AnchorSim targets the collapse mechanism directly. It is built on two complementary signals: a contrastive anchor that forces predictions with and without the visual pathway to differ, and a simulation-anchored teacher that supplies reasoning targets which actually consume those latents.
1. Contrastive Latent Anchoring
For every reasoning step we form two next-token distributions from the student policy \(\pi_S\): one conditioned on the full context \(C_{<k}\), and one on a visual-blind context \(\tilde C_{<k}\) where all previously generated latents \(\{z_1,\ldots,z_{k-1}\}\) are masked out. We then penalize agreement between the two, since agreement means the visual stream contributed nothing:
\[\mathcal{L}_\text{anchor}(\theta) = -\,\mathbb{E}_{\mathcal{T},k}\!\left[\frac{1}{|t_k|}\sum_{n=1}^{|t_k|} \mathrm{JSD}\!\Bigl(\pi_S(\cdot \mid C_{<k}, t_{k,<n}) \,\Big\|\, \mathrm{sg}\bigl[\pi_S(\cdot \mid \tilde C_{<k}, t_{k,<n})\bigr]\Bigr)\right]\]
The stop-gradient on the blind branch prevents the model from degrading its blind pass to "win" the contrast, so the only way to increase the divergence is to make the latent-aware pass carry real, consequential visual content.
2. Anchored Reasoning Distillation
Contrastive anchoring says use the latents; distillation says use them well. We keep an exponential-moving-average teacher \(\pi_T\) that shares the student's architecture but is conditioned on the ground-truth answer as a privileged prefix. This lets the teacher interpret each student-generated latent \(z_{k-1}\) and produce a textual reasoning chunk that coherently bridges the visual state to the correct answer. The student distills this answer-anchored reasoning:
\[\mathcal{L}_\text{distill}(\theta) = \mathbb{E}_{\mathcal{T},k}\!\left[\frac{1}{|t_k|}\sum_{n=1}^{|t_k|} \mathrm{JSD}\!\Bigl(\pi_T(\cdot \mid C_{<k}, a, t_{k,<n}) \,\Big\|\, \pi_S(\cdot \mid C_{<k}, t_{k,<n})\Bigr)\right]\]
The AnchorSim Objective
The full training loss combines the two signals:
\[\mathcal{L}_\text{AnchorSim}(\theta) = \mathcal{L}_\text{distill}(\theta) + \lambda\,\mathcal{L}_\text{anchor}(\theta)\]
At inference, the visual-blind branch is discarded and the model simply generates standard interleaved trajectories, now with latents that are causally consequential to the answer.