Andreas Bergmeister

Andreas Bergmeister, Manish Krishan Lal, Stefanie Jegelka et al.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

Andreas Bergmeister, Stefanie Jegelka, Nikolas Nüsken et al.

Diffusion and flow-matching models scale because pretraining is supervised regression: a clean sample is noised analytically, and a model regresses against a closed-form target. RL post-training aligns the model with a reward. In image generation, this makes samples compose objects correctly, render text legibly, and match human preferences. Existing methods rely on costly SDE rollouts, reward gradients, or surrogate losses, sacrificing pretraining's regression structure. We show that the structure extends to RL post-training. Under KL-regularized reward maximization, the optimal generative process tilts the clean-endpoint distribution towards samples with higher reward and leaves the noising law unchanged. Combining this with the adjoint-matching optimality condition and a REINFORCE identity, we derive Reinforce Adjoint Matching (RAM): a consistency loss that corrects the pretraining target with the reward. At each step, we draw a clean endpoint from the current model, evaluate its reward, noise it as in pretraining, and regress. No SDE rollouts, backward adjoint sweeps, or reward gradients are required. Like the pretraining objective, RAM is simple and scales. On Stable Diffusion 3.5M, RAM achieves the highest reward on composability, text rendering, and human preference, reaching Flow-GRPO's peak reward in up to $50\times$ fewer training steps.

Andreas Bergmeister, Karolis Martinkus, Nathanaël Perraudin et al.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

Kadek Hendrawan Palgunadi, Andreas Bergmeister, Andrea Bosisio et al.

Accurate prediction and synthesis of seismic waveforms are crucial for seismic-hazard assessment and earthquake-resistant infrastructure design. Existing prediction methods, such as ground-motion models and physics-based wave-field simulations, often fail to capture the full complexity of seismic wavefields, particularly at higher frequencies. This study introduces HighFEM, a novel, computationally efficient, and scalable (i.e., capable of generating many seismograms simultaneously) generative model for high-frequency seismic-waveform generation. Our approach leverages a spectrogram representation of the seismic-waveform data, which is reduced to a lower-dimensional manifold via an autoencoder. A state-of-the-art diffusion model is trained to generate this latent representation conditioned on key input parameters: earthquake magnitude, recording distance, site conditions, hypocenter depth, and azimuthal gap. The model generates waveforms with frequency content up to 50 Hz. Any scalar ground-motion statistic, such as peak ground-motion amplitudes and spectral accelerations, can be readily derived from the synthesized waveforms. We validate our model using commonly employed seismological metrics and performance metrics from image-generation studies. Our results demonstrate that the openly available model can generate realistic high-frequency seismic waveforms across a wide range of input parameters, even in data-sparse regions. For the scalar ground-motion statistics commonly used in seismic-hazard and earthquake-engineering studies, we show that our model accurately reproduces both the median trends of the real data and their variability. To evaluate and compare the growing number of these and similar Generative Waveform Models (GWMs), we argue that they should be openly available and included in community ground-motion-model evaluation efforts.