Unlike other deep learning frameworks, JAX does not maintain gradients within the parameter objects themselves because the parameters and the network architecture are decoupled. Instead of tracking gradients over neural network parameters directly, JAX allows the user to express their computation as a pure Python function and applies the grad transformation to compute derivatives.

JAX Gradient Tracking and Transformation

In Flax and JAX, the model architecture and its parameters are decoupled. When a model is defined via the `Sequential` class, the network must first be initialized to generate a dictionary of parameters. A specific layer's parameters can then be accessed using the keys of this dictionary. For example, `params['params']['layers_2']` retrieves the parameters for a layer designated as `layers_2`, returning a `FrozenDict` that contains the `kernel` (weights) and `bias` arrays.

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In deep learning frameworks, the parameters of any specific layer within a `Sequential` model can be accessed systematically. For most frameworks, this involves indexing directly into the model as if it were a list to select the desired layer, and then retrieving its parameters (such as weights and biases) through framework-specific attributes. In frameworks that decouple the model architecture from its parameters, the parameters are instead accessed using specific layer keys within an initialized parameters dictionary.

Parameter Access in Sequential Models

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In PyTorch, when a model is defined using the `Sequential` class, the parameters of a specific layer can be inspected by indexing the model and calling the `state_dict()` method. For instance, to access the parameters of the third layer in a model named `net`, one would use `net[2].state_dict()`. This method returns an `OrderedDict` containing the layer's parameters, specifically its `weight` and `bias` tensors.

Parameter Access in PyTorch Sequential Models

In MXNet, the parameters of a layer within a `Sequential` model can be accessed by indexing into the network and referencing the `params` attribute. For example, calling `net[1].params` retrieves the parameters for the second layer. This returns an object detailing the individual parameters—such as the specific `weight` and `bias` arrays—along with their respective shapes and data types.

Parameter Access in MXNet Sequential Models

Parameter Access in JAX Sequential Models

In TensorFlow, a layer within a `Sequential` model can be accessed by indexing the `layers` list, and its parameters are retrieved using the `weights` attribute. For example, `net.layers[2].weights` returns a list of the parameter variables for the third layer. This list typically includes the `tf.Variable` objects corresponding to the layer's `kernel` (weights) and `bias`.

Parameter Access in TensorFlow Sequential Models

Deep learning parameters are typically represented as complex class instances rather than simple numerical arrays. A parameter object encapsulates the underlying numerical values (such as weights or biases), the computed gradients necessary for optimization, and other framework-specific metadata. Consequently, users must explicitly request either the numerical value or the gradient when interacting with a parameter.

Components of Neural Network Parameters

Accessing neural network parameters layer-by-layer becomes highly tedious and unwieldy, especially in complex architectures containing nested modules where users would otherwise need to recursively traverse the entire module tree. To address this inefficiency, deep learning frameworks provide built-in methods designed to systematically extract or apply operations to all parameters across an entire network simultaneously.

Bulk Parameter Access in Nested Networks

In deep learning frameworks, parameters can be shared or 'tied' across multiple layers within a sequential model. This is typically achieved by explicitly allocating a layer—such as a fully connected layer—and referencing that exact same object multiple times when constructing the network architecture. Because the tied layers are represented by the identical underlying parameter tensor in memory, they are not merely equal in value; any modification applied to the parameters of one layer will immediately alter the parameters of all other layers tied to it.

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