Internal noise in deep neural networks: interplay of depth, neuron number, and noise injection step

This study examines the impact of additive and multiplicative noise on both a single leaky integrate-and-fire (LIF) neuron and a trained spiking neural network (SNN). Noise was introduced at different stages of neural processing, including the input current, membrane potential, and output spike generation. The results show that multiplicative noise applied to the membrane potential has the most detrimental effect on network performance, leading to a significant degradation in accuracy. This is primarily due to its tendency to suppress membrane potentials toward large negative values, effectively silencing neuronal activity. To address this issue, input pre-filtering strategies were evaluated, with a sigmoid-based filter demonstrating the best performance by shifting inputs to a strictly positive range. Under these conditions, additive noise in the input current becomes the dominant source of performance degradation, while other noise configurations reduce accuracy by no more than 1%, even at high noise intensity. Additionally, the study compares the effects of common and uncommon noise across neuron populations in hidden layer, revealing that SNNs exhibit greater robustness to common noise. Overall, the findings identify the most critical noise mechanisms affecting SNNs and provide practical approaches for improving their robustness.

Geophysical data collected from active field sites are often contaminated by complex and heterogeneous noise, obscuring weak seismic events, and complicating automated interpretation. Although deep learning offers promising solutions for seismic processing, its performance is highly sensitive to the nature of training noise, especially under out-of-distribution (OOD) conditions. This study investigates the influence of noise parameters, such as type, scale, and complexity on the performance, generalization and robustness of neural networks in two geophysical tasks: first break picking and denoising. We simulate seismic-while-drilling data and apply controlled input source noise augmentation using stochastic generators to vary the noise characteristics. Different neural networks are trained on fixed noise types and scales, then evaluated across both seen and unseen noise scenarios. We incrementally increase the complexity of the noise by introducing compound noise mixtures and assess the performance of the model under increasingly challenging OOD conditions. This yields a robustness matrix that captures the generalizability of each model relative to its training configuration. Results indicate that larger noise scales boost generalization, and that effective alignment between noise type, task complexity, and architecture is key for maximizing generalization gains. In addition, training with compound noises mitigate weaknesses associated with single-noise training, acting as an additional implicit regularizer to improving robustness. These findings highlight key factors influencing model resilience in noisy geophysical environments and offer guidance for developing deep learning models that generalize effectively across diverse and unpredictable noise conditions.

Internal noise in deep networks is usually inherited from heuristics such as dropout, hard masking, or additive perturbation. We ask two questions: what correlation geometry should internal noise have, and is the implemented perturbation compatible with the representations it acts on? We answer these questions through Variational Kernel Design (VKD), a framework in which a noise mechanism is specified by a law family, a correlation kernel, and an injection operator, and is derived from learning desiderata. In a solved spatial subfamily, a quadratic maximum-entropy principle over latent log-fields yields a Gaussian optimizer with precision given by the Dirichlet Laplacian, so the induced geometry is the Dirichlet Green kernel. Wick normalization then gives a canonical positive mean-one gate, Gaussian Chaos Noise (GCh). For the sample-wise gate used in practice, we prove exact Gaussian control of pairwise log-ratio deformation, margin-sensitive ranking stability, and an exact expected intrinsic roughness budget; hard binary masks instead induce singular or coherence-amplified distortions on positive coherent representations. On ImageNet and ImageNet-C, GCh consistently improves calibration and under shift also improves NLL at competitive accuracy.