arXiv subjects

Tom Deakin

Publications and source records attributed to Tom Deakin.

7 recordsLinked to original sources

arXiv2025

An Asynchronous Many-Task Algorithm for Unstructured $S_{N}$ Transport on Shared Memory Systems

Discrete ordinates $S_N$ transport solvers on unstructured meshes pose a challenge to scale due to complex data dependencies, memory access patterns and a high-dimensional domain. In this paper, we review the performance bottlenecks within the shared memory parallelization scheme of an existing transport solver on modern many-core architectures with high core counts. With this analysis, we then survey the performance of this solver across a variety of compute hardware. We then present a new Asynchronous Many-Task (AMT) algorithm for shared memory parallelism, present results showing an increase in computational performance over the existing method, and evaluate why performance is improved.

cs.DC↗

arXiv2025

Weight-Space Linear Recurrent Neural Networks

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 4 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

cs.LG↗

arXiv2025

Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts

As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on $K$-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

cs.LG↗

arXiv2024

Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulation

Contextual Self-Modulation (CSM) (Nzoyem et al., 2025) is a potent regularization mechanism for Neural Context Flows (NCFs) which demonstrates powerful meta-learning on physical systems. However, CSM has limitations in its applicability across different modalities and in high-data regimes. In this work, we introduce two extensions: $i$CSM which expands CSM to infinite-dimensional variations by embedding the contexts into a function space, and StochasticNCF which improves scalability by providing a low-cost approximation of meta-gradient updates through a sampled set of nearest environments. These extensions are demonstrated through comprehensive experimentation on a range of tasks, including dynamical systems, computer vision challenges, and curve fitting problems. Additionally, we incorporate higher-order Taylor expansions via Taylor-Mode automatic differentiation, revealing that higher-order approximations do not necessarily enhance generalization. Finally, we demonstrate how CSM can be integrated into other meta-learning frameworks with FlashCAVIA, a computationally efficient extension of the CAVIA meta-learning framework (Zintgraf et al., 2019). Together, these contributions highlight the significant benefits of CSM and indicate that its strengths in meta-learning and out-of-distribution tasks are particularly well-suited to physical systems. Our open-source library, designed for modular integration of self-modulation into contextual meta-learning workflows, is available at https://github.com/ddrous/self-mod.

cs.LG↗

arXiv2024

Neural Context Flows for Meta-Learning of Dynamical Systems

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications. Our code is openly available at https://github.com/ddrous/ncflow.

cs.LG↗

arXiv2024

Preliminary report: Initial evaluation of StdPar implementations on AMD GPUs for HPC

Recently, AMD platforms have not supported offloading C++17 PSTL (StdPar) programs to the GPU. Our previous work highlights how StdPar is able to achieve good performance across NVIDIA and Intel GPU platforms. In that work, we acknowledged AMD's past effort such as HCC, which unfortunately is deprecated and does not support newer hardware platforms. Recent developments by AMD, Codeplay, and AdaptiveCpp (previously known as hipSYCL or OpenSYCL) have enabled multiple paths for StdPar programs to run on AMD GPUs. This informal report discusses our experiences and evaluation of currently available StdPar implementations for AMD GPUs. We conduct benchmarks using our suite of HPC mini-apps with ports in many heterogeneous programming models, including StdPar. We then compare the performance of StdPar, using all available StdPar compilers, to contemporary heterogeneous programming models supported on AMD GPUs: HIP, OpenCL, Thrust, Kokkos, OpenMP, SYCL. Where appropriate, we discuss issues encountered and workarounds applied during our evaluation. Finally, the StdPar model discussed in this report largely depends on Unified Shared Memory (USM) performance and very few AMD GPUs have proper support for this feature. As such, this report demonstrates a proof-of-concept host-side userspace pagefault solution for models that use the HIP API. We discuss performance improvements achieved with our solution using the same set of benchmarks.

cs.DC↗

arXiv2023

A Comparison of Mesh-Free Differentiable Programming and Data-Driven Strategies for Optimal Control under PDE Constraints

The field of Optimal Control under Partial Differential Equations (PDE) constraints is rapidly changing under the influence of Deep Learning and the accompanying automatic differentiation libraries. Novel techniques like Physics-Informed Neural Networks (PINNs) and Differentiable Programming (DP) are to be contrasted with established numerical schemes like Direct-Adjoint Looping (DAL). We present a comprehensive comparison of DAL, PINN, and DP using a general-purpose mesh-free differentiable PDE solver based on Radial Basis Functions. Under Laplace and Navier-Stokes equations, we found DP to be extremely effective as it produces the most accurate gradients; thriving even when DAL fails and PINNs struggle. Additionally, we provide a detailed benchmark highlighting the limited conditions under which any of those methods can be efficiently used. Our work provides a guide to Optimal Control practitioners and connects them further to the Deep Learning community.

cs.LG↗