arXiv subjects

Niklas Nolte

Publications and source records attributed to Niklas Nolte.

22 records · Page 2Linked to original sources

arXiv2023

Robust and Provably Monotonic Networks

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep learning models that can also be generalized to other architectures. The method relies on a simple weight normalization scheme during training that ensures the Lipschitz constant of every layer is below an upper limit specified by the analyst. A simple monotonic residual connection can then be used to make the model monotonic in any subset of its inputs, which is useful in scenarios where domain knowledge dictates such dependence. Examples can be found in algorithmic fairness requirements or, as presented here, in the classification of the decays of subatomic particles produced at the CERN Large Hadron Collider. Our normalization is minimally constraining and allows the underlying architecture to maintain higher expressiveness compared to other techniques which aim to either control the Lipschitz constant of the model or ensure its monotonicity. We show how the algorithm was used to train a powerful, robust, and interpretable discriminator for heavy-flavor-quark decays, which has been adopted for use as the primary data-selection algorithm in the LHCb real-time data-processing system in the current LHC data-taking period known as Run 3. In addition, our algorithm has also achieved state-of-the-art performance on benchmarks in medicine, finance, and other applications.

cs.LG↗

arXiv2022

Towards Understanding Grokking: An Effective Theory of Representation Learning

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

cs.LG↗

arXiv2022

Finding NEEMo: Geometric Fitting using Neural Estimation of the Energy Mover's Distance

A novel neural architecture was recently developed that enforces an exact upper bound on the Lipschitz constant of the model by constraining the norm of its weights in a minimal way, resulting in higher expressiveness compared to other techniques. We present a new and interesting direction for this architecture: estimation of the Wasserstein metric (Earth Mover's Distance) in optimal transport by employing the Kantorovich-Rubinstein duality to enable its use in geometric fitting applications. Specifically, we focus on the field of high-energy particle physics, where it has been shown that a metric for the space of particle-collider events can be defined based on the Wasserstein metric, referred to as the Energy Mover's Distance (EMD). This metrization has the potential to revolutionize data-driven collider phenomenology. The work presented here represents a major step towards realizing this goal by providing a differentiable way of directly calculating the EMD. We show how the flexibility that our approach enables can be used to develop novel clustering algorithms.

stat.ML↗

arXiv2021

Evolution of the energy efficiency of LHCb's real-time processing

The upgraded LHCb detector, due to start datataking in 2022, will have to process an average data rate of 4~TB/s in real time. Because LHCb's physics objectives require that the full detector information for every LHC bunch crossing is read out and made available for real-time processing, this bandwidth challenge is equivalent to that of the ATLAS and CMS HL-LHC software read-out, but deliverable five years earlier. Over the past six years, the LHCb collaboration has undertaken a bottom-up rewrite of its software infrastructure, pattern recognition, and selection algorithms to make them better able to efficiently exploit modern highly parallel computing architectures. We review the impact of this reoptimization on the energy efficiency of the real-time processing software and hardware which will be used for the upgrade of the LHCb detector. We also review the impact of the decision to adopt a hybrid computing architecture consisting of GPUs and CPUs for the real-time part of LHCb's future data processing. We discuss the implications of these results on how LHCb's real-time power requirements may evolve in the future, particularly in the context of a planned second upgrade of the detector.

physics.ins-det↗