To protect deep neural networks (DNNs) from adversarial attacks, adversarial training (AT) is developed by incorporating adversarial examples (AEs) into model training. Recent studies show that adversarial attacks disproportionately impact the patterns within the phase of the sample's frequency spectrum---typically containing crucial semantic information---more than those in the amplitude, resulting in the model's erroneous categorization of AEs. We find that, by mixing the amplitude of training samples' frequency spectrum with those of distractor images for AT, the model can be guided to focus on phase patterns unaffected by adversarial perturbations. As a result, the model's robustness can be improved. Unfortunately, it is still challenging to select appropriate distractor images, which should mix the amplitude without affecting the phase patterns.

Language exhibits structure at a wide range of scales, from subwords to words, sentences, paragraphs, and documents. We propose building models that isolate scale-specific information in deep representations, and develop methods for encouraging models during training to learn more about particular scales of interest. Our method for creating scale-specific neurons in deep NLP models constrains how the activation of a neuron can change across the tokens of an input by interpreting those activations as a digital signal and filtering out parts of its frequency spectrum. This technique enables us to extract scale-specific information from BERT representations: by filtering out different frequencies we can produce new representations that perform well on part of speech tagging (word-level), dialog speech acts classification (utterance-level), or topic classification (document-level), while performing poorly on the other tasks. We also present a prism layer for use during training, which constrains different neurons of a BERT model to different parts of the frequency spectrum. Our proposed BERT + Prism model is better able to predict masked tokens using long-range context, and produces individual multiscale representations that perform with comparable or improved performance across all three tasks. Our methods are general and readily applicable to other domains besides language, such as images, audio, and video.

Quantum machine learning research has expanded rapidly due to potential computational advantages over classical methods. Angle encoding has emerged as a popular choice as feature map (FM) for embedding classical data into quantum models due to its simplicity and natural generation of truncated Fourier series, providing universal function approximation capabilities. Efficient FMs within quantum circuits can exploit exponential scaling of Fourier frequencies, with multi-dimensional inputs introducing additional exponential growth through mixed-frequency terms. Despite this promising expressive capability, practical implementation faces significant challenges. Through controlled experiments with white-box target functions, we demonstrate that training failures can occur even when all relevant frequencies are theoretically accessible. We illustrate how two primary known causes lead to unsuccessful optimization: insufficient trainable parameters relative to the model's frequency content, and limitations imposed by the ansatz's dynamic lie algebra dimension, but also uncover an additional parameter burden: the necessity of controlling non-unique frequencies within the model. To address this, we propose near-zero weight initialization to suppress unnecessary duplicate frequencies. For target functions with a priori frequency knowledge, we introduce frequency selection as a practical solution that reduces parameter requirements and mitigates the exponential growth that would otherwise render problems intractable due to parameter insufficiency. Our frequency selection approach achieved near-optimal performance (median $R^2 \approx 0.95$) with 78\% of the parameters needed by the best standard approach in 10 randomly chosen target functions.

The expressive power of a QNN model can be characterized by the function classes that it can approximate.

FBM extracts explicit frequency features while preserving temporal characteristics, enabling the mapping network to capture the time-frequency relationships.

To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequency-based representations of the same example are located close together in the time-frequency space.

Drive-by inspection for bridge health monitoring has gained increasing attention over the past decade. This method involves analysing the coupled vehicle-bridge response, recorded by an instrumented inspection vehicle, to assess structural integrity and detect damage. However, the vehicles mechanical and dynamic properties significantly influence detection performance, limiting the effectiveness of the approach. This study presents a framework for optimising the inspection vehicle to enhance damage sensitivity. An unsupervised deep learning methodbased on adversarial autoencoders (AAE)is used to reconstruct the frequency-domain representation of acceleration responses. The mass and stiffness of the tyre suspension system of a two-axle vehicle are optimised by minimising the Wasserstein distance between damage index distributions for healthy and damaged bridge states. A Kriging meta-model is employed to approximate this objective function efficiently and identify optimal vehicle configurations in both dimensional and non-dimensional parameter spaces. Results show that vehicles with frequency ratios between 0.3 and 0.7 relative to the bridges' first natural frequency are most effective, while those near resonance perform poorly. Lighter vehicles require lower natural frequencies for optimal detection. This is the first study to rigorously optimise the sensing platform for drive-by sensing and to propose a purpose-built inspection vehicle.

W e investigate the impact of the data representation and the pre-processing steps for this classification tasks and compare different network structures.