Vili Kohonen

Tom Gustafsson, Antti Hannukainen, Vili Kohonen et al.

We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element method for the saddle point formulation where a Lagrange multiplier enforces the underlying constraint. The Nitsche method is then presented in a general minimization form, suitable for adding constraints to nonlinear finite element methods and allowing straightforward computational implementation with automatic differentation. This extends the method beyond classical boundary condition enforcement. To validate these ideas, we present Nitsche formulations for a range of problems in solid mechanics and give numerical evidence of the convergence rates of the Nitsche method.

Maxime Riché, Daniel Tan, Vili Kohonen et al.

Inoculation prompting is a selective generalization technique used against Emergent Misalignment. We introduce inoculation adapters (IA), which similarly diminish the optimization pressure to learn undesired traits by strengthening the trait at train time. Inoculation adapters are LoRAs that are trained and used over three steps: 1) trained on undesired traits; 2) attached frozen while a separate task adapter is trained on data exhibiting both desired and undesired traits; 3) at deployment, the IA is discarded, and only the task adapter is kept. We show across six model families and several undesired traits including emergent misalignment, that inoculation adapters are more effective at suppressing undesired traits, while avoiding two drawbacks of inoculation prompting: inoculation adapters can suppress capabilities and traits that cannot be reliably elicited by a prompt, and they introduce fewer surprising backdoors than inoculation prompting under our probes. While undesired traits are better suppressed by inoculation adapters, the retention of desired traits is not consistently improved upon inoculation prompting and remains a challenge for both techniques.