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Graph Transformers excel in long-range dependency modeling, but generally require quadratic memory complexity in the number of nodes in an input graph, and hence have trouble scaling to large graphs. Sparse attention variants such as Exphormer can help, but may require high-degree augmentations to the input graph for good performance, and do not attempt to sparsify an already-dense input graph. As the learned attention mechanisms tend to use few of these edges, such high-degree connections may be unnecessary. We show (empirically and with theoretical backing) that attention scores on graphs are usually quite consistent across network widths, and use this observation to propose a two-stage procedure, which we call Spexphormer: first, train a narrow network on the full augmented graph. Next, use only the active connections to train a wider network on a much sparser graph. We establish theoretical conditions when a narrow network's attention scores can match those of a wide network, and show that Spexphormer achieves good performance with drastically reduced memory requirements on various graph datasets.

Transductive tasks on graphs differ fundamentally from typical supervised machine learning tasks, as the independent and identically distributed (i.i.d.) assumption does not hold among samples. Instead, all train/test/validation samples are present during training, making them more akin to a semi-supervised task. These differences make the analysis of the models substantially different from other models. Recently, Graph Transformers have significantly improved results on these datasets by overcoming long-range dependency problems. However, the quadratic complexity of full Transformers has driven the community to explore more efficient variants, such as those with sparser attention patterns. While the attention matrix has been extensively discussed, the hidden dimension or width of the network has received less attention. In this work, we establish some theoretical bounds on how and under what conditions the hidden dimension of these networks can be compressed. Our results apply to both sparse and dense variants of Graph Transformers.

Molecular dynamics triggered by interaction with light often involve the excitation of several electronic, vibrational, and rotational states. Characterizing the resulting coupled electronic and nuclear wave packet motion represents a severe challenge, even for small polyatomic systems. In this Letter, we demonstrate how the interplay between vibrational, rotational, and electronic degrees of freedom governs the evolution of molecular wave packets in the low-lying states of strong-field-ionized sulfur dioxide. Using time-resolved Coulomb explosion imaging (CEI) in combination with quantum mechanical wave packet simulations, we directly map bending vibrations of the molecule, show how the vibrational wave packet is influenced by molecular alignment, and elucidate the role of the coupling between the two lowest electronic states of the cation. A conical intersection between these states couples the bending and asymmetric stretching coordinates, which is clearly reflected in the correlated fragment momenta. Our results suggest that multi-coincident CEI represents an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.

Coulomb explosion imaging (CEI) with x-ray free electron lasers has recently been shown to be a powerful method for obtaining detailed structural information of gas-phase planar ring molecules [R. Boll et al. Nat. Phys. 18, 423-428 (2022)]. In this Letter, we investigate the potential of CEI driven by a tabletop laser and extend this approach to differentiating three-dimensional (3D) structures. We study the static CEI patterns of planar and nonplanar organic molecules that resemble the structures of typical products formed in ring-opening reactions. Our results reveal that each molecule exhibits a well-localized and distinctive pattern in 3D fragment-ion momentum space. We find that these patterns yield direct information about the molecular structures and can be qualitatively reproduced using a classical Coulomb explosion simulation. Our findings suggest that laser-induced CEI can serve as a robust method for differentiating molecular structures of organic ring and chain molecules. As such, it holds great promise as a method for following ultrafast structural changes, e.g., during ring-opening reactions, by tracking the motion of individual atoms in pump-probe experiments.

In this study, we present a novel platform based on scanning microwave microscopy for manipulating and detecting tiny vibrations of nanoelectromechanical resonators using a single metallic tip. The tip is placed on the top of a grounded silicon nitride membrane, acting as a movable top gate of the coupled resonator. We demonstrate its ability to map mechanical modes and investigate mechanical damping effects in a capacitive coupling scheme, based on its spatial resolution. We also manipulate the energy transfer coherently between the mode of the scanning tip and the underlying silicon nitride membrane, via parametric coupling. Typical features of optomechanics, such as anti-damping and electromechanically induced transparency, have been observed. Since the microwave optomechanical technology is fully compatible with quantum electronics and very low temperature conditions, it should provide a powerful tool for studying phonon tunnelling between two spatially separated vibrating elements, which could potentially be applied to quantum sensing.

Molecular photoabsorption results in an electronic excitation/ionization which couples to the rearrangement of the nuclei. The resulting intertwined change of nuclear and electronic degrees of freedom determines the conversion of photoenergy into other molecular energy forms. Nucleobases are excellent candidates for studying such dynamics, and great effort has been taken in the past to observe the electronic changes induced by the initial excitation in a time-resolved manner using ultrafast electron spectroscopy. The linked geometrical changes during nucleobase photorelaxation have so far not been observed directly in time-resolved experiments. Here, we present a study on a thionucleobase, where we extract comprehensive information on the molecular rearrangement using Coulomb explosion imaging. Our measurement links the extracted deplanarization of the molecular geometry to the previously studied temporal evolution of the electronic properties of the system. In particular, the protons of the exploded molecule are well-suited messengers carrying rich information on the molecule's geometry at distinct times after the initial electronic excitation. The combination of ultrashort laser pulses to trigger molecular dynamics, intense X-ray free-electron laser pulses for the explosion of the molecule, and multi-particle coincidence detection opens new avenues for time-resolved studies of complex molecules in the gas phase., Comment: 19 pages, 8 figures

Each person has a unique gait, i.e., walking style, that can be used as a biometric for personal identification. Recent works have demonstrated effective gait recognition using deep neural networks, however most of these works predominantly focus on classification accuracy rather than model efficiency. In order to perform gait recognition using wearable devices on the edge, it is imperative to develop highly efficient low-power models that can be deployed on to small form-factor devices such as microcontrollers. In this paper, we propose a small CNN model with 4 layers that is very amenable for edge AI deployment and realtime gait recognition. This model was trained on a public gait dataset with 20 classes augmented with data collected by the authors, aggregating to 24 classes in total. Our model achieves 96.7% accuracy and consumes only 5KB RAM with an inferencing time of 70 ms and 125mW power, while running continuous inference on Arduino Nano 33 BLE Sense. We successfully demonstrated realtime identification of the authors with the model running on Arduino, thus underscoring the efficacy and providing a proof of feasiblity for deployment in practical systems in near future.