Loss Landscape Vocabulary Framework

v12 · April 2026 · Atlas Heritage Systems Inc. · Working document — not a finished product

Macro-Topology Shapes

Large-scale terrain features produced by the interaction of terrain properties across parameter space. Determines where models converge, stall, or drift. The archaeological signal Atlas seeks lives in specific topological regions.

Bowlsymmetric minimum

Inward gradients from all directions. Single smooth minimum. Stable convergence. Produces laminar flow. Archaeological signal absent — remagnetization likely complete.

Goodfellow et al. (2014) neural network optimization problems

Valleyelongated minimum

Two-sided inward gradients, flat floor. Stall-prone along valley axis. Flat minima generalize better than sharp ones.

Keskar et al. (2016); Izmailov et al. (2018) stochastic weight averaging

Saddle Pointdownhill / uphill

Downhill in some parameter directions, uphill in others. High-perplexity, turbulent. Primary archaeological territory — competing orientations were never resolved into clean convergence here.

Dauphin et al. (2014) saddle point problem in high-dimensional optimization

Plateaustalled

Near-zero gradient everywhere. No signal. Training dies silently. Highest effective drag. Vanishing gradient problem is plateau behavior.

Glorot & Bengio (2010) vanishing gradient; Ioffe & Szegedy (2015) batch normalization

Ridgebasin boundary

High curvature boundary between basins. Unstable traversal. Which side you fall to matters — determines which attractor captures the model.

Li et al. (2018) initialization and optimization role

Basinwide / narrow

The catchment region around a minimum. Wide basins generalize better. Narrow basins are sensitive to perturbation. The model's training path determines which basin it occupies.

basin width ∝ 1/max(λ_i) of local Hessian

Keskar et al. (2016); Izmailov et al. (2018)