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Edge stability is a phenomenon of large-step-size gradient descent training discovered in recent years: when the step size exceeds the classical stability threshold, the loss does not diverge; instead, sharpness fluctuates around a critical value and the loss still converges.
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11/6/2026
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UnverifiedFor finite step sizes, even if a stationary point is unstable under continuous-time gradient flow, if the step size is too large it may skip over the escape direction and cause numerical divergence, while if the step size is too small the escape time may grow exponentially and appear as stagnation.75% similarUnverifiedStandard backpropagation is essentially a discrete iteration of gradient descent, and when the learning rate is regarded as an infinitesimally small time step, this discrete process converges to the gradient flow ordinary differential equation dθ/dt = −∇L(θ).71% similarUnverifiedOrdinary gradient descent is equivalent to solving the gradient flow ODE using the explicit Euler method, and the Euler method is extremely inefficient when facing stiff equations, requiring very small step sizes to maintain stability.70% similarUnverifiedIn a closed-loop system, the two objectives of optimizing the offline loss and guaranteeing closed-loop stability are not aligned, and the former may even actively select parameters that cause trajectory divergence.69% similarUnverifiedGradient descent naturally tends to select flatter, simpler solutions from among the many solutions that perfectly fit the training set, and this implicit regularization effect is closely related to generalization ability.69% similar
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