Scaling LLM Knowledge Boundaries via Distribution-Optimized Synthesis

Knowledge injection via synthetic data is crucial for enhancing Large Language Models (LLMs). However, current synthesis methods simply stop at preset token counts or fixed data ratios, lacking awareness of knowledge distribution. This results in some domains being sparse while others are redundant, limiting LLM knowledge boundaries. We revisit knowledge injection from a distribution perspective and hypothesize that an optimal knowledge distribution exists to maximize knowledge boundary expansion. We propose KDoS (Knowledge Distribution-optimized Synthesis), a framework that introduces knowledge density to drive synthesis through a three-stage feedback mechanism, shifting from blind generation to distribution-optimized synthesis. We construct Wikipedia-based synthetic data with varying knowledge distributions and conduct experiments on models from 0.6B to 16B (Qwen, Ling, LLaMA) and data scales from 1B to 5B tokens. Our key findings are: (1) an optimal knowledge distribution consistently maximizes boundary expansion; (2) this distribution is stable across backbones and scales; (3) KDoS outperforms baselines across six knowledge benchmarks. Our work offers a new perspective and practical framework for synthetic data-driven knowledge injection.

Symbolic and Abstractive Reasoning with Complex Visual Queries

Understanding and reasoning over abstract visual content remains a challenge for current multi-modal large language models (MLLMs). In this paper, we explore a novel abstract data type termed complex visual query (CVQ), designed to probe symbolic and abstractive reasoning, which is a critical yet underexplored dimension of human-like neuro-symbolic reasoning for MLLMs. We present a comprehensive investigation from three perspectives: \textbf{Data $\times$ Paradigm $\times$ Exploration}. Specifically, we propose a scalable pipeline for synthesizing CVQs grounded in large-scale multi-modal knowledge graphs, generating a diverse dataset encompassing 14 distinct query types via systematic combinations of first-order logic operators. We further introduce a two-stage training framework that progressively equips MLLMs with robust visual reasoning capabilities. We conduct extensive experiments to rigorously evaluate MLLMs across multiple dimensions, including reasoning performance on CVQs, as well as cross-task and cross-scenario generalization. We believe our work opens new perspectives and avenues for advancing the reasoning frontiers of MLLMs.