TRAM: Enhancing Multimodal Reasoning with Trajectory-Derived Auxiliary Memory

Multimodal Large Reasoning Models (MLRMs) have achieved strong performance on tasks requiring visual understanding and multi-step inference. However, as reasoning trajectories grow, models may become less effective at using information established earlier in the context, increasing the risk of reasoning errors. Existing approaches primarily address this problem by sustaining visual grounding throughout reasoning. However, reasoning also transforms visual observations into task-specific relations, constraints, and intermediate conclusions whose influence may weaken over long trajectories. Our attribution analysis suggests that correctness is not consistently separated by image attribution alone, but is more closely associated with whether trajectories retain and integrate such reasoning-derived information across stages. Motivated by this, we introduce TRAM (TRajectory-derived Auxiliary Memory), a training-free method that augments standard decoding with an auxiliary memory pathway derived from the model's own reasoning trajectory. TRAM consolidates completed reasoning into a compact latent memory, updates it online through fast and slow recurrent streams, and feeds it back into selected decoder layers through a lightweight residual pathway. Experiments across four MLRM variants on eight benchmarks show that TRAM improves performance over vanilla decoding on mathematical, scientific, and general visual reasoning tasks without additional training.