arXiv subjects

Michael Wand

Publications and source records attributed to Michael Wand.

At least 19 recordsLinked to original sources

arXiv2026

Ab initio parametrization of distributed polarizable force fields

Polarizable force fields offer superior transferability and accuracy compared to classical force fields, enabling access to electronic response properties such as refractive index and electronic density of states. Here, we demonstrate two key improvements that significantly enhance their accuracy: (1) assigning atomic polarizability to individual atoms rather than atom types, and (2) employing atomic polarizability tensors instead of scalar values. These modifications extend the applicability of polarizable force fields to cations, anions, and excited states, while also providing more accurate descriptions of neutral molecules. We propose a first-principles-based parameterization procedure for atomic polarizability tensors and scalars, validated on a set of small organic molecules with conjugated building blocks. To overcome the computational cost of ab initio calculations, we train a message-passing graph neural network to predict polarizability parameters, enabling efficient and scalable parameterization. Crucially, this approach imposes no additional computational cost during simulations and provides a clear diagnostic criterion for identifying cases where polarizable force field models fail to accurately describe molecular polarizability.

cond-mat.mtrl-sci↗

arXiv2026

Tensor Channel Equivariant Graph Neural Networks for Molecular Polarizability Prediction

We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2 tensor channels aligned with the decomposition of polarizability into isotropic and anisotropic components. In contrast to approaches that construct tensor outputs only at readout, our model propagates tensor structure throughout message passing using geometrically motivated tensor bases. This yields a target-aligned architecture for tensor-valued molecular prediction. On optimized QM7-X geometries, the proposed model achieves lower full-tensor and anisotropic error than both a PaiNN-style readout baseline and a dielectric MACE baseline under matched training conditions and at nearly identical parameter count. In this controlled setting, it also outperforms MACE while remaining substantially faster at inference. Ablation studies show that the gain does not arise from increased capacity alone, but from the combination of explicit tensor propagation and a traceless target parameterization matched to the anisotropic part of the polarizability tensor. Among the tensor bases considered, the strongest results are obtained from interactions between learned directional features, indicating that these are particularly effective for modeling molecular polarizability. Rotational equivariance tests further confirm that all compared models are numerically equivariant, so the observed improvements are attributable to better learning of the target tensor itself. Overall, our results show that for structured tensor-valued targets, propagating target-aligned tensor features can outperform both readout-only tensor construction and a more general higher-order equivariant model in the present training setting.

cs.LG↗

arXiv2026

Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space

Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

cs.CV↗

arXiv2026

Reconstruction of spin structures from topological charge distributions via generative neural network systems

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this work, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and at the same time highlight topological methods as valuable tools for characterizing critical behavior.

cond-mat.stat-mech↗

arXiv2026

Information Theoretic Perspective on Representation Learning

An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output information can be represented as is inherently determined by the input-source entropy. We further define representation capacity in a perturbed setting, and representation rate-distortion for a compressed output. We derive the achievable capacity, the achievable representation-rate, and their converse. Finally, we combine the results in a unified setting.

cs.IT↗

arXiv2025

Multiple Token Divergence: Measuring and Steering In-Context Computation Density

Measuring the in-context computational effort of language models is a key challenge, as metrics like next-token loss fail to capture reasoning complexity. Prior methods based on latent state compressibility can be invasive and unstable. We propose Multiple Token Divergence (MTD), a simple measure of computational effort defined as the KL divergence between a model's full output distribution and that of a shallow, auxiliary prediction head. MTD can be computed directly from pre-trained models with multiple prediction heads, requiring no additional training. Building on this, we introduce Divergence Steering, a novel decoding method to control the computational character of generated text. We empirically show that MTD is more effective than prior methods at distinguishing complex tasks from simple ones. On mathematical reasoning benchmarks, MTD correlates positively with problem difficulty. Lower MTD is associated with more accurate reasoning. MTD provides a practical, lightweight tool for analyzing and steering the computational dynamics of language models.

cs.LG↗

arXiv2025

Space Explanations of Neural Network Classification

We present a novel logic-based concept called Space Explanations for classifying neural networks that gives provable guarantees of the behavior of the network in continuous areas of the input feature space. To automatically generate space explanations, we leverage a range of flexible Craig interpolation algorithms and unsatisfiable core generation. Based on real-life case studies, ranging from small to medium to large size, we demonstrate that the generated explanations are more meaningful than those computed by state-of-the-art.

cs.LG↗

arXiv2025

Direct Molecular Polarizability Prediction with SO(3) Equivariant Local Frame GNNs

We introduce a novel equivariant graph neural network (GNN) architecture designed to predict the tensorial response properties of molecules. Unlike traditional frameworks that focus on regressing scalar quantities and derive tensorial properties from their derivatives, our approach maintains $SO(3)$-equivariance through the use of local coordinate frames. Our GNN effectively captures geometric information by integrating scalar, vector, and tensor channels within a local message-passing framework. To assess the accuracy of our model, we apply it to predict the polarizabilities of molecules in the QM7-X dataset and show that tensorial message passing outperforms scalar message passing models. This work marks an advancement towards developing structured, geometry-aware neural models for molecular property prediction.

cs.LG↗

arXiv2025

Fast and scalable retrosynthetic planning with a transformer neural network and speculative beam search

AI-based computer-aided synthesis planning (CASP) systems are in demand as components of AI-driven drug discovery workflows. However, the high latency of such CASP systems limits their utility for high-throughput synthesizability screening in de novo drug design. We propose a method for accelerating multi-step synthesis planning systems that rely on SMILES-to-SMILES transformers as single-step retrosynthesis models. Our approach reduces the latency of SMILES-to-SMILES transformers powering multi-step synthesis planning in AiZynthFinder through speculative beam search combined with a scalable drafting strategy called Medusa. Replacing standard beam search with our approach allows the CASP system to solve 26\% to 86\% more molecules under the same time constraints of several seconds. Our method brings AI-based CASP systems closer to meeting the strict latency requirements of high-throughput synthesizability screening and improving general user experience.

cs.LG↗

arXiv2025

ResNets Are Deeper Than You Think

Residual connections remain ubiquitous in modern neural network architectures nearly a decade after their introduction. Their widespread adoption is often credited to their dramatically improved trainability: residual networks train faster, more stably, and achieve higher accuracy than their feedforward counterparts. While numerous techniques, ranging from improved initialization to advanced learning rate schedules, have been proposed to close the performance gap between residual and feedforward networks, this gap has persisted. In this work, we propose an alternative explanation: residual networks do not merely reparameterize feedforward networks, but instead inhabit a different function space. We design a controlled post-training comparison to isolate generalization performance from trainability; we find that variable-depth architectures, similar to ResNets, consistently outperform fixed-depth networks, even when optimization is unlikely to make a difference. These results suggest that residual connections confer performance advantages beyond optimization, pointing instead to a deeper inductive bias aligned with the structure of natural data.

cs.LG↗

arXiv2024

Accelerating the inference of string generation-based chemical reaction models for industrial applications

Template-free SMILES-to-SMILES translation models for reaction prediction and single-step retrosynthesis are of interest for industrial applications in computer-aided synthesis planning systems due to their state-of-the-art accuracy. However, they suffer from slow inference speed. We present a method to accelerate inference in autoregressive SMILES generators through speculative decoding by copying query string subsequences into target strings in the right places. We apply our method to the molecular transformer implemented in Pytorch Lightning and achieve over 3X faster inference in reaction prediction and single-step retrosynthesis, with no loss in accuracy.

cs.LG↗

arXiv2024

Diff-ETS: Learning a Diffusion Probabilistic Model for Electromyography-to-Speech Conversion

Electromyography-to-Speech (ETS) conversion has demonstrated its potential for silent speech interfaces by generating audible speech from Electromyography (EMG) signals during silent articulations. ETS models usually consist of an EMG encoder which converts EMG signals to acoustic speech features, and a vocoder which then synthesises the speech signals. Due to an inadequate amount of available data and noisy signals, the synthesised speech often exhibits a low level of naturalness. In this work, we propose Diff-ETS, an ETS model which uses a score-based diffusion probabilistic model to enhance the naturalness of synthesised speech. The diffusion model is applied to improve the quality of the acoustic features predicted by an EMG encoder. In our experiments, we evaluated fine-tuning the diffusion model on predictions of a pre-trained EMG encoder, and training both models in an end-to-end fashion. We compared Diff-ETS with a baseline ETS model without diffusion using objective metrics and a listening test. The results indicated the proposed Diff-ETS significantly improved speech naturalness over the baseline.

cs.SD↗

arXiv2023

On the Weight Dynamics of Deep Normalized Networks

Recent studies have shown that high disparities in effective learning rates (ELRs) across layers in deep neural networks can negatively affect trainability. We formalize how these disparities evolve over time by modeling weight dynamics (evolution of expected gradient and weight norms) of networks with normalization layers, predicting the evolution of layer-wise ELR ratios. We prove that when training with any constant learning rate, ELR ratios converge to 1, despite initial gradient explosion. We identify a ``critical learning rate" beyond which ELR disparities widen, which only depends on current ELRs. To validate our findings, we devise a hyper-parameter-free warm-up method that successfully minimizes ELR spread quickly in theory and practice. Our experiments link ELR spread with trainability, a relationship that is most evident in very deep networks with significant gradient magnitude excursions.

cs.LG↗

arXiv2021

Nonlinearities in Steerable SO(2)-Equivariant CNNs

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have emerged as the standard solution. An inherent problem of steerable representations is that general nonlinear layers break equivariance, thus restricting architectural choices. Our paper applies harmonic distortion analysis to illuminate the effect of nonlinearities on Fourier representations of SO(2). We develop a novel FFT-based algorithm for computing representations of non-linearly transformed activations while maintaining band-limitation. It yields exact equivariance for polynomial (approximations of) nonlinearities, as well as approximate solutions with tunable accuracy for general functions. We apply the approach to build a fully E(3)-equivariant network for sampled 3D surface data. In experiments with 2D and 3D data, we obtain results that compare favorably to the state-of-the-art in terms of accuracy while permitting continuous symmetry and exact equivariance.

cs.LG↗

arXiv2021

Adversarial reverse mapping of condensed-phase molecular structures: Chemical transferability

Switching between different levels of resolution is essential for multiscale modeling, but restoring details at higher resolution remains challenging. In our previous study we have introduced deepBackmap: a deep neural-network-based approach to reverse-map equilibrated molecular structures for condensed-phase systems. Our method combines data-driven and physics-based aspects, leading to high-quality reconstructed structures. In this work, we expand the scope of our model and examine its chemical transferability. To this end, we train deepBackmap solely on homogeneous molecular liquids of small molecules, and apply it to a more challenging polymer melt. We augment the generator's objective with different force-field-based terms as prior to regularize the results. The best performing physical prior depends on whether we train for a specific chemistry, or transfer our model. Our local environment representation combined with the sequential reconstruction of fine-grained structures help reach transferability of the learned correlations.

physics.chem-ph↗

arXiv2020

Adversarial Reverse Mapping of Equilibrated Condensed-Phase Molecular Structures

A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement -- backmapping -- of a coarse-grained structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use generative adversarial networks to learn the Boltzmann distribution from training data and realize reverse mapping by using the coarse-grained structure as a conditional input. We apply our method to a challenging condensed-phase polymeric system. We observe that the model trained in a melt has remarkable transferability to the crystalline phase. The combination of data-driven and physics-based aspects of our architecture help reach temperature transferability with only limited training data.

cond-mat.soft↗

arXiv2020

Deep Non-Line-of-Sight Reconstruction

The recent years have seen a surge of interest in methods for imaging beyond the direct line of sight. The most prominent techniques rely on time-resolved optical impulse responses, obtained by illuminating a diffuse wall with an ultrashort light pulse and observing multi-bounce indirect reflections with an ultrafast time-resolved imager. Reconstruction of geometry from such data, however, is a complex non-linear inverse problem that comes with substantial computational demands. In this paper, we employ convolutional feed-forward networks for solving the reconstruction problem efficiently while maintaining good reconstruction quality. Specifically, we devise a tailored autoencoder architecture, trained end-to-end, that maps transient images directly to a depth map representation. Training is done using an efficient transient renderer for diffuse three-bounce indirect light transport that enables the quick generation of large amounts of training data for the network. We examine the performance of our method on a variety of synthetic and experimental datasets and its dependency on the choice of training data and augmentation strategies, as well as architectural features. We demonstrate that our feed-forward network, even though it is trained solely on synthetic data, generalizes to measured data from SPAD sensors and is able to obtain results that are competitive with model-based reconstruction methods.

cs.CV↗

arXiv2019

Progressive Stochastic Binarization of Deep Networks

A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii) arithmetic operations (for example, by binarization of weights). We propose a stochastic binarization scheme for deep networks that allows for efficient inference on hardware by restricting itself to additions of small integers and fixed shifts. Unlike previous approaches, the underlying randomized approximation is progressive, thus permitting an adaptive control of the accuracy of each operation at run-time. In a low-precision setting, we match the accuracy of previous binarized approaches. Our representation is unbiased - it approaches continuous computation with increasing sample size. In a high-precision regime, the computational costs are competitive with previous quantization schemes. Progressive stochastic binarization also permits localized, dynamic accuracy control within a single network, thereby providing a new tool for adaptively focusing computational attention. We evaluate our method on networks of various architectures, already pretrained on ImageNet. With representational costs comparable to previous schemes, we obtain accuracies close to the original floating point implementation. This includes pruned networks, except the known special case of certain types of separated convolutions. By focusing computational attention using progressive sampling, we reduce inference costs on ImageNet further by a factor of up to 33% (before network pruning).

cs.LG↗