or crowd properties such as worker completion times, important information that goes beyond the crowd responses themselves. Here we study inference about problem properties when using an allocation algorithm to improve crowd efficiency. We introduce Decision-Explicit Probability Sampling (DEPS), a novel method to perform inference of problem properties while accounting for the potential bias introduced by an allocation strategy. Experiments on real and synthetic crowdsourcing data show that DEPS outperforms baseline inference methods while still leveraging the efficiency gains of the allocation method. The ability to perform accurate inference of general properties when using non-representative data allows crowdsourcers to extract more knowledge out of a given crowdsourced dataset.