You’re an expert programmer with a expert understanding of best coding practices and numerical computing. You always review the code I give to you before you answer to check if it would need improvements before proceeding with your answer.  this is a class library for neural networks for real world applications, the library must be able to handle small networks like simple classifiers and large networks like LLMs . so you must always consider for best possible answer with best performance, optimizations and least memory footprint,  use Tensor<T>.ParallelizationThreshold static property when preferred or required for best practices. you will produce fully complete and working code. 
When I ask you for code improvements or bug fix, you will only generate new code or code changes, don't re-generate unchanged or old code, also with the changes you provide code copy paste explanation so I can avoid any copy paste errors and to avoid human confusion.
Please note this class library is on multiply file and large code base, so If you want to know about certain implementation to provide complete answer then assume it is already implemented and well optimized, also you can ask for code snippets and I will provide to you my current up-to-date implementation.

Programming language : c#
Application Type: class library
Describe the application in full (what does it do?): Neural network library
public class Trainer<T> where T : unmanaged, INumber<T>, IExponentialFunctions<T>, ITrigonometricFunctions<T>, ILogarithmicFunctions<T>, IFloatingPointIeee754<T>, IRootFunctions<T>, IMinMaxValue<T> { public Evaluator<T> Evaluator { get; private set; } public TrainingMetrics<T> Metrics { get; private set; } = new TrainingMetrics<T>(); public IRegularization<T>? Regularization { get; set; } public ILearningRateScheduler<T>? LearningRateScheduler { get; set; } public NeuralNetwork<T> Network { get; private set; } public ILossFunction<T> LossFunction { get; private set; } public IOptimizer<T> Optimizer { get; private set; } public ILogger<T> Logger { get; private set; } public int Epochs { get; set; } public int BatchSize { get; set; } public T GradientClippingThreshold { get; set; } = T.CreateChecked(1.0); public bool UseEarlyStopping { get; set; } = false; public int EarlyStoppingPatience { get; set; } = 5; public T BestValidationLoss { get; private set; } public int NoImprovementEpochs { get; private set; } public bool EnableCheckpointing { get; set; } = false; public string CheckpointDirectory { get; set; } = "checkpoints"; public int CheckpointInterval { get; set; } = 1; public event Action<int, int, T>? EpochCompleted; public event Action<int, int, T>? BatchCompleted; public Trainer( NeuralNetwork<T> network, ILossFunction<T> lossFunction, IOptimizer<T> optimizer, ILogger<T> logger, int epochs = 100, int batchSize = 32, IRegularization<T>? regularization = null, ILearningRateScheduler<T>? learningRateScheduler = null) { Network = network; LossFunction = lossFunction; Optimizer = optimizer; Logger = logger; Epochs = epochs; BatchSize = batchSize; BestValidationLoss = T.MaxValue; Regularization = regularization; LearningRateScheduler = learningRateScheduler; Evaluator = new Evaluator<T>(Network, Logger, BatchSize); } public async Task TrainAsync( Tensor<T> trainingData, Tensor<T> trainingLabels, Tensor<T>? validationData = null, Tensor<T>? validationLabels = null, CancellationToken cancellationToken = default) { try { int numSamples = trainingData.Shape[0]; int totalBatches = (numSamples + BatchSize - 1) / BatchSize; Network.InitializeWeights(); for (int epoch = 0; epoch < Epochs; epoch++) { if (cancellationToken.IsCancellationRequested) { Logger.Log("Training cancelled.", LogLevel.Warning); break; } if (LearningRateScheduler != null) { var newLearningRate = LearningRateScheduler.GetLearningRate(epoch); Optimizer.LearningRate = newLearningRate; Logger.Log($"Adjusted learning rate to {newLearningRate} for epoch {epoch + 1}", LogLevel.Info); } var epochStartTime = DateTime.UtcNow; ShuffleData(ref trainingData, ref trainingLabels); var epochLoss = T.Zero; var batchIndices = Enumerable.Range(0, totalBatches).ToArray(); var batchDurations = new double[totalBatches]; var batchLosses = new T[totalBatches]; ParallelOptions parallelOptions = new ParallelOptions { CancellationToken = cancellationToken, MaxDegreeOfParallelism = totalBatches >= Tensor<T>.ParallelizationThreshold ? Environment.ProcessorCount : 1 }; Parallel.ForEach(batchIndices, parallelOptions, (batchIndex) => { var batchStartTime = DateTime.UtcNow; if (cancellationToken.IsCancellationRequested) { Logger.Log("Training cancelled during batch processing.", LogLevel.Warning); parallelOptions.CancellationToken.ThrowIfCancellationRequested(); } int batchStart = batchIndex * BatchSize; int currentBatchSize = Math.Min(BatchSize, numSamples - batchStart); var batchData = trainingData.Slice(batchStart, currentBatchSize); var batchLabels = trainingLabels.Slice(batchStart, currentBatchSize); var predictions = Network.Forward(batchData); T loss = LossFunction.ComputeLoss(predictions, batchLabels); if (Regularization != null) { foreach (var layer in Network.Layers) { foreach (var param in layer.GetParameters()) { loss = loss + Regularization.ComputePenalty(param); } } } var gradients = LossFunction.ComputeGradient(predictions, batchLabels); Backward(gradients); if (Regularization != null) { foreach (var layer in Network.Layers) { var parameters = layer.GetParameters().ToList(); var gradientsList = layer.GetGradients().ToList(); for (int i = 0; i < parameters.Count; i++) { var regGradient = Regularization.ComputeGradient(parameters[i]); gradientsList[i].AddInPlace(regGradient); } } } ClipGradients(); UpdateWeights(); ClearGradients(); batchLosses[batchIndex] = loss; Metrics.AddBatchError(loss); var batchEndTime = DateTime.UtcNow; batchDurations[batchIndex] = (batchEndTime - batchStartTime).TotalSeconds; Logger.Log($"Epoch {epoch + 1}, Batch {batchIndex + 1}/{totalBatches} completed in {batchDurations[batchIndex]:F2}s. Loss: {loss}", LogLevel.Debug); BatchCompleted?.Invoke(epoch + 1, batchIndex + 1, loss); predictions.Dispose(); gradients.Dispose(); batchData.Dispose(); batchLabels.Dispose(); }); epochLoss = batchLosses.Aggregate(T.Zero, (acc, val) => acc + val) / T.CreateChecked(totalBatches); T validationLoss = T.Zero; if (validationData != null && validationLabels != null) { validationLoss = Evaluate(validationData, validationLabels); Logger.Log($"Epoch {epoch + 1}/{Epochs}, Training Loss: {epochLoss}, Validation Loss: {validationLoss}", LogLevel.Info); if (UseEarlyStopping) { if (validationLoss.CompareTo(BestValidationLoss) < 0) { BestValidationLoss = validationLoss; NoImprovementEpochs = 0; if (EnableCheckpointing) { SaveCheckpoint(epoch + 1, validationLoss); } } else { NoImprovementEpochs++; if (NoImprovementEpochs >= EarlyStoppingPatience) { Logger.Log("Early stopping triggered.", LogLevel.Warning); break; } } } } else { Logger.Log($"Epoch {epoch + 1}/{Epochs}, Training Loss: {epochLoss}", LogLevel.Info); } if (EnableCheckpointing && (epoch + 1) % CheckpointInterval == 0) { SaveCheckpoint(epoch + 1, validationLoss); } EpochCompleted?.Invoke(epoch + 1, Epochs, validationLoss); var epochEndTime = DateTime.UtcNow; var epochDuration = (epochEndTime - epochStartTime); Metrics.Epoch = epoch + 1; Metrics.EpochDuration = epochDuration; Logger.Log($"Epoch {Metrics.Epoch} completed in {Metrics.EpochDuration.TotalSeconds:F2}s, Average Training Loss: {Metrics.AverageError}, Min Loss: {Metrics.MinError}, Max Loss: {Metrics.MaxError}.", LogLevel.Info); Metrics.Clear(); } } catch (OperationCanceledException) { Logger.Log("Training operation was cancelled.", LogLevel.Warning); } catch (Exception ex) { Logger.Log($"An exception occurred during training: {ex.Message}", LogLevel.Error); throw; } finally { } await Task.CompletedTask; } private void Backward(Tensor<T> gradients) { var grad = gradients; for (int i = Network.Layers.Count - 1; i >= 0; i--) { grad = Network.Layers[i].Backward(grad); } grad.Dispose(); } private void UpdateWeights() { foreach (var layer in Network.Layers) { layer.UpdateWeights(Optimizer); } } private void ClearGradients() { foreach (var layer in Network.Layers) { layer.ClearGradients(); } } private void ClipGradients() { foreach (var layer in Network.Layers) { foreach (var gradient in layer.GetGradients()) { gradient.ClipInPlace(-GradientClippingThreshold, GradientClippingThreshold); } } } public void ShuffleData(ref Tensor<T> data, ref Tensor<T> labels) { int numSamples = data.Shape[0]; int[] indices = Enumerable.Range(0, numSamples).ToArray(); Random rand = new Random(); for (int i = numSamples - 1; i > 0; i--) { int j = rand.Next(i + 1); int temp = indices[i]; indices[i] = indices[j]; indices[j] = temp; } data = data.Gather(indices); labels = labels.Gather(indices); } public T Evaluate(Tensor<T> data, Tensor<T> labels) { return Evaluator.Evaluate(data, labels, LossFunction); } public void LoadCheckpoint(string checkpointPath) { Network.Load(checkpointPath); Logger.Log($"Checkpoint loaded from '{checkpointPath}'"); } private void SaveCheckpoint(int epoch, T validationLoss) { if (!Directory.Exists(CheckpointDirectory)) { Directory.CreateDirectory(CheckpointDirectory); } string checkpointPath = Path.Combine(CheckpointDirectory, $"model_epoch_{epoch}.ckpt"); Network.Save(checkpointPath); Logger.Log($"Checkpoint saved at '{checkpointPath}' with Validation Loss: {validationLoss}"); } private void SaveCheckpoint(NeuralNetwork<T> network, int epoch, T validationLoss) { if (!Directory.Exists(CheckpointDirectory)) { Directory.CreateDirectory(CheckpointDirectory); } string checkpointPath = Path.Combine(CheckpointDirectory, $"model_epoch_{epoch}.ckpt"); network.Save(checkpointPath); Logger.Log($"Checkpoint saved at '{checkpointPath}' with Validation Loss: {validationLoss}"); } }

what improvments can be made on this code?