Formalizing Latent Visual Reasoning: A Theoretical Framework for Token Dynamics

TL;DR: What if we could write down equations for how latent visual reasoning tokens work, just like in physics or logic? Developing a formal model could help us understand, predict, and improve their behavior.

Research Question: Can we develop a formal mathematical or logical framework to describe the dynamics and properties of latent visual reasoning tokens, enabling principled analysis and improvement?

Hypothesis: A formalization—drawing on recent work in perception tokens (Bigverdi et al., 2024) and differentiable physics models (Ding et al., 2021)—will reveal the strengths and weaknesses of latent token mechanisms and suggest new, principled architectural or training modifications.

Experiment Plan: Develop mathematical models describing token formation, interaction, and information flow (e.g., as graphical models or differentiable simulators). Simulate and analyze these models to predict when certain token configurations yield robust abstraction or fail to capture critical scene structure. Validate predictions empirically by comparing model behavior to theoretical expectations on synthetic and real-world datasets. Use insights to propose and test new token regularization or dynamic adaptation strategies.

References:

• Bigverdi, M., Luo, Z., Hsieh, C.-Y., Shen, E., Chen, D., Shapiro, L., & Krishna, R. (2024). Perception Tokens Enhance Visual Reasoning in Multimodal Language Models. Computer Vision and Pattern Recognition.
• Ding, M., Chen, Z., Du, T., Luo, P., Tenenbaum, J., & Gan, C. (2021). Dynamic Visual Reasoning by Learning Differentiable Physics Models from Video and Language. Neural Information Processing Systems.
• Li, K., Shang, C., Karlinsky, L., Feris, R., Darrell, T., & Herzig, R. (2025). Latent Implicit Visual Reasoning.