Perparameter

Perparameter, or per-parameter, is a design principle in which each parameter of a model or system is assigned its own configuration or treatment rather than applying a single global setting across all parameters. The concept is encountered in optimization, machine learning, and related fields, where parameters include weights, biases, or other tunable quantities. In a per-parameter approach, individual parameters can have distinct learning rates, regularization strengths, initialization scales, or pruning thresholds.

In practice, per-parameter configurations are often supported by adaptive optimization methods that maintain separate state for each parameter (for example, optimizers like Adam or RMSprop) or by explicit mappings from parameters to values. Per-parameter learning rates or regularization coefficients can offer more flexible fitting, especially in heterogeneous networks where different parameters contribute differently to the loss.

Advantages of per-parameter treatment include potential performance gains from finer-grained control, better accommodation of scale differences among parameters, and the ability to tailor optimization to specific parameters. Challenges include increased memory and computational cost, a higher risk of overfitting, and greater complexity in tuning and interpretability. Effective use often relies on automated hyperparameter optimization, meta-learning, or structured priors to manage the expanded parameter space.

Examples include per-parameter initialization variances (different sigma values for weights), per-parameter L2 penalties (lambda_i for each parameter), and per-parameter pruning thresholds or dropout probabilities. See also hyperparameter optimization, adaptive optimization, meta-learning, and regularization.