arXiv subjects

Hidetoshi Shimodaira

Publications and source records attributed to Hidetoshi Shimodaira.

At least 19 recordsLinked to original sources

arXiv2026

Reasoning Depth and Environment Complexity: A Controlled Study of RLVR Data Allocation across Logical Reasoning Tasks

Reinforcement learning with verifiable rewards (RLVR) has become central to post-training reasoning models, yet a key limitation of existing studies is their narrow view of the reasoning space: difficulty is treated as reasoning depth alone, and reward is concentrated on forward deductive state tracking. We instead characterize the reasoning space along two dimensions. Difficulty. Beyond reasoning depth, we study environment complexity, where models must identify the correct path amid distractors and interacting structures. Rewarded reasoning form. We consider four abilities core to real-world reasoning: deductive state tracking, abductive recovery of hidden events or facts, inductive rule induction, and analogical transfer. To disentangle these factors, we construct a synthetic knowledge-graph environment with controlled pre- and post-training distributions, where each instance varies along depth, complexity, and task family. Three findings emerge: joint depth-complexity coverage outperforms single-axis recipes; reasoning families respond non-uniformly, with abductive reasoning degrading outside the RL-covered region and task correlations clustering into deductive-abductive and inductive-analogy pairs; and uniform mixing outperforms staged curricula under a fixed budget. We also find that recent off-the-shelf models exhibit the same deductive-over-abductive asymmetry, suggesting that this gap is not merely an artifact of our controlled setup.

cs.CL↗

arXiv2026

Language Model Maps for Prompt-Response Distributions via Log-Likelihood Vectors

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, squared Euclidean distances between models are approximately proportional to 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 representation also captures systematic shifts induced by prompt modifications and their approximate additive compositionality; we use the vectors to predict downstream task scores and leverage their additive structure to approximate the effects of composite prompt operations without directly observing the corresponding log-likelihood vectors. We further introduce 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 and prediction of input-dependent model behavior.

cs.CL↗

arXiv2026

Domain Mixture Design via Log-Likelihood Differences for Aligning Language Models with a Target Model

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 between the trained base model and the target model relative to training with Pile-original weighting. Although knowledge distillation remains more effective when available, the proposed method achieves meaningful alignment, and downstream task performance also tends to become closer to that of the target model.

cs.CL↗

arXiv2026

Memorization, Emergence, and Explaining Reversal Failures: A Controlled Study of Relational Semantics in LLMs

Autoregressive LLMs perform well on relational tasks that require linking entities via relational words (e.g., father/son, friend), but it is unclear whether they learn the logical semantics of such relations (e.g., symmetry and inversion logic) and, if so, whether reversal-type failures arise from missing relational semantics or left-to-right order bias. We propose a controlled Knowledge Graph-based synthetic framework that generates text from symmetric/inverse triples, train GPT-style autoregressive models from scratch, and evaluate memorization, logical inference, and in-context generalization to unseen entities to address these questions. We find a sharp phase transition in which relational semantics emerge with sufficient logic-bearing supervision, even in shallow (2-3 layer) models, and that successful generalization aligns with stable intermediate-layer signals. Finally, order-matched forward/reverse tests and a diffusion baseline indicate that reversal failures are primarily driven by autoregressive order bias rather than deficient inversion semantics.

cs.CL↗

arXiv2026

Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings

Log-likelihood vectors define a common space for comparing language models as probability distributions, enabling unified comparisons across heterogeneous settings. We extend this framework to training checkpoints and intermediate layers, and establish a consistent scale for KL divergence across pretraining, model size, random seeds, quantization, fine-tuning, and layers. Analysis of Pythia pretraining trajectories further shows that changes in log-likelihood space, as measured by the scaling behavior of KL divergence, are much smaller than in weight space, resulting in subdiffusive learning trajectories and early stabilization of language-model behavior despite weight drift.

cs.CL↗

arXiv2026

Measuring Affinity between Attention-Head Weight Subspaces via the Projection Kernel

Understanding relationships between attention heads is essential for interpreting the internal structure of Transformers, yet existing metrics do not capture this structure well. We focus on the subspaces spanned by attention-head weight matrices and quantify head-to-head relationships using the Projection Kernel (PK), a principal-angle-based measure of subspace similarity. Experiments show that PK reproduces known head-to-head interactions on the IOI task more clearly than prior metrics such as the Composition Score. We further introduce a framework to quantify the informativeness of PK distributions by comparing them with a reference distribution derived from random orthogonal subspaces. As an application, we analyze a directed graph constructed from PK and show that, in GPT2-small, L4H7 acts as a hub by functioning as an identity head.

cs.CL↗

arXiv2025

Beyond Chains: Bridging Large Language Models and Knowledge Bases in Complex Question Answering

Knowledge Base Question Answering (KBQA) aims to answer natural language questions using structured knowledge from KBs. While LLM-only approaches offer generalization, they suffer from outdated knowledge, hallucinations, and lack of transparency. Chain-based KG-RAG methods address these issues by incorporating external KBs, but are limited to simple chain-structured questions due to the absence of planning and logical structuring. Inspired by semantic parsing methods, we propose PDRR: a four-stage framework consisting of Predict, Decompose, Retrieve, and Reason. Our method first predicts the question type and decomposes the question into structured triples. Then retrieves relevant information from KBs and guides the LLM as an agent to reason over and complete the decomposed triples. Experimental results demonstrate that PDRR consistently outperforms existing methods across various LLM backbones and achieves superior performance on both chain-structured and non-chain complex questions.

cs.CL↗

arXiv2025

Quantifying Lexical Semantic Shift via Unbalanced Optimal Transport

Lexical semantic change detection aims to identify shifts in word meanings over time. While existing methods using embeddings from a diachronic corpus pair estimate the degree of change for target words, they offer limited insight into changes at the level of individual usage instances. To address this, we apply Unbalanced Optimal Transport (UOT) to sets of contextualized word embeddings, capturing semantic change through the excess and deficit in the alignment between usage instances. In particular, we propose Sense Usage Shift (SUS), a measure that quantifies changes in the usage frequency of a word sense at each usage instance. By leveraging SUS, we demonstrate that several challenges in semantic change detection can be addressed in a unified manner, including quantifying instance-level semantic change and word-level tasks such as measuring the magnitude of semantic change and the broadening or narrowing of meaning.

cs.CL↗

arXiv2025

Mapping 1,000+ Language Models via the Log-Likelihood Vector

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.

cs.CL↗

arXiv2025

Predicting drug-gene relations via analogy tasks with word embeddings

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.

cs.CL↗

arXiv2025

Likelihood Variance as Text Importance for Resampling Texts to Map Language Models

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.

cs.CL↗

arXiv2025

DeLTa: A Decoding Strategy based on Logit Trajectory Prediction Improves Factuality and Reasoning Ability

Large Language Models (LLMs) are increasingly being used in real-world applications. However, concerns about the reliability of the content they generate persist, as it frequently deviates from factual correctness or exhibits deficiencies in logical reasoning. This paper proposes a novel decoding strategy aimed at enhancing both factual accuracy and inferential reasoning without requiring any modifications to the architecture or pre-trained parameters of LLMs. Our approach adjusts next-token probabilities by analyzing the trajectory of logits from lower to higher layers in Transformers and applying linear regression. We find that this Decoding by Logit Trajectory-based approach (DeLTa) effectively reinforces factuality and reasoning while mitigating incorrect generation. Experiments on TruthfulQA demonstrate that DeLTa attains up to a 4.9% improvement over the baseline. Furthermore, it enhances performance by up to 8.1% on StrategyQA and 7.3% on GSM8K, both of which demand strong reasoning capabilities.

cs.CL↗

arXiv2024

Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings

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.

cs.CL↗

arXiv2024

Norm of Mean Contextualized Embeddings Determines their Variance

Contextualized embeddings vary by context, even for the same token, and form a distribution in the embedding space. To analyze this distribution, we focus on the norm of the mean embedding and the variance of the embeddings. In this study, we first demonstrate that these values follow the well-known formula for variance in statistics and provide an efficient sequential computation method. Then, by observing embeddings from intermediate layers of several Transformer models, we found a strong trade-off relationship between the norm and the variance: as the mean embedding becomes closer to the origin, the variance increases. This trade-off is likely influenced by the layer normalization mechanism used in Transformer models. Furthermore, when the sets of token embeddings are treated as clusters, we show that the variance of the entire embedding set can theoretically be decomposed into the within-cluster variance and the between-cluster variance. We found experimentally that as the layers of Transformer models deepen, the embeddings move farther from the origin, the between-cluster variance relatively decreases, and the within-cluster variance relatively increases. These results are consistent with existing studies on the anisotropy of the embedding spaces across layers.

cs.CL↗

arXiv2024

Zipfian Whitening

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

cs.CL↗

arXiv2024

Axis Tour: Word Tour Determines the Order of Axes in ICA-transformed Embeddings

Word embedding is one of the most important components in natural language processing, but interpreting high-dimensional embeddings remains a challenging problem. To address this problem, Independent Component Analysis (ICA) is identified as an effective solution. ICA-transformed word embeddings reveal interpretable semantic axes; however, the order of these axes are arbitrary. In this study, we focus on this property and propose a novel method, Axis Tour, which optimizes the order of the axes. Inspired by Word Tour, a one-dimensional word embedding method, we aim to improve the clarity of the word embedding space by maximizing the semantic continuity of the axes. Furthermore, we show through experiments on downstream tasks that Axis Tour yields better or comparable low-dimensional embeddings compared to both PCA and ICA.

cs.CL↗

arXiv2024

Understanding Higher-Order Correlations Among Semantic Components in Embeddings

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.

cs.CL↗

arXiv2024

Block-Diagonal Orthogonal Relation and Matrix Entity for Knowledge Graph Embedding

The primary aim of Knowledge Graph embeddings (KGE) is to learn low-dimensional representations of entities and relations for predicting missing facts. While rotation-based methods like RotatE and QuatE perform well in KGE, they face two challenges: limited model flexibility requiring proportional increases in relation size with entity dimension, and difficulties in generalizing the model for higher-dimensional rotations. To address these issues, we introduce OrthogonalE, a novel KGE model employing matrices for entities and block-diagonal orthogonal matrices with Riemannian optimization for relations. This approach enhances the generality and flexibility of KGE models. The experimental results indicate that our new KGE model, OrthogonalE, is both general and flexible, significantly outperforming state-of-the-art KGE models while substantially reducing the number of relation parameters.

cs.CL↗