arXiv subjects

Zachary Weller-Davies

Publications and source records attributed to Zachary Weller-Davies.

At least 19 recordsLinked to original sources

arXiv2026

E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPU

We present e3j, a fast Euclid-equivariance backend for geometric deep learning applications with JAX bindings for GPU and TPU. Leveraging both optimized CUDA and Pallas kernels and algorithmic improvements, the library achieves state-of-the-art throughput and runtime on both forward and backward paths. On a machine learning interatomic potential (MLIP) use case, it outperforms established backends, measuring up to 34% speed-up over cuEquivariance on water box NPT simulation using MACE, while remaining fully open source. E3j achieves over 80% efficiency over the H100 maximum memory bandwidth on tensor product operations, and in many cases more than doubles throughput of message passing convolutions forward compared to previously available backends. In addition, with the release of dedicated Pallas TPU kernel, e3j opens the possibility of large scale equivariant deep learning workloads on TPU architectures, which has so far been difficult to achieve. Our benchmarks show that e3j also achieves over 80% of a TPUv6e memory bandwidth, up to one order of magnitude more than e3nn-jax. The library is available on GitHub, PyPI and is released under an open source Apache 2.0 license.

cs.LG↗

arXiv2026

Integral Formulas for Vector Signal Tensor Products

We derive integral formulas that simplify the Vector Signal Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to anti-symmetric couplings. In particular, we obtain explicit closed-form expressions for the anti-symmetric analogues of the Gaunt coefficients. This enables us to simulate the Clebsch-Gordan tensor product using a single Vector Signal Tensor Product, yielding up to a $9\times$ reduction in the required tensor product evaluations. Our results enable efficient and practical implementations of the Vector Signal Tensor Product, paving the way for applications of this generalization of Gaunt Tensor Products in $\mathrm{SO}(3)$-equivariant neural networks. Moreover, we discuss how the Gaunt and the Vector Signal Tensor Products allow to control the expressivity-runtime tradeoff associated with the usual Clebsch-Gordan Tensor Products. Finally, we investigate low rank decompositions of the normalizations of the considered tensor products in view of their use in equivariant neural networks.

cs.LG↗

arXiv2026

Machine Learning Interatomic Potentials: Advancing Open-Source Software for Efficient and Scalable Molecular Simulation

Machine learning interatomic potentials (MLIPs) enable atomistic simulations with near ab initio accuracy at significantly reduced computational cost, but their broader adoption is often limited by fragmented tooling, limited scalability, and inflexible software design. We present mlip v2, a new generation of the mlip library that advances efficient and scalable molecular simulation through a unified and extensible framework. The new release features a targeted API redesign with improved modularity and control, enabling flexible customization of training, data processing, and simulation workflows. It further integrates a new high-performance backend for equivariant operations, e3j, significantly accelerating model inference and simulations. In addition, the framework introduces a range of entirely new capabilities, including the eSEN architecture with a Mixture-of-Experts formulation for scalable training on large and diverse datasets, improved handling of electrostatics through more physically grounded charge modeling and long-range interaction treatment, and advanced simulation features such as NPT ensembles and nudged elastic band methods. Together, these extensions significantly broaden the scope of MLIP applications, enabling efficient modeling of complex, reactive, and out-of-equilibrium systems, and bridging the gap between ML research and practical molecular simulation applications. The library is available on GitHub and on PyPI under the Apache license 2.0.

physics.chem-ph↗

arXiv2026

Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs

Training machine learning interatomic potentials (MLIPs) for reactive chemistry is often bottlenecked by the high cost of quantum chemical labels and the scarcity of transition state configurations in candidate pools. Active learning (AL) can mitigate these costs, but its effectiveness hinges on the acquisition rule. We investigate whether the latent space of a pretrained MLIP already contains the information necessary for effective acquisition, eliminating the need for auxiliary uncertainty heads, Bayesian training and fine-tuning, or committee ensembles. We introduce two acquisition signals derived directly from a pretrained MACE potential: a finite-width neural tangent kernel (NTK) and an activation kernel built from hidden latent space features. On reactive-chemistry benchmarks, both kernels consistently outperform fixed-descriptor baselines, committee disagreement, and random acquisition, reducing the data required to reach performance targets by an average of 38% for energy error and 28% for force error. We further show that the pretrained model induces similarity spaces that preserve chemically meaningful structure and provide more reliable residual uncertainty estimates than randomly initialised or fixed-descriptor-based kernels. Our results suggest that pretraining aligns latent-space geometry with model error, yielding a practical and sufficient acquisition signal for reactive MLIP fine-tuning.

cs.LG↗

arXiv2026

Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

Active learning for machine-learning interatomic potentials (MLIPs) must address several challenges to be practical: scaling to large candidate pools, leveraging energy-force supervision, and maintaining robustness when candidate pools are biased relative to the target distribution. In this work, we jointly address these challenges. We first introduce a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting. By avoiding materialisation of the candidate and train set kernels, this approach enables screening of ~200k structures within hours and applies broadly to acquisition strategies that score candidates based on molecular similarity metrics. We then extend the Neural Tangent Kernel (NTK) to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. We demonstrate the effectiveness of the joint energy-force NTK on the OC20 dataset, where force-aware acquisition is crucial: it achieves the lowest energy and force MAE and RMSE across all metrics and distribution splits. Across T1x, PMechDB, and RGD benchmarks, our force NTK methods remain competitive with established baselines while being significantly more efficient than committee-based approaches. Under a controlled candidate-pool shift case study on T1x, acquisition based on pretrained MLIP embeddings and NTKs remains robust, whereas committee-based methods exhibit higher variance. Overall, these results show that a single pretrained MLIP can enable scalable, force-aware, and distribution-robust active learning for foundation-model fine-tuning.

cs.LG↗

arXiv2025

A one-world interpretation of quantum mechanics

The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.

quant-ph↗

arXiv2025

Covariant path integrals for quantum fields back-reacting on classical space-time

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master equation methods. These path integrals allow one to readily impose space-time symmetries, including Lorentz invariance or diffeomorphism invariance. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the stochastic path integral of classical stochastic dynamics while respecting symmetry principles. We introduce a path integral formulation of general relativity where the space-time metric is treated classically. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics. The theory is manifestly covariant, and may be inequivalent to the theory derived using master-equation methods. We prove that entanglement cannot be created via the classical field, reinforcing proposals to test the quantum nature of gravity via entanglement generation.

gr-qc↗

arXiv2025

Path integrals for classical-quantum dynamics

Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations, we derive a general path integral representation for such dynamics in terms of a classical-quantum action, which includes the necessary and sufficient conditions for complete positivity and trace preservation. The path integral we study is a generalization of the Feynman path integral for quantum systems, and the stochastic path integral used to study classical stochastic processes, allowing for interaction between the classical and quantum systems. When the classical-quantum Hamiltonian is at most quadratic in the momenta we are able to derive a configuration space path integral, providing a map between master equations and covariant classical-quantum path integrals.

quant-ph↗

arXiv2024

A healthier semi-classical dynamics

We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider an unravelling approach, describing the system in terms of a classical-quantum trajectory. We derive the general form of the dynamics under the assumptions that the classical trajectories are continuous and the evolution is autonomous, and the requirement that the dynamics is linear and completely positive in the combined classical-quantum state. This requirement is necessary in order to consistently describe probabilities, and forces the dynamics to be stochastic when the back-reaction is non-zero. The resulting equations of motion are natural generalisations of the standard semi-classical equations of motion, but since the resulting dynamics is linear in the combined classical-quantum state, it does not lead to the pathologies which usually follow from evolution laws based on expectation values. In particular, the evolution laws we present account for correlations between the classical and quantum system, which resolves issues associated with other semi-classical approaches. In addition, despite a breakdown of predictability in the classical degrees of freedom, the quantum state evolves deterministically conditioned on the classical trajectory, provided a trade-off between decoherence and diffusion is saturated. As a result, the quantum state remains pure when conditioned on the classical trajectory. To illustrate these points, we numerically simulate a number of semi-classical toy models, including one of vacuum fluctuations as a source driving the expansion of the universe. Finally, we discuss the application of these results to semi-classical gravity, and the black-hole information problem.

quant-ph↗

arXiv2024

Quantum gravity with dynamical wave-function collapse via a classical scalar field

In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement outcomes. It has recently been shown that covariant classical-quantum dynamics can be constructed using path integral methods, with the dynamics encoded in a combined action for the classical and quantum variables. This work introduces a classical-quantum model whereby quantum gravity interacts with a classical scalar field. The scalar field can be viewed as fundamentally classical or effectively classical due to the decoherence of a quantum gravity theory. The dynamics act to collapse quantum spacetimes according to their Ricci scalar, with corresponding diffusion in the scalar field due to the quantum back-reaction. In the classical limit, the diffusion in the scalar field manifests itself via stochastic fluctuations in the Newtonian potential. Because we couple a classical scalar field to perturbative quantum gravity, we find the theory is not renormalizable but is instead to be viewed as an effective field theory. However, it is an effective field theory that does not necessarily require a measurement postulate. More generally, our work shows it is possible to integrate collapse dynamics with high-energy physics and covariance.

gr-qc↗

arXiv2024

Diffeomorphism invariant classical-quantum path integrals for Nordstrom gravity

When classical degrees of freedom and quantum degrees of freedom are consistently coupled, the former diffuse, while the latter undergo decoherence. Here, we construct a theory of quantum matter fields and Nordstrom gravity in which the space-time metric is treated classically. The dynamics is constructed via the classical-quantum path integral and is completely positive, trace preserving (CPTP), and respects the classical-quantum split. The weak field limit of the model matches the Newtonian limit of the full covariant path integral but it is easier to show that the theory is both diffeomorphism invariant, CPTP, and has the appropriate classical limit.

gr-qc↗

arXiv2023

Gravitation from optimized computation: Einstein and beyond

A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the linearized level, in holographic theories with Einstein gravity duals, assuming the so-called 'Complexity-Volume' (CV) proposal. We expand on this proof in two significant directions. First, we derive higher-derivative gravitational equations by including appropriate corrections to the CV dictionary. Second, we show semi-classical equations arise by considering the leading bulk quantum corrections to CV. Our proof is valid for two-dimensional dilaton gravities, where the problem of semi-classical backreaction can be solved exactly. However, we argue the principle should hold more generally, leading us to a concrete proposal for bulk complexity of perturbative excited states in arbitrary dimensions. Our results demonstrate the robustness of spacetime complexity as a guiding principle to understand gravity in terms of quantum computation.

hep-th↗

arXiv2023

The weak field limit of quantum matter back-reacting on classical spacetime

Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic.

gr-qc↗

arXiv2023

Objective trajectories in hybrid classical-quantum dynamics

Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the back-reaction of quantum fields on space-time which does not suffer from the pathologies of the semi-classical equations. Here we introduce several toy models in which to study hybrid classical-quantum evolution, including a qubit coupled to a particle in a potential, and a quantum harmonic oscillator coupled to a classical one. We present an unravelling approach to calculate the dynamics, and provide code to numerically simulate it. Unlike the purely quantum case, the trajectories (or histories) of this unravelling can be unique, conditioned on the classical degrees of freedom for discrete realisations of the dynamics, when different jumps in the classical degrees of freedom are accompanied by the action of unique operators on the quantum system. As a result, the ``measurement postulate'' of quantum theory is not needed; quantum systems become classical because they interact with a fundamentally classical field.

quant-ph↗

arXiv2022

Computing spacetime

Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein's equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation.

hep-th↗

arXiv2022

Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity

We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.

quant-ph↗

arXiv2022

The two classes of hybrid classical-quantum dynamics

Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law must be a completely positive and norm preserving map. We prove that if the dynamics is memoryless, there are two classes of these dynamics, one which features finite sized jumps in the classical phase space and one which is continuous. We find the most general form of each class of classical-quantum master equation. This is achieved by applying the complete positivity conditions using a generalized Cauchy-Schwartz inequality applicable to classical-quantum systems. The key technical result is a generalisation of the Pawula theorem.

quant-ph↗

arXiv2022

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Holographic entanglement entropy was recently recast in terms of Riemannian flows or 'bit threads'. We consider the Lorentzian analog to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or 'gatelines'. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific 'canonical' thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of 'spacetime complexity'. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [arXiv:2105.12735], including several new results.

hep-th↗