Explicit unit-circle and neighbor losses impose a 2D timbre space

Limberg, Zhang, Schulz & Weinzierl train a VAE (pGESAM) encoding EnCodec audio embeddings into a 2D timbre latent space disentangled from pitch, with a downstream Transformer generating audio from a chosen (timbre, pitch) pair [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space] The 2D circular geometry is imposed by explicit loss terms, not emergent: an L2-norm hinge loss constrains latent means within the unit circle and an attractive/repulsive neighbor loss forms the instrument clusters [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space] Disentanglement is quantified by a component-wise variance ratio: within-instrument-across-pitch variance (~1.1e-7) is six orders of magnitude below across-instrument-within-pitch variance (0.179) [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space] V_pitch ~0.179 approaches the ~0.25 value expected for points spread near-uniformly across the unit disc [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space] A four-configuration loss ablation attributes geometry to specific terms: removing the neighbor loss collapses V_pitch to ~2e-3 (points crowd the origin), while removing the family classifier slightly raises V_inst [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space] A 2D scatter confirms macro-clusters by instrument family and micro-clusters by individual instrument appearing as near-single points [limberg-etal-2025-pitch-conditioned-instrument-sound-synthesis-interactive-timbre-latent-space]