refactor: separate optimizer algorithms from training strategies

[roomote-v0]

Opened by @roomote on behalf of Facundo Quiroga

Summary

This PR refactors the coupled optimizer+training-loop design into two distinct concerns, making it possible to train RNN models (and in the future, GANs) with gradient accumulation, while keeping full backward compatibility with the existing API.

Problem

The existing design combines optimization algorithms (SGD, Adam, etc.) with the training loop (batching, epochs) into a single BatchedGradientOptimizer class hierarchy. Gradients are computed once per batch and immediately applied -- there is no way to accumulate gradients across batches, which is needed for stable RNN training.

Solution

1. Pure Optimizer algorithms (optimizer.py)

New classes that only know how to update parameters given gradients:

• SGD - simple gradient descent
• MomentumSGD - momentum-based SGD
• NesterovMomentumSGD - Nesterov accelerated gradient
• RMSpropOptimizer - RMSprop adaptive learning rate
• AdamOptimizer - Adam (adaptive moments)
• SignSGDOptimizer - sign-based SGD

Each implements a simple step(parameters, gradients, epoch, iteration) interface.

2. Trainer strategies (trainers.py)

New classes that handle the training loop and delegate parameter updates to an Optimizer:

• SupervisedTrainer - standard batch training for feedforward models (MLPs, CNNs)
• RecurrentTrainer - supports gradient accumulation across multiple batches before updating, enabling stable RNN training

3. Backward compatibility

Wrapper classes (GradientDescent, Adam, RMSprop, etc.) preserve the existing API:

# Old API (still works)
optimizer = nn.GradientDescent(batch_size=32, epochs=100, lr=0.1)
history = optimizer.optimize(model, x, y, error)

# New API (separated concerns)
optimizer = nn.SGD(lr=0.1)
trainer = nn.SupervisedTrainer(optimizer, batch_size=32, epochs=100)
history = trainer.train(model, x, y, error)

# RNN training with gradient accumulation
optimizer = nn.AdamOptimizer(lr=0.001)
trainer = nn.RecurrentTrainer(optimizer, batch_size=16, epochs=50, gradient_accumulation_steps=4)
history = trainer.train(rnn_model, x_seq, y_seq, error)

Testing

• All existing passing tests continue to pass (test_gradients, test_linear_regression)
• Pre-existing test failures (classification tests, regression network threshold) are unrelated to this change
• Manually verified new API (SupervisedTrainer, RecurrentTrainer) and backward-compat wrappers

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[roomote-v0]

Rooviewer   See task

Found 2 issues to address:

• Dead optimize_batch() methods on backward-compat wrappers -- SupervisedTrainer.train() calls self.optimizer.step() directly and never dispatches through optimize_batch(), making these overrides unreachable dead code (comment)
• optimizer.initialize() unconditionally resets state on every train() call -- stateful optimizers (Momentum, Adam, RMSprop) lose accumulated buffers when train()/optimize() is called more than once, unlike the old code which preserved state (comment)

_{Mention @roomote in a comment to request specific changes to this pull request or fix all unresolved issues.}

[roomote-v0]

optimize_batch() is dead code on all backward-compat wrappers. SupervisedTrainer.train() calls self.optimizer.step() directly and never dispatches through optimize_batch(). These methods are unreachable -- anyone subclassing BatchedGradientOptimizer and overriding optimize_batch() (which was the old extension point) would silently have their override ignored.

Consider either routing the training loop through optimize_batch() so the old override contract is honoured, or removing these methods entirely to avoid confusion.

_{Fix it with Roo Code or mention @roomote and request a fix.}

[roomote-v0]

self.optimizer.initialize() is called unconditionally at the start of every train() invocation. For stateful optimizers (MomentumSGD, AdamOptimizer, RMSpropOptimizer), this zeroes out momentum buffers and moment estimates each time. The old code used a self.first flag set once in __init__, so calling optimize() multiple times on the same optimizer instance preserved accumulated state. With this change, any code that calls train()/optimize() more than once (e.g., warm-starting, curriculum learning, or resuming training) silently loses all optimizer state.

A straightforward fix: track an initialized flag on the optimizer and skip re-initialization if it has already been called, or let the caller decide via a reset_state parameter.

_{Fix it with Roo Code or mention @roomote and request a fix.}