Momose Oyama

Momose Oyama, Sho Yokoi, Hidetoshi Shimodaira

Distributed representations of words encode lexical semantic information, but what type of information is encoded and how? Focusing on the skip-gram with negative-sampling method, we found that the squared norm of static word embedding encodes the information gain conveyed by the word; the information gain is defined by the Kullback-Leibler divergence of the co-occurrence distribution of the word to the unigram distribution. Our findings are explained by the theoretical framework of the exponential family of probability distributions and confirmed through precise experiments that remove spurious correlations arising from word frequency. This theory also extends to contextualized word embeddings in language models or any neural networks with the softmax output layer. We also demonstrate that both the KL divergence and the squared norm of embedding provide a useful metric of the informativeness of a word in tasks such as keyword extraction, proper-noun discrimination, and hypernym discrimination.

Momose Oyama, Hiroaki Yamagiwa, Hidetoshi Shimodaira

Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this assumption. Consequently, non-independencies remain between the estimated components, which ICA cannot eliminate. We quantified these non-independencies using higher-order correlations and demonstrated that when the higher-order correlation between two components is large, it indicates a strong semantic association between them, along with many words sharing common meanings with both components. The entire structure of non-independencies was visualized using a maximum spanning tree of semantic components. These findings provide deeper insights into embeddings through ICA.

Yusuke Takase, Momose Oyama, Hidetoshi Shimodaira

We propose a method that represents language models by log-likelihood vectors over prompt-response pairs and constructs model maps for comparing their conditional distributions. In this space, distances between models approximate the KL divergence between the corresponding conditional distributions. Experiments on a large collection of publicly available language models show that the maps capture meaningful global structure, including relationships to model attributes and task performance. The method also captures systematic shifts induced by prompt modifications and their approximate additive compositionality, suggesting a way to analyze and predict the effects of composite prompt operations. We further introduce pointwise mutual information (PMI) vectors to reduce the influence of unconditional distributions; in some cases, PMI-based model maps better reflect training-data-related differences. Overall, the framework supports the analysis of input-dependent model behavior.

Ryo Kishino, Riku Shiomi, Hiroaki Yamagiwa et al.

Instead of directly distilling a language model, this study addresses the problem of aligning a base model with a target model in distribution by designing the domain mixture of training data for pretraining or continued pretraining as a fixed training recipe. We propose a method for determining domain weights by viewing models as points in log-likelihood space and aligning the training update direction with the direction toward the target model. Experiments with NanoGPT show that the proposed method consistently reduces the KL divergence to the target model compared with uniform weighting over the Pile. Although knowledge distillation remains more effective when available, the proposed method still achieves meaningful alignment, and downstream task performance also tends to become closer to that of the target model.

Momose Oyama, Hiroaki Yamagiwa, Yusuke Takase et al.

To compare autoregressive language models at scale, we propose using log-likelihood vectors computed on a predefined text set as model features. This approach has a solid theoretical basis: when treated as model coordinates, their squared Euclidean distance approximates the Kullback-Leibler divergence of text-generation probabilities. Our method is highly scalable, with computational cost growing linearly in both the number of models and text samples, and is easy to implement as the required features are derived from cross-entropy loss. Applying this method to over 1,000 language models, we constructed a "model map," providing a new perspective on large-scale model analysis.

Momose Oyama, Ryo Kishino, Hiroaki Yamagiwa et al.

We address the computational cost of constructing a model map, which embeds diverse language models into a common space for comparison via KL divergence. The map relies on log-likelihoods over a large text set, making the cost proportional to the number of texts. To reduce this cost, we propose a resampling method that selects important texts with weights proportional to the variance of log-likelihoods across models for each text. Our method significantly reduces the number of required texts while preserving the accuracy of KL divergence estimates. Experiments show that it achieves comparable performance to uniform sampling with about half as many texts, and also facilitates efficient incorporation of new models into an existing map. These results enable scalable and efficient construction of language model maps.

Ryo Kishino, Yusuke Takase, Momose Oyama et al.

A recently proposed method enables efficient estimation of the KL divergence between language models, including models with different architectures, by assigning coordinates based on log-likelihood vectors. To better understand the behavior of this metric, we systematically evaluate KL divergence across a wide range of conditions using publicly available language models. Our analysis covers comparisons between pretraining checkpoints, fine-tuned and base models, and layers via the logit lens. We find that trajectories of language models, as measured by KL divergence, exhibit a spiral structure during pretraining and thread-like progressions across layers. Furthermore, we show that, in terms of diffusion exponents, model trajectories in the log-likelihood space are more constrained than those in weight space.

Hiroaki Yamagiwa, Momose Oyama, Hidetoshi Shimodaira

Cosine similarity is widely used to measure the similarity between two embeddings, while interpretations based on angle and correlation coefficient are common. In this study, we focus on the interpretable axes of embeddings transformed by Independent Component Analysis (ICA), and propose a novel interpretation of cosine similarity as the sum of semantic similarities over axes. The normalized ICA-transformed embeddings exhibit sparsity, enhancing the interpretability of each axis, and the semantic similarity defined by the product of the components represents the shared meaning between the two embeddings along each axis. The effectiveness of this approach is demonstrated through intuitive numerical examples and thorough numerical experiments. By deriving the probability distributions that govern each component and the product of components, we propose a method for selecting statistically significant axes.

Hiroaki Yamagiwa, Ryoma Hashimoto, Kiwamu Arakane et al.

Natural language processing (NLP) is utilized in a wide range of fields, where words in text are typically transformed into feature vectors called embeddings. BioConceptVec is a specific example of embeddings tailored for biology, trained on approximately 30 million PubMed abstracts using models such as skip-gram. Generally, word embeddings are known to solve analogy tasks through simple vector arithmetic. For example, subtracting the vector for man from that of king and then adding the vector for woman yields a point that lies closer to queen in the embedding space. In this study, we demonstrate that BioConceptVec embeddings, along with our own embeddings trained on PubMed abstracts, contain information about drug-gene relations and can predict target genes from a given drug through analogy computations. We also show that categorizing drugs and genes using biological pathways improves performance. Furthermore, we illustrate that vectors derived from known relations in the past can predict unknown future relations in datasets divided by year. Despite the simplicity of implementing analogy tasks as vector additions, our approach demonstrated performance comparable to that of large language models such as GPT-4 in predicting drug-gene relations.

Hiroaki Yamagiwa, Momose Oyama, Hidetoshi Shimodaira

This study utilizes Independent Component Analysis (ICA) to unveil a consistent semantic structure within embeddings of words or images. Our approach extracts independent semantic components from the embeddings of a pre-trained model by leveraging anisotropic information that remains after the whitening process in Principal Component Analysis (PCA). We demonstrate that each embedding can be expressed as a composition of a few intrinsic interpretable axes and that these semantic axes remain consistent across different languages, algorithms, and modalities. The discovery of a universal semantic structure in the geometric patterns of embeddings enhances our understanding of the representations in embeddings.