Performing deliberate mathematical reasoning in visual contexts is a hallmark of expert-level Multimodal Large Language Models (MLLMs) and requires a sophisticated synthesis of perceptual grounding and symbolic logic. However, in the realm of mathematical functions, our investigation reveals a critical *modality interference phenomenon*: even advanced models, while performing textual computational reasoning, tend to disregard or misinterpret essential visual cues. To address this challenge, we propose **Func-R1**, which synergistically harmonizes precise visual perception and rigorous logical reasoning. Concretely, built upon an explicitly decoupled architecture, we employ a hierarchical post-training framework to progressively identify critical visual evidence and conduct in-depth theoretical reasoning. Furthermore, the *Perception-Aligned Theoretic Optimization (PATO)* strategy is proposed to steer policy updating towards internalizing fundamental theoretical properties while dynamically rectifying heterogeneous visual information throughout the reasoning process. Extensive experiments across diverse benchmarks demonstrate that Func-R1 delivers the optimal performance among open-source MLLMs, even surpassing GPT-5 with an 8.4% improvement on MathVerse’s function-oriented tasks.

While the massive scale of modern LLMs enables remarkable performance, their static, input-agnostic computational graph incurs substantial resource wastage and high latency during inference. Existing dynamic schemes, such as early-exit and layer-drop reduce FLOPs but break batch processing or introduce KV-cache inconsistency. We propose Deputy, a dynamic low-rank substitution framework that employs a lightweight decision module at each layer to dynamically determine the execution branch for different tokens: Attention layers choose between full and low-rank computation to mitigate the KV cache issue, while FFN layers additionally support skipping to further reduce computation. We fine-tune the LLM with LoRA and then derive an additional low-rank matrix C via a least-squares fit BC ≈ W_pre, where B is the shared LoRA matrix, so that only one extra low-rank matrix is introduced, effectively reducing memory overhead. Moreover, a hybrid KV cache strategy stores KV values generated by the low-rank branch, achieving a 38% reduction in cache storage. Experiments on Llama models demonstrate that Deputy reduces computation by approximately 40% compared to the original dense model while outperforming existing baseline methods.

Large language models (LLMs) have demonstrated state-of-the-art accuracies across various tasks. However, the latency of inference and the large GPU memory consumption of LLMs restrict their deployment performance. Recently, there have been some efficient attempts to quantize LLMs, yet inference with large batch size or long sequence still has the issue of being compute-bound. Fine-grained quantization methods have showcased their proficiency in achieving low-bit quantization for LLMs, while requiring FP16 data type for linear layer computations, which is time-consuming when dealing with large batch size or long sequence. In this paper, we introduce a method called FlattenQuant, which significantly reduces the maximum value of the tensor by flattening the larger channels in the tensor, to achieve low bit per-tensor quantization with minimal accuracy loss. Our experiments show that FlattenQuant can directly use 4 bits to achieve 48.29% of the linear layer calculation in LLMs, with the remaining layer using 8 bits. The 4-bit matrix multiplication introduced in the FlattenQuant method can effectively address the compute-bound caused by large matrix calculation. Our work achieves up to 2× speedup and 2.3× memory reduction for LLMs with negligible loss in accuracy.