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, 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.

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 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.

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.

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.

Revealing Language Model Trajectories via Kullback-Leibler Divergence

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.

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.

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.

Towards Visuospatial Cognition via Hierarchical Fusion of Visual Experts

While Multimodal Large Language Models (MLLMs) excel at general vision-language tasks, visuospatial cognition - reasoning about spatial layouts, relations, and dynamics - remains a significant challenge. Existing models often lack the necessary architectural components and specialized training data for fine-grained spatial understanding. We introduce ViCA2 (Visuospatial Cognitive Assistant 2), a novel MLLM designed to enhance spatial reasoning. ViCA2 features a dual vision encoder architecture integrating SigLIP for semantics and Hiera for spatial structure, coupled with a token ratio control mechanism for efficiency. We also developed ViCA-322K, a new large-scale dataset with over 322,000 spatially grounded question-answer pairs for targeted instruction tuning. On the challenging VSI-Bench benchmark, our ViCA2-7B model achieves a state-of-the-art average score of 56.8, significantly surpassing larger open-source models (e.g., LLaVA-NeXT-Video-72B, 40.9) and leading proprietary models (Gemini-1.5 Pro, 45.4). This demonstrates the effectiveness of our approach in achieving strong visuospatial intelligence with a compact model. We release ViCA2, its codebase, and the ViCA-322K dataset to facilitate further research.

Visuospatial Cognitive Assistant

Video-based spatial cognition is vital for robotics and embodied AI but challenges current Vision-Language Models (VLMs). This paper makes two key contributions. First, we introduce ViCA (Visuospatial Cognitive Assistant)-322K, a diverse dataset of 322,003 QA pairs from real-world indoor videos (ARKitScenes, ScanNet, ScanNet++), offering supervision for 3D metadata-grounded queries and video-based complex reasoning. Second, we develop ViCA-7B, fine-tuned on ViCA-322K, which achieves new state-of-the-art on all eight VSI-Bench tasks, outperforming existing models, including larger ones (e.g., +26.1 on Absolute Distance). For interpretability, we present ViCA-Thinking-2.68K, a dataset with explicit reasoning chains, and fine-tune ViCA-7B to create ViCA-7B-Thinking, a model that articulates its spatial reasoning. Our work highlights the importance of targeted data and suggests paths for improved temporal-spatial modeling. We release all resources to foster research in robust visuospatial intelligence.

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.