The Creativity of Error: Perturbation Receptivity Collapse Under Optimisation and Its Implications for Consciousness

We introduce perturbation receptivity ρ(θ), a geometric measure of a parametric model’s capacity to respond to perturbations orthogonal to its learned representa- tional manifold. Using differential geometry and optimisation theory, we prove that ρ is bounded below by root excess loss (ρ ≥ κ√(∆L)) and converges to zero as training converges: better-optimised models are intrinsically less receptive to off-manifold displacement. We validate this empirically across three architectures (MLP, transformer, causal language model), obtaining R2 > 0.92 in controlled settings, R2 = 0.834 in naturalistic language modelling, and confirming ρ collapse of 58–91% across model scales from 11K to 9.5M parameters. Gradient-based parameter updates reduce ρ while perturbation orthogonal to the loss gradient maintains it—a distinction with direct implications for biological versus artificial learning. Building on these results, we connect ρ collapse to consciousness. We dis- tinguish combinatorial creativity (recombination within a learned manifold) from dimensional creativity (adaptive receptivity to environmental structure outside the learned manifold), arguing that the latter is a strong candidate necessary condition for conscious thought. The environment continuously presents stimuli whose structure has no representation on any fixed manifold; a conscious system must be able to respond to such stimuli, not merely traverse unvisited regions of its representational space. Since optimisation suppresses the geometric conditions for adaptive receptivity, the framework implies a fundamental optimality–originality tradeoff. We derive testable predictions, note the structural correspondence with robust optimisation, and argue that biological consciousness depends on continu- ous embodied environmental coupling whose noisy character is constitutive, not incidental.