Training Large Language Models (LLMs) to process extensive context lengths incurs prohibitive computational costs. Prevailing techniques for extending context capabilities in LLMs typically require not only additional training procedures but also access to datasets with long context (e.g., sequences of 32K tokens), presupposing substantial GPU expenditures. To address the aforementioned issues, we introduce a novel solution named Efficient and Extreme length extension for Large Language Models (E2-LLM). E2-LLM entails a singular training process over considerably short sequences (e.g., 4K tokens), which greatly mitigates the cost of continual-pretraining or fine-tuning. Within the training phase, we incorporate a dual augmentation strategy with Rotary Position Embeddings (RoPE) that adjusts the scale and position indices across distinct training samples. E 2 -LLM is meticulously designed to enhance the model’s robustness to diverse relative positions. The experimental results on multiple benchmark datasets demonstrate the superior performance of E 2 -LLM on demanding tasks of processing long contexts.

This paper introduces ConceptMath, a bilingual (English and Chinese), fine-grained benchmark that evaluates concept-wise mathematical reasoning of Large Language Models (LLMs). Unlike traditional benchmarks that evaluate general mathematical reasoning with an average accuracy, ConceptMath systemically organizes math problems under a hierarchy of math concepts, so that mathematical reasoning can be evaluated at different granularity with concept-wise accuracies. Based on our ConcepthMath, we then evaluate a broad range of LLMs, and we observe existing LLMs, though achieving high average accuracies on traditional benchmarks, exhibit significant performance variations across different math concepts and may even fail catastrophically on the most basic ones. Besides, we also introduce an efficient fine-tuning strategy to enhance the weaknesses of existing LLMs. Finally, we hope ConceptMath could guide the developers to understand the fine-grained mathematical abilities of their models and facilitate the growth of foundation models. Code is available at https://github.com/conceptmath/conceptmath.