arXiv subjects

Chenyi Li

Publications and source records attributed to Chenyi Li.

22 records · Page 2Linked to original sources

arXiv2025

Formalization of Optimality Conditions for Smooth Constrained Optimization Problems

Optimality conditions are central to analysis of optimization problems, characterizing necessary criteria for local minima. Formalizing the optimality conditions within the type-theory-based proof assistant Lean4 provides a precise, robust, and reusable framework essential for rigorous verification in optimization theory. In this paper, we introduce a formalization of the first-order optimality conditions (also known as the Karush-Kuhn-Tucker (KKT) conditions) for smooth constrained optimization problems by beginning with concepts such as the Lagrangian function and constraint qualifications. The geometric optimality conditions are then formalized, offering insights into local minima through tangent cones. We also establish the critical equivalence between the tangent cone and linearized feasible directions under appropriate constraint qualifications. Building on these key elements, the formalization concludes the KKT conditions through the proof of the Farkas lemma. Additionally, this study provides a formalization of the dual problem and the weak duality property.

math.OC↗

arXiv2024

Formalization of Complexity Analysis of the First-order Algorithms for Convex Optimization

The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our goal is making a significant step forward in the formal mathematical representation of optimization techniques using the Lean4 theorem prover. We first formalize the gradient for smooth functions and the subgradient for convex functions on a Hilbert space, laying the groundwork for the accurate formalization of algorithmic structures. Then, we extend our contribution by proving several properties of differentiable convex functions that have not yet been formalized in Mathlib. Finally, a comprehensive formalization of these algorithms is presented. These developments are not only noteworthy on their own but also serve as essential precursors to the formalization of a broader spectrum of numerical algorithms and their applications in machine learning as well as many other areas.

math.OC↗

arXiv2022

Enhancing Speaking Styles in Conversational Text-to-Speech Synthesis with Graph-based Multi-modal Context Modeling

Comparing with traditional text-to-speech (TTS) systems, conversational TTS systems are required to synthesize speeches with proper speaking style confirming to the conversational context. However, state-of-the-art context modeling methods in conversational TTS only model the textual information in context with a recurrent neural network (RNN). Such methods have limited ability in modeling the inter-speaker influence in conversations, and also neglect the speaking styles and the intra-speaker inertia inside each speaker. Inspired by DialogueGCN and its superiority in modeling such conversational influences than RNN based approaches, we propose a graph-based multi-modal context modeling method and adopt it to conversational TTS to enhance the speaking styles of synthesized speeches. Both the textual and speaking style information in the context are extracted and processed by DialogueGCN to model the inter- and intra-speaker influence in conversations. The outputs of DialogueGCN are then summarized by attention mechanism, and converted to the enhanced speaking style for current utterance. An English conversation corpus is collected and annotated for our research and released to public. Experiment results on this corpus demonstrate the effectiveness of our proposed approach, which outperforms the state-of-the-art context modeling method in conversational TTS in both MOS and ABX preference rate.

cs.SD↗

arXiv2022

Embedding Decomposition for Artifacts Removal in EEG Signals

Electroencephalogram (EEG) recordings are often contaminated with artifacts. Various methods have been developed to eliminate or weaken the influence of artifacts. However, most of them rely on prior experience for analysis. Here, we propose an deep learning framework to separate neural signal and artifacts in the embedding space and reconstruct the denoised signal, which is called DeepSeparator. DeepSeparator employs an encoder to extract and amplify the features in the raw EEG, a module called decomposer to extract the trend, detect and suppress artifact and a decoder to reconstruct the denoised signal. Besides, DeepSeparator can extract the artifact, which largely increases the model interpretability. The proposed method is tested with a semi-synthetic EEG dataset and a real task-related EEG dataset, suggesting that DeepSeparator outperforms the conventional models in both EOG and EMG artifact removal. DeepSeparator can be extended to multi-channel EEG and data of any length. It may motivate future developments and application of deep learning-based EEG denoising. The code for DeepSeparator is available at https://github.com/ncclabsustech/DeepSeparator.

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