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is the number of parameters in the model. is the number of tokens in the training set. is the average negative log-likelihood loss per token (nats/token), achieved by the trained LLM on the test dataset. represents the loss of an ideal generative process on the test data
For convolutional networks, the filter size also affects the number of parameters. Limiting the number of parameters restricts the predictive power of the network directly, reducing the complexity of the function that it can perform on the data, and thus limits the amount of overfitting. This is equivalent to a "zero norm".
In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer).
A common use of the phrase "ANN model" is really the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons, number of layers or their connectivity).
The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size. [citation needed] The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers. [citation needed]
The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. [5] The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization ...
The NTK can be studied for various ANN architectures, [2] in particular convolutional neural networks (CNNs), [19] recurrent neural networks (RNNs) and transformers. [20] In such settings, the large-width limit corresponds to letting the number of parameters grow, while keeping the number of layers fixed: for CNNs, this involves letting the number of channels grow.
In a neural network, batch normalization is achieved through a normalization step that fixes the means and variances of each layer's inputs. Ideally, the normalization would be conducted over the entire training set, but to use this step jointly with stochastic optimization methods, it is impractical to use the global information.