Spectral-Progressive Thought Flow for Lightweight Multimodal Reasoning

Multimodal spatial reasoning often relies on long chains of intermediate textual and visual thoughts, where accumulating visual tokens and dense cross-modal attention incur substantial computation and memory overhead. To address this challenge, we propose Spectral-Progressive Thought Flow (SpecFlow), a novel lightweight multimodal spatial reasoning framework that represents intermediate visual thoughts in a fixed-size discrete cosine space. By exploiting strong energy compaction, SpecFlow preserves global layout and relational structure while introducing high-frequency details only when increased spatial precision is required. To align visual state evolution with linguistic intent, classifier-free guidance enables autoregressive textual thoughts to steer flow-based updates of the visual workspace/state without expanding the context. As a result, SpecFlow maintains a bounded visual workspace whose updates depend only on the current visual state and accumulated textual trace, enabling long-horizon inference with stable latency and memory usage independent of reasoning depth. Empirical results show that SpecFlow achieves competitive or superior reasoning performance while reducing computation and KV cache costs by up to 2.1 times.