Patchless Continuous Vision: Autonomous Receptive Field Solitons on C^inf Manifolds Without Grid Tokenization

Vision Transformers and convolutional architectures partition visual space into discrete Cartesian grids, typically 16x16 or 4x4 pixel patches. Although computationally widespread, discrete partitioning imposes coordinate bias, fractures continuous edges across rigid boundaries, and restricts models to fixed token resolutions with quadratic self-attention complexity. We introduce Patchless Soliton Vision, a continuous visual formulation that eliminates discrete spatial slicing entirely. Visual fields are represented via an analytical linear superposition of K dynamic, anisotropic Gabor-Morlet solitons ψ_k(u, v) over a continuous spatial manifold Ω ⊂ ℝ² with C^∞ smoothness. Each continuous token functions as an autonomous physical wave packet possessing independent degrees of freedom: a dynamic receptive field center μ_k ∈ [-1, 1]², an adaptive anisotropic bandwidth σ_k ∈ ℝ⁺ × ℝ⁺, and an internal carrier wavevector k_k ∈ ℝ². Under Relativistic Euler-Lagrange phase flow with Lorentz velocity clamping (||θ̇|| < c), tokens autonomously foveate onto high-curvature contours and fine textures while expanding over smooth background fields, saturating the optimal Heisenberg-Gabor uncertainty bound Δx · Δk = 1/2. Empirical evaluations on synthetic manifolds, architectural scenes (scipy.datasets.ascent), and natural color images (CIFAR-10) demonstrate: 1. Zero-Shot C^∞ Continuous Super-Resolution: Up to 16x sample density with analytical sub-pixel continuity, eliminating bicubic grid aliasing;2. Semantic Handwritten Digit Perception: 91.33% test accuracy on 1,797 samples with strictly zero hidden layers, zero convolutions, and zero attention heads;3. Continuous SO(2) Lie Rotational Equivariance: Invariant representation energy under planar rotations without D₄ grid fracturing;4. Natural Photographic CIFAR-10 Compression: 16x raw pixel compression into continuous soliton embeddings, attaining 32.00% test accuracy under a flat linear readout (3.2x above chance). Open-Source Code & 60 FPS Interactive Laboratory: https://github.com/shu195/patchless-soliton-vision