Color plays an important role in human perception and usually provides critical clues in visual reasoning. However, it is unclear whether and how vision-language models (VLMs) can perceive, understand, and leverage color as humans.This paper introduces ColorBench, an innovative benchmark meticulously crafted to assess the capabilities of VLMs in color understanding, including color perception, reasoning, and robustness. By curating a suite of diverse test scenarios, with grounding in real applications, ColorBench evaluates how these models perceive colors, infer meanings from color-based cues, and maintain consistent performance under varying color transformations. Through an extensive evaluation of 32 VLMs with varying language models and vision encoders, our paper reveals some undiscovered findings: (i) The scaling law (larger models are better) still holds on ColorBench, while the language model plays a more important role than the vision encoder. (ii) However, the performance gaps across models are relatively small, indicating that color understanding has been largely neglected by existing VLMs. (iii) CoT reasoning improves color understanding accuracies and robustness, though they are vision-centric tasks. (iv) Color clues are indeed leveraged by VLMs on ColorBench but they can also mislead models in some tasks.These findings highlight the critical limitations of current VLMs and underscore the need to enhance color comprehension. Our ColorBench can serve as a foundational tool for advancing the study of human-level color understanding of multimodal AI.

Neural network capability in symbolic computation has emerged in much recent work. However, symbolic computation is always treated as an end-to-end blackbox prediction task, where human-like symbolic deductive logic is missing. In this paper, we argue that any complex symbolic computation can be broken down to a sequence of finite Fundamental Computation Transformations (FCT), which are grounded as certain mathematical expression computation transformations. The entire computation sequence represents a full human understandable symbolic deduction process. Instead of studying on different end-to-end neural network applications, this paper focuses on approximating FCT which further build up symbolic deductive logic. To better mimic symbolic computations with math expression transformations, we propose a novel tree representation learning architecture GATE (Graph Aggregation Transformer Encoder) for math expressions. We generate a large-scale math expression transformation dataset for training purpose and collect a real-world dataset for validation. Experiments demonstrate the feasibility of producing step-by-step human-like symbolic deduction sequences with the proposed approach, which outperforms other neural network approaches and heuristic approaches.