Latent Space Refinement for Intrinsic Multi-Step Reasoning Umair Akbar · Follow 81 min read · Just now — Abstract Multi-step reasoning in neural networks remains fragile and externally dependent in existing paradigms. We present Latent Space Refinement — a theoretical framework that internalizes reasoning as smooth trajectories on a Riemannian manifold embedded in a model’s latent space. By unifying differential geometry, contrastive self-supervision, energy-based modeling, and Morse-theoretic topology , we rigorously derive conditions under which a neural network can intrinsically perform multi-step inference with stability and coherence. We prove that our latent refinement paradigm yields geodesic reasoning paths that minimize abrupt jumps, ensuring each intermediate inference state lies on a high-density, plausible manifold region. Formal theorems establish that this approach guarantees convergence to correct solutions under mild topological constraints, […]
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