# InfluenceField: A Differentiable Field with Interventionally Identifiable Causal Structure for Multimodal World Modeling

arXiv: https://arxiv.org/abs/2609.07874 · HTML: https://mlsanity.com/paper/2609.07874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 1 of its 47 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 1 of 1)

- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)

## Abstract (arXiv)

Multimodal large language models often capture visual-linguistic correlations but struggle to predict how local visual interventions propagate and affect downstream answers. We introduce InfluenceField, an intervention-aware latent field inserted between the visual encoder and language decoder. It lifts patch features into a continuous spatial representation, propagates directed influence over multiple steps, and predicts local intervention effects through a shared transition operator. Training jointly optimizes language modeling, cross-environment invariance, counterfactual rollout supervision, and structural regularization. For a nonlinear finite-basis population model, we show that target-aligned interventional supervision, together with a one-step separation condition on the transition, restricts admissible representations to within-location reparameterizations, so that the directed dependency graph of the full transition is recovered exactly. A linear specialization gives an exact partial-coverage characterization and a finite-loss stability bound, and the field analysis derives the spatial profile of coefficient interventions together with a shared-channel calibration result. On CausalVQA, InfluenceField improves overall accuracy over its backbone by 13.1 percentage points, with the largest gains on the planning and hypothetical categories. Capacity-matched baselines and structural controls attribute the gains in robustness and factual-counterfactual consistency to the causal objectives rather than to added capacity.