Daily Papers

This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We rigorously analyze the diagonal empirical Fisher information matrix (FIM) in Adam, clarifying all detailed approximations and advocating for the use of log probability functions as loss, which should be based on discrete distributions, due to the limitations of empirical FIM. Our analysis uncovers flaws in the original Adam algorithm, leading to proposed corrections such as enhanced momentum calculations, adjusted bias corrections, and gradient clipping. We refine the weight decay term based on our theoretical framework. Our modified algorithm, Fisher Adam (FAdam), demonstrates superior performance across diverse domains including LLM, ASR, and VQ-VAE, achieving state-of-the-art results in ASR.

Contrastive learning has been attracting much attention for learning unsupervised sentence embeddings. The current state-of-the-art unsupervised method is the unsupervised SimCSE (unsup-SimCSE). Unsup-SimCSE takes dropout as a minimal data augmentation method, and passes the same input sentence to a pre-trained Transformer encoder (with dropout turned on) twice to obtain the two corresponding embeddings to build a positive pair. As the length information of a sentence will generally be encoded into the sentence embeddings due to the usage of position embedding in Transformer, each positive pair in unsup-SimCSE actually contains the same length information. And thus unsup-SimCSE trained with these positive pairs is probably biased, which would tend to consider that sentences of the same or similar length are more similar in semantics. Through statistical observations, we find that unsup-SimCSE does have such a problem. To alleviate it, we apply a simple repetition operation to modify the input sentence, and then pass the input sentence and its modified counterpart to the pre-trained Transformer encoder, respectively, to get the positive pair. Additionally, we draw inspiration from the community of computer vision and introduce a momentum contrast, enlarging the number of negative pairs without additional calculations. The proposed two modifications are applied on positive and negative pairs separately, and build a new sentence embedding method, termed Enhanced Unsup-SimCSE (ESimCSE). We evaluate the proposed ESimCSE on several benchmark datasets w.r.t the semantic text similarity (STS) task. Experimental results show that ESimCSE outperforms the state-of-the-art unsup-SimCSE by an average Spearman correlation of 2.02% on BERT-base.