AMRITA: Controlled Singularities in Hydrodynamic State Space Models

Think of SSMs like water flowing through a pipe with friction: information enters, but the walls constantly drain energy until everything settles to stillness. Great for stability, terrible for remembering that one critical data point from 10,000 samples ago—it's been bled dry by the time you need it. AMRITA is like switching from a leaky pipe to a frictionless whirlpool: information doesn't drain, it circulates. The Pressure Operator acts like the walls of a container—it stops things from exploding outward, but nothing inside gets absorbed. Your signal stays in orbit instead of spiraling down the drain. The Singularity Gate is your anomaly detector built into the dynamics: when a high-energy input arrives (a fraud transaction, a rare event, a critical marker), the system expands to capture it rather than smoothing it away like noise. Normal inputs pass through; outliers get inscribed. Practical upshot: if you've ever watched an RNN or SSM "forget" something important because it happened too long ago—even though sequence length was technically handled—that's viscous decay doing its job. AMRITA suggests you can have bounded, stable states and persistent memory. The cost is sequential training; the gain is actually capturing dependencies your current models architecturally cannot.