Fanxu Meng

Fanxu Meng, Haotong Yang, Yiding Wang et al. · pku

The human brain is naturally equipped to comprehend and interpret visual information rapidly. When confronted with complex problems or concepts, we use flowcharts, sketches, and diagrams to aid our thought process. Leveraging this inherent ability can significantly enhance logical reasoning. However, current Large Language Models (LLMs) do not utilize such visual intuition to help their thinking. Even the most advanced version language models (e.g., GPT-4V and LLaVA) merely align images into textual space, which means their reasoning processes remain purely verbal. To mitigate such limitations, we present a Chain of Images (CoI) approach, which can convert complex language reasoning problems to simple pattern recognition by generating a series of images as intermediate representations. Furthermore, we have developed a CoI evaluation dataset encompassing 15 distinct domains where images can intuitively aid problem-solving. Based on this dataset, we aim to construct a benchmark to assess the capability of future multimodal large-scale models to leverage images for reasoning. In supporting our CoI reasoning, we introduce a symbolic multimodal large language model (SyMLLM) that generates images strictly based on language instructions and accepts both text and image as input. Experiments on Geometry, Chess and Common Sense tasks sourced from the CoI evaluation dataset show that CoI improves performance significantly over the pure-language Chain of Thoughts (CoT) baselines. The code is available at https://github.com/GraphPKU/CoI.

Haotong Yang, Fanxu Meng, Zhouchen Lin et al.

The pre-trained large language models (LLMs) have shown their extraordinary capacity to solve reasoning tasks, even on tasks that require a complex process involving multiple sub-steps. However, given the vast possible generation space of all the tasks, how the pretrained model learns the reasoning ability remains an open question. We firstly propose that an intrinsic structural constraint on the generated sequence of language-based reasoning -- we called it template-content structure (T-C structure) -- is the key to explain why LLMs can solve a large number of complex reasoning problems with limited training data by showing this structure can reduce the possible space from exponential level to linear level. Furthermore, by generalizing this structure to the hierarchical case, we demonstrate that models can achieve task composition, further reducing the space needed to learn from linear to logarithmic, thereby effectively learning on complex reasoning involving multiple steps. We provide both examples and formal theory of our T-C structure. We also experimentally validate the existence of the T-C structure in some current LLMs and its effectiveness for reasoning.

Yanan Li, Fanxu Meng, Muhan Zhang et al.

As Large Language Models (LLMs) are frequently updated, LoRA weights trained on earlier versions quickly become obsolete. The conventional practice of retraining LoRA weights from scratch on the latest model is costly, time-consuming, and environmentally detrimental, particularly as the diversity of LLMs and downstream tasks expands. This motivates a critical question: "How can we efficiently leverage existing LoRA weights to adapt to newer model versions?" To address this, we propose LoRASuite, a modular approach tailored specifically to various types of LLM updates. First, we compute a transfer matrix utilizing known parameters from both old and new LLMs. Next, we allocate corresponding layers and attention heads based on centered kernel alignment and cosine similarity metrics, respectively. A subsequent small-scale, skillful fine-tuning step ensures numerical stability. Experimental evaluations demonstrate that LoRASuite consistently surpasses small-scale vanilla LoRA methods. Notably, on backbone LLMs such as MiniCPM and Qwen, LoRASuite even exceeds the performance of full-scale LoRA retraining, with average improvements of +1.4 and +6.6 points on math tasks, respectively. Additionally, LoRASuite significantly reduces memory consumption by 5.5 GB and computational time by 78.23%.

Fanxu Meng, Pingzhi Tang, Fan jiang et al.

Decoder-only models generate tokens autoregressively by caching key/value vectors, but as the cache grows, inference becomes memory-bound. To address this issue, we introduce CLOVER (Cross-Layer Orthogonal Vectors), a novel approach that treats pairs of attention layers as a set of low-rank decompositions. CLOVER applies Singular Value Decomposition (SVD) to the \( Q \)-\( K \) and \( V \)-\( O \) pairs within each attention head. The resulting singular values can either guide pruning or serve as trainable parameters for efficient fine-tuning of all orthogonal vectors. After pruning or fine-tuning, these values are reintegrated into the model without increasing its parameter count. We apply CLOVER to various models, including GPT-2 XL, DeepSeek-V2-Lite, Whisper-Large-v3, Stable Diffusion XL, and LLaMA-3.2-11B-Vision. Our results demonstrate that CLOVER significantly improves pruning efficiency. For instance, the perplexity of pruning 70\% of the \( Q \)-\( K \) pairs in GPT-2 XL is similar to that of pruning just 8\% with vanilla methods. Fine-tuning the singular values further results in a full-rank update, outperforming state-of-the-art methods (LoRA, DoRA, HiRA, and PiSSA) by 7.6\%, 5.5\%, 3.8\%, and 0.7\%, respectively, on eight commonsense tasks for LLaMA-2 7B.