Research map / Probabilistic and scientific modeling / Differential equations and PDEs
A Solvable High-Dimensional Model of GAN
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Model the generator and discriminator with finite-dimensional feature parameters while letting data dimension grow | Single-layer linear GAN · High-dimensional limit | macroscopic dynamics: C(T)/√n | Helped |
| Retain finite-step stochasticity in the microscopic dynamics rather than taking a small-learning-rate deterministic limit | Single-layer linear GAN · High-dimensional limit | microscopic dynamics | Helped |
| Use an intermediate background-noise level satisfying the stated stability condition | Single-layer linear GAN · Feature recovery | feature recovery: 1/2 max_ℓ {Λ_ℓ − Λ̃_ℓ + αΛ̃_ℓ} ≤ τ overline{η²} < min_ℓ Λ_ℓ | Helped |
| Increase background noise until a feature's signal-to-noise ratio falls below the stated threshold | Single-layer linear GAN · Feature recovery | feature recovery: Λ_ℓ < τ overline{η²} | Hurt |
| Reduce background noise below the stability condition | Single-layer linear GAN · Training dynamics | convergence stability | Hurt |
| Take the small-learning-rate limit and let the learning-rate ratio tend to zero | Single-layer linear GAN · Feature recovery | feature alignment: P* = I | Helped |
| Use a single-feature discriminator while training a generator with multiple features | Single-layer linear GAN · Numerical simulation, d=2 | feature recovery | Helped |
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