01. Abstract & The Discontinuity Paradox
Classical simulation models multibody kinematics through discrete-time numerical integration of Newton-Euler differential equations. While mathematically sound in continuous time, discretization produces catastrophic failure modes at high actuator velocities: penetration tunneling, numerical stiffness divergence, and unbounded constraint solving times.
Nyxium NX-1 resolves this paradox by casting physical dynamics as an autoregressive neural prediction over continuous space-time manifolds. By replacing polyhedral mesh collision detection with continuous implicit Signed Distance Fields (SDFs) and Hamiltonian energy conservation constraints, NX-1 computes contact forces in constant Ο(1) time regardless of scene geometric complexity.
02. Continuous SE(3) Equivariant Architecture
A physical world model must be equivariant under translation and 3D spatial rotation. Let \(X \in \mathbb{R}^{N \times 3}\) represent spatial point tokens and \(V \in \mathbb{R}^{N \times 3}\) velocity vectors. Our transformation group satisfies:
Unlike naive vision transformers that require rotational data augmentation, NX-1 guarantees rotational equivariance at the layer level. Spatial Rotary Position Embeddings (S-RoPE) encode 3D spatial distances into attention weight matrices without breaking physical conservation of angular momentum.
03. Low-Latency Hardware Matrix Acceleration
To maintain a closed-loop robot control frequency of 1,000 Hz, end-to-end inference latency must not exceed 1,000 microseconds (1.0 ms).
Fused FP8 Matrix Kernels
Direct hardware register fusion eliminates SRAM-to-HBM intermediate round-trips. Attention and feed-forward operations execute within unified compute blocks.
Zero-Copy Shared Memory Interconnect
Robotics sensor streams (LiDAR, stereo cameras, tactile strain gauges) bypass CPU kernel drivers, writing directly to GPU virtual address spaces.