High-quality long-context data is essential for training large language models (LLMs) capable of processing extensive documents, yet existing synthesis approaches using relevance-based aggregation face challenges of computational efficiency. We present LiteLong, a resource-efficient method for synthesizing long-context data through structured topic organization and multi-agent debate. Our approach leverages the BISAC book classification system to provide a comprehensive hierarchical topic organization, and then employs a debate mechanism with multiple LLMs to generate diverse, high-quality topics within this structure. For each topic, we use lightweight BM25 retrieval to obtain relevant documents and concatenate them into 128K-token training samples. Experiments on HELMET and Ruler benchmarks demonstrate that LiteLong achieves competitive long-context performance and can seamlessly integrate with other long-dependency enhancement methods. LiteLong makes high-quality long-context data synthesis more accessible by reducing both computational and data engineering costs, facilitating further research in long-context language training.

Layer normalization (LN) is a ubiquitous technique in deep learning but our theoretical understanding to it remains elusive. This paper investigates a new theoretical direction for LN, regarding to its nonlinearity and representation capacity. We investigate the representation capacity of a network with layerwise composition of linear and LN transformations, referred to as LN-Net. We theoretically show that, given $m$ samples with any label assignment, an LN-Net with only 3 neurons in each layer and $O(m)$ LN layers can correctly classify them. We further show the lower bound of the VC dimension of an LN-Net. The nonlinearity of LN can be amplified by group partition, which is also theoretically demonstrated with mild assumption and empirically supported by our experiments. Based on our analyses, we consider to design neural architecture by exploiting and amplifying the nonlinearity of LN, and the effectiveness is supported by our experiments.