In this paper, we study deep signal representations that are near-invariant to groups of transformations and stable to the action of diffeomorphisms without losing signal information. This is achieved by generalizing the multilayer kernel introduced in the context of convolutional kernel networks and by studying the geometry of the corresponding reproducing kernel Hilbert space. We show that the signal representation is stable, and that models from this functional space, such as a large class of convolutional neural networks, may enjoy the same stability.

In this paper, we study deep signal representations that are near-invariant to groups of transformations and stable to the action of diffeomorphisms without losing signal information. This is achieved by generalizing the multilayer kernel introduced in the context of convolutional kernel networks and by studying the geometry of the corresponding reproducing kernel Hilbert space. We show that the signal representation is stable, and that models from this functional space, such as a large class of convolutional neural networks, may enjoy the same stability.

How are firing rates in a spiking network related to neural input, connectivity and network function? This is an important problem because firing rates are one of the most important measures of network activity, in both the study of neural computation and neural network dynamics. However, it is a difficult problem, because the spiking mechanism of individual neurons is highly non-linear, and these individual neurons interact strongly through connectivity. We develop a new technique for calculating firing rates in optimal balanced networks. These are particularly interesting networks because they provide an optimal spike-based signal representation while producing cortex-like spiking activity through a dynamic balance of excitation and inhibition.

Level-of-detail (LoD) representation is critical for efficiently modeling and transmitting various types of signals, such as images and 3D shapes. In this work, we propose a novel network architecture that enables LoD signal representation. Our approach builds on a modified Multi-Layer Perceptron (MLP), which inherently operates at a single scale and thus lacks native LoD support. Specifically, we introduce the Tailed Multi-Layer Perceptron (T -MLP), which extends the MLP by attaching an output branch, also called tail, to each hidden layer. Each tail refines the residual between the current prediction and the ground-truth signal, so that the accumulated outputs across layers correspond to the target signals at different LoDs, enabling multi-scale modeling with supervision from only a single-resolution signal. Extensive experiments demonstrate that our T -MLP outperforms existing neural LoD baselines across diverse signal representation tasks. Representing signals with neural networks is an active research direction, known as implicit neural representation (INR) (Sun et al., 2022; Molaei et al., 2023; Essakine et al., 2024). Unlike traditional discrete signal representation that stores signal values on a fixed-size grid, INR represents a continuous mapping from coordinates to signal values using a neural network, offering a more compact representation than conventional discrete grid-based representations.

Malware classification is a contemporary and ongoing challenge in cyber-security: modern obfuscation techniques are able to evade traditional static analysis, while dynamic analysis is too resource intensive to be deployed at a large scale. One prominent line of research addresses these limitations by converting malware binaries into 2D images by heuristically reshaping them into a 2D grid before resizing using Lanczos resampling. These images can then be classified based on their textural information using computer vision approaches. While this approach can detect obfuscated malware more effectively than static analysis, the process of converting files into 2D images results in significant information loss due to both quantisation noise, caused by rounding to integer pixel values, and the introduction of 2D dependencies which do not exist in the original data. This loss of signal limits the classification performance of the downstream model. This work addresses these weaknesses by instead resizing the files into 1D signals which avoids the need for heuristic reshaping, and additionally these signals do not suffer from quantisation noise due to being stored in a floating-point format. It is shown that existing 2D CNN architectures can be readily adapted to classify these 1D signals for improved performance. Furthermore, a bespoke 1D convolutional neural network, based on the ResNet architecture and squeeze-and-excitation layers, was developed to classify these signals and evaluated on the MalNet dataset. It was found to achieve state-of-the-art performance on binary, type, and family level classification with F1 scores of 0.874, 0.503, and 0.507, respectively, paving the way for future models to operate on the proposed signal modality.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology into the dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, yielding localized spectral topological filter frames. The learning problem is cast to jointly infer the underlying cell complex and optimize the dictionary coefficients and the sparse signal representation. We efficiently solve the problem via iterative alternating algorithms. Numerical results on both synthetic and real data show the effectiveness of the proposed procedure in jointly learning the sparse representations and the underlying relational structure of topological signals.

Automatic Modulation Classification (AMC), as a crucial technique in modern non-cooperative communication networks, plays a key role in various civil and military applications. However, existing AMC methods usually are complicated and can work in batch mode only due to their high computational complexity. This paper introduces a new online AMC scheme based on Isolation Distributional Kernel. Our method stands out in two aspects. Firstly, it is the first proposal to represent baseband signals using a distributional kernel. Secondly, it introduces a pioneering AMC technique that works well in online settings under realistic time-varying channel conditions. Through extensive experiments in online settings, we demonstrate the effectiveness of the proposed classifier. Our results indicate that the proposed approach outperforms existing baseline models, including two state-of-the-art deep learning classifiers. Moreover, it distinguishes itself as the first online classifier for AMC with linear time complexity, which marks a significant efficiency boost for real-time applications.

In this work, we introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, leverages multi-view learning to construct more interpretable representations within the latent space. Subsequently, we present the Analytic Neural Network, which implements a consistency penalty that encourages analytic signal representations in the Steinmetz neural network's latent space. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Utilizing an information-theoretic construction, we demonstrate that the upper bound on the generalization error posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments demonstrate the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.

Based on audio recordings made once a month during the first 12 months of a child's life, we propose a new method for clustering this set of vocalizations. We use a topologically augmented representation of the vocalizations, employing two persistence diagrams for each vocalization: one computed on the surface of its spectrogram and one on the Takens' embeddings of the vocalization. A synthetic persistent variable is derived for each diagram and added to the MFCCs (Mel-frequency cepstral coefficients). Using this representation, we fit a non-parametric Bayesian mixture model with a Dirichlet process prior to model the number of components. This procedure leads to a novel data-driven categorization of vocal productions. Our findings reveal the presence of 8 clusters of vocalizations, allowing us to compare their temporal distribution and acoustic profiles in the first 12 months of life.