We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regu-lariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

Neural audio codecs have made significant strides in efficiently mapping raw audio waveforms into discrete token representations, which are foundational for contemporary audio generative models. However, most existing codecs are optimized primarily for reconstruction quality, often at the expense of the downstream modelability of the encoded tokens. Motivated by the need to overcome this bottleneck, we introduce $\textbf{MagiCodec}$, a novel single-layer, streaming Transformer-based audio codec. MagiCodec is designed with a multistage training pipeline that incorporates Gaussian noise injection and latent regularization, explicitly targeting the enhancement of semantic expressiveness in the generated codes while preserving high reconstruction fidelity. We analytically derive the effect of noise injection in the frequency domain, demonstrating its efficacy in attenuating high-frequency components and fostering robust tokenization. Extensive experimental evaluations show that MagiCodec surpasses state-of-the-art codecs in both reconstruction quality and downstream tasks. Notably, the tokens produced by MagiCodec exhibit Zipf-like distributions, as observed in natural languages, thereby improving compatibility with language-model-based generative architectures. The code and pre-trained models are available at https://github.com/Ereboas/MagiCodec.

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.

Natural language understanding (NLU) is the task of semantic decoding of human languages by machines. NLU models rely heavily on large training data to ensure good performance. However, substantial languages and domains have very few data resources and domain experts. It is necessary to overcome the data scarcity challenge, when very few or even zero training samples are available. In this thesis, we focus on developing cross-lingual and cross-domain methods to tackle the low-resource issues. First, we propose to improve the model's cross-lingual ability by focusing on the task-related keywords, enhancing the model's robustness and regularizing the representations. We find that the representations for low-resource languages can be easily and greatly improved by focusing on just the keywords. Second, we present Order-Reduced Modeling methods for the cross-lingual adaptation, and find that modeling partial word orders instead of the whole sequence can improve the robustness of the model against word order differences between languages and task knowledge transfer to low-resource languages. Third, we propose to leverage different levels of domain-related corpora and additional masking of data in the pre-training for the cross-domain adaptation, and discover that more challenging pre-training can better address the domain discrepancy issue in the task knowledge transfer. Finally, we introduce a coarse-to-fine framework, Coach, and a cross-lingual and cross-domain parsing framework, X2Parser. Coach decomposes the representation learning process into a coarse-grained and a fine-grained feature learning, and X2Parser simplifies the hierarchical task structures into flattened ones. We observe that simplifying task structures makes the representation learning more effective for low-resource languages and domains.