Pranav Vaidhyanathan

George Whittle, Pranav Vaidhyanathan, Juliusz Ziomek et al.

Wide neural networks in the feature-learning regime drive modern deep learning, and yet they remain far less studied than their kernel-regime counterparts. We consider a critical yet under-explored difference between these two regimes: the regulariser and prior implied by gradient flow training. This canonical regularisation property is well-studied in kernel regime networks -- of all the infinite global minima, gradient flow selects exactly the vanishing ridge solution -- and underpins the celebrated NN-GP correspondence, precisely allowing the modelling of noise during training. However, we prove ridge regularisation biases gradient flow in feature-learning regime networks, even in the infinitesimal limit of vanishing regularisation. Over training, ridge distorts the inductive bias of the network, with a particular damage done to pretrained networks where the implicit prior is informative. We resolve this by axiomatising the canonical regulariser as a regime-agnostic function-space energy and lift, which uniquely identifies ridge in the kernel regime, and crucially generalises to the feature-learning regime. By studying the Riemannian geometry of feature-learning networks, we derive geodesic ridge from our framework, generalising ridge to the feature-learning regime. Correspondingly, we prove the canonical function-space prior is a Riemannian Gibbs Process, generalising the more familiar Gaussian Process. As a practical contribution, we propose arc ridge as a minimax-robust, scalable surrogate to geodesic ridge, revealing a deep relationship between early stopping and canonical regularisation across learning regimes. Finally, we demonstrate the consequences of our theory empirically on both image processing and NLP transfer-learning problems.

Lucas Schorling, Pranav Vaidhyanathan, Jonas Schuff et al.

While machine learning holds great promise for quantum technologies, most current methods focus on predicting or controlling a specific quantum system. Meta-learning approaches, however, can adapt to new systems for which little data is available, by leveraging knowledge obtained from previous data associated with similar systems. In this paper, we meta-learn dynamics and characteristics of closed and open two-level systems, as well as the Heisenberg model. Based on experimental data of a Loss-DiVincenzo spin-qubit hosted in a Ge/Si core/shell nanowire for different gate voltage configurations, we predict qubit characteristics i.e. $g$-factor and Rabi frequency using meta-learning. The algorithm we introduce improves upon previous state-of-the-art meta-learning methods for physics-based systems by introducing novel techniques such as adaptive learning rates and a global optimizer for improved robustness and increased computational efficiency. We benchmark our method against other meta-learning methods, a vanilla transformer, and a multilayer perceptron, and demonstrate improved performance.

Pranav Vaidhyanathan, Florian Marquardt, Mark T. Mitchison et al.

Attention-based neural networks such as transformers have revolutionized various fields such as natural language processing, genomics, and vision. Here, we demonstrate the use of transformers for quantum feedback control through a supervised learning approach. In particular, due to the transformer's ability to capture long-range temporal correlations and training efficiency, we show that it can surpass some of the limitations of previous control approaches, e.g.~those based on recurrent neural networks trained using a similar approach or reinforcement learning. We numerically show, for the example of state stabilization of a two-level system, that our bespoke transformer architecture can achieve unit fidelity to a target state in a short time even in the presence of inefficient measurement and Hamiltonian perturbations that were not included in the training set. We also demonstrate that this approach generalizes well to the control of non-Markovian systems. Our approach can be used for quantum error correction, fast control of quantum states in the presence of colored noise, as well as real-time tuning, and characterization of quantum devices.

Pranav Vaidhyanathan, Aristotelis Papatheodorou, Mark T. Mitchison et al.

Scalable and generalizable physics-aware deep learning has long been considered a significant challenge with various applications across diverse domains ranging from robotics to molecular dynamics. Central to almost all physical systems are symplectic forms, the geometric backbone that underpins fundamental invariants like energy and momentum. In this work, we introduce a novel deep learning framework, MetaSym. In particular, MetaSym combines a strong symplectic inductive bias obtained from a symplectic encoder, and an autoregressive decoder with meta-attention. This principled design ensures that core physical invariants remain intact, while allowing flexible, data-efficient adaptation to system heterogeneities. We benchmark MetaSym with highly varied and realistic datasets, such as a high-dimensional spring-mesh system (Otness et al., 2021), an open quantum system with dissipation and measurement backaction, and robotics-inspired quadrotor dynamics. Our results demonstrate superior performance in modeling dynamics under few-shot adaptation, outperforming state-of-the-art baselines that use larger models.

Rahul Marchand, Lucas Schorling, Cornelius Carlsson et al.

Transformer models and end-to-end learning frameworks are rapidly revolutionizing the field of artificial intelligence. In this work, we apply object detection transformers to analyze charge stability diagrams in semiconductor quantum dot arrays, a key task for achieving scalability with spin-based quantum computing. Specifically, our model identifies triple points and their connectivity, which is crucial for virtual gate calibration, charge state initialization, drift correction, and pulse sequencing. We show that it surpasses convolutional neural networks in performance on three different spin qubit architectures, all without the need for retraining. In contrast to existing approaches, our method significantly reduces complexity and runtime, while enhancing generalizability. The results highlight the potential of transformer-based end-to-end learning frameworks as a foundation for a scalable, device- and architecture-agnostic tool for control and tuning of quantum dot devices.

Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares et al.

Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high accuracy. However, in systems with dissipation and holonomic constraints, ubiquitous in legged locomotion and multibody robotics, the canonical symplectic form becomes degenerate, undermining the very invariants that guarantee stability and long-term prediction. In this work, we tackle this foundational limitation by introducing Presymplectification Networks (PSNs), the first framework to learn the symplectification lift via Dirac structures, restoring a non-degenerate symplectic geometry by embedding constrained systems into a higher-dimensional manifold. Our architecture combines a recurrent encoder with a flow-matching objective to learn the augmented phase-space dynamics end-to-end. We then attach a lightweight Symplectic Network (SympNet) to forecast constrained trajectories while preserving energy, momentum, and constraint satisfaction. We demonstrate our method on the dynamics of the ANYmal quadruped robot, a challenging contact-rich, multibody system. To the best of our knowledge, this is the first framework that effectively bridges the gap between constrained, dissipative mechanical systems and symplectic learning, unlocking a whole new class of geometric machine learning models, grounded in first principles yet adaptable from data.

Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares et al.

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous algorithms, including the ubiquitous Adam, operate at the so-called adaptive edge of stability regime during training, leading to rapid oscillations and slowed convergence of loss. However, VRAdam adds a higher order penalty on the learning rate based on the velocity such that the algorithm automatically slows down whenever weight updates become large. In practice, we observe that the effective dynamic learning rate shrinks in high-velocity regimes, and damping oscillations. By combining this velocity-based regularizer for global damping with per-parameter scaling of Adam, we create a powerful hybrid optimizer. For this optimizer, we provide rigorous theoretical analysis of operation at the edge of stability from a physical and control perspective for the momentum. Furthermore, we derive convergence bounds with the rate $\mathcal{O}(\ln(N)/\sqrt{N})$ for a stochastic non convex objective under mild assumptions. We demonstrate that VRAdam exceeds the performance against standard optimizers including AdamW. We benchmark various tasks such as image classification, language modeling, and generative modeling using diverse architectures and training methodologies including Convolutional Neural Networks (CNNs), Transformers, and GFlowNets.