Wavelet Scattering Transforms

Federated Learning (FL) enables collaborative model training without exposing raw data, yet remains vulnerable to malicious clients injecting poisoned datasets. Existing defenses are typically reactive (operating during training) or supervised (requiring prior knowledge of attack types) - assumptions that rarely hold in open-ended IoT deployments. We propose WaSA, a fully unsupervised, offline framework for malicious client detection. Before training, each client transmits a single, privacy-preserving spectral summary of its data to the server. A denoising autoencoder, trained solely on clean auxiliary data, scores clients based on their deviation from the learned benign manifold, identifying corruptions regardless of the attack type. WaSA requires no attack labels, generalizes to unseen anomalies, and introduces a Boltzmann sampling strategy for client selection that smoothly interpolates between hard exclusion and standard aggregation. Experiments on MNIST, CIFAR-10, and CIFAR-100 under diverse attack scenarios (up to 90 % malicious clients) demonstrate consistent improvements over supervised baselines and robust aggregation methods, with negligible communication overhead. Code is available at https://github.com/alelicciardi99/wavelet_autoencoders_malicious.

We develop a principled framework for constructing neural networks whose specific parameter realizations admit an explicit algorithmic interpretation. Existing algorithm-inspired architectures can explain the computational structure of a network, yet after standard training the learned parameters need not retain a clear relation to the motivating algorithm. We address this gap as follows. First, we model each data point as a sample of a class-dependent stochastic process and assume that statistics of this process can be estimated from a single sample and these statistics are sufficient to distinguish the classes. We then construct a neural network whose initial parameters exactly implement an algorithm for estimating these statistics, making the network fully interpretable. To account for mismatch between the idealized model and real data, we fine-tune this network while controlling its deviation from the algorithmic initialization. The trained network hence roughly retains the interpretation of the initial network. A PAC-Bayesian analysis yields a uniform generalization bound whose complexity term scales with the fine-tuning radius, providing a statistical motivation for our approach. We instantiate the framework for texture classification using the scattering transform to estimate the discriminative statistics.

Clustered Federated Learning (FL) partitions a client population into groups of similar local distributions and trains one specialized model per cluster, mitigating client drift that degrades single-model methods under non-IID data. Prior methods discover cluster structure inside the training loop through gradient similarity, loss evaluation, or EM-style updates, thus increasing communication overhead, exposing gradients to inversion attacks, and providing no mechanism to assign clients absent from training. We propose RIPPLE, a clustered FL framework in which cluster assignment is computed entirely offline from a spectral characterization of each client's local data: a variance-weighted principal-component prototype embedded via the Wavelet Scattering Transform and decoded by a Gaussian Mixture VAE trained server-side on synthetic client populations before federation begins. Per-round communication cost matches FedAvg exactly, and a client absent from training obtains a personalized model from a single forward pass, without gradient computation, model evaluation, or extra communication round. We prove that the gap between RIPPLE's surrogate clustered objective and the oracle is bounded by a computable quantity decaying with client sample size and independent of federation duration; per-cluster convergence matches the minimax-optimal rate for non-convex smooth objectives. Across five benchmarks spanning controlled and realistic heterogeneity, RIPPLE consistently outperforms all baselines, with margins growing on the most realistic partitions.

The acoustic front-end determines which forensic cues a speech deepfake detector can exploit. The wavelet scattering transform (WST) provides stable multiscale coefficients with explicit coordinates, yet direct flattening obscures the parent relation between paths. We introduce WST-Graph, reconstructing these paths as a sparse modulation-carrier grid for an AASIST graph backend. Modulation-level normalization and length-aware adaptive local attention pooling produce fixed relative-time representations while retaining the acoustic axes before learned adaptation. This yields a waveform-to-graph interface with a fixed, parameter-free WST. Our configurations remain competitive with AASIST while using approximately 60% fewer trainable parameters and show clear gains on selected out-of-domain benchmarks. These results underscore the value of preserving parent-child relations within the carrier-modulation topology when constructing a compact, physically grounded interface for graph-based speech deepfake detection. Code will be released at https://github.com/saki-ciallo/wst-graph.

Schizophrenia is a debilitating neuropsychiatric disorder characterized by profound cortical network dysregulation, for which objective, clinically translatable EEG based biomarkers remain underdeveloped. Existing automated classification pipelines rely predominantly on static power spectral density features inherently blind to amplitude modulation dynamics and cross-frequency coupling, phenomena central to schizophrenia pathophysiology, while adopting epoch level cross validation strategies that introduce temporal data leakage, artificially inflate reported performance. This study introduces a mathematically principled diagnostic framework integrating the multi-order Wavelet Scattering Transform(WST), strict Leave One Subject Out (LOSO) cross-validation, and SHAP explainability for simultaneous EEG classification and biomarker discovery. Hierarchical WST coefficients capturing multi-scale amplitude modulation structure were extracted from resting state multichannel EEG. Subject-level ANOVA with Benjamini Hochberg false discovery rate correction identified significant biomarkers, with Random Forest and SVM classifiers evaluated under strict LOSO cross validation and subject-level majority voting. Second-order scattering coefficients encoding cross frequency coupling dominated the discriminative biomarker set, with gamma-band features most prevalent, demonstrating that temporal amplitude modulation constitutes the primary electrophysiological signature of schizophrenia. Electrode P3 was identified as the single most discriminative site. Under rigorous subject independent evaluation, the Random Forest achieved 90.48% accuracy (AUC = 0.9339; sensitivity = 95.56%). The proposed WST framework establishes a rigorous, interpretable standard for EEG-driven psychiatric biomarker discovery that can also be applicable in the detection of schizophrenia subtypes in the future.

In this paper, we propose a reconstruction framework that leverages the Wavelet Scattering Transform (WST) as a multi-scale feature extractor to impose statistical priors under sparse observation conditions. The reconstruction problem is formulated as an optimization task and solved using a neural field, with the WST incorporated into the training loss function. As a proof of concept, we validate the proposed method on HRTF upsampling. A masking strategy is applied to the WST coefficients, resulting in a two-phase procedure. The first phase learns a binary mask from a small multi-subject dataset, while the second phase applies the learned mask to the WST coefficients of an individual HRTF to preserve informative statistical structures during reconstruction. Validation against baseline methods, which also serve as an ablation study of the different components of the framework, demonstrates the effectiveness of the proposed approach.

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this information by explicitly preserving phase in skip connections. On image denoising (BSD68), breaking translation invariance improves PSNR by $+2.17$~dB; phase preservation adds $+1.03$~dB. A novel spatial shuffling ablation ($-1.26$~dB penalty) demonstrates phase encodes location-dependent structure. We conduct a preliminary extensibility study on a second dense prediction task (ISIC skin lesion segmentation), with full cross-validation as ongoing work. This work advances principled wavelet-deep learning integration, showing how phase information complements scattering's stability-expressiveness trade-off in pixel-level prediction.

The use of hearing aids will increase in the coming years due to demographic change. One open problem that remains to be solved by a new generation of hearing aids is the cocktail party problem. A possible solution is electroencephalography-based auditory attention decoding. This has been the subject of several studies in recent years, which have in common that they use the same preprocessing methods in most cases. In this work, in order to achieve an advantage, the use of a scattering transform is proposed as an alternative to these preprocessing methods. The two-layer scattering transform is compared with a regular filterbank, the synchrosqueezing short-time Fourier transform and the common preprocessing. To demonstrate the performance, the known and the proposed preprocessing methods are compared for different classification tasks on two widely used datasets, provided by the KU Leuven (KUL) and the Technical University of Denmark (DTU). Both established and new neural-network-based models, CNNs, LSTMs, and recent Transformer/graph-based models are used for classification. Various evaluation strategies were compared, with a focus on the task of classifying speakers who are unknown from the training. We show that the two-layer scattering transform can significantly improve the performance for subject-related conditions, especially on the KUL dataset. However, on the DTU dataset, this only applies to some of the models, or when larger amounts of training data are provided, as in 10-fold cross-validation. This suggests that the scattering transform is capable of extracting additional relevant information.

Existing front-ends for speech deepfake detection are primarily categorized into two types. Hand-crafted filterbank features are transparent but limited in capturing higher-level information. SSL features, in turn, lack interpretability and may overlook fine-grained spectral anomalies. We propose WaveScat, a novel family of feature extractors that combines the best of both worlds via the wavelet scattering transform (WST), which cascades wavelet convolutions with modulus nonlinearities to produce deformation-stable, multi-scale features. Experiments on the recent Deepfake-Eval-2024 benchmark, together with cross-dataset evaluations on SpoofCeleb, In-the-Wild, and ASVspoof 5, show that WaveScat outperforms existing front-ends by a wide margin. Our analysis reveals that a small averaging scale combined with high-frequency and directional resolutions is critical for capturing subtle artifacts. This underscores the value of stable and translation-invariant features for speech deepfake detection. The code and supplementary materials are available at https://github.com/xxuan-acoustics/WaveScat.