11. Sequential Modeling: Vanilla RNNs & The Vanishing / Exploding Gradient Problem • Deep Learning & PyTorch Neural Networks Architecture • Rishabh Ki Kaksha

Deep Learning & PyTorch Neural Networks Architecture › 11. Sequential Modeling: Vanilla RNNs & The Vanishing / Exploding Gradient Problem

45 mins

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Course Syllabus

Module 1: PyTorch Tensors, Autograd & Computational Graphs

01. PyTorch Tensor Architecture: Strides, Storage Buffers, Memory Layout (Contiguous vs Non-Contiguous) 02. Dynamic Computational Graphs & The PyTorch Autograd Engine (grad_fn, requires_grad, backward) 03. GPU Acceleration with CUDA: Tensor Device Placement (to("cuda")), CUDA Streams & Pinned Memory

Module 2: Multi-Layer Perceptrons (MLPs) & Custom Training Loops

04. Building Custom nn.Module Classes, Custom Parameters & Activation Functions (ReLU, GELU, Swish) 05. Custom Datasets & High-Performance DataLoaders (num_workers, collate_fn, pin_memory) 06. The Enterprise Training Loop: Forward Pass, Loss Computation, Zero Grad, Backward Pass & Optimizer Step 07. Neural Regularization Techniques: Dropout, Batch Normalization (BatchNorm1d) & Layer Normalization (LayerNorm)

Module 3: Convolutional Neural Networks (CNNs) & Computer Vision Architecture

08. Convolutional Operations: Kernels, Filters, Strides, Padding & Feature Map Dilation 09. Modern CNN Architectures: Residual Connections (ResNet), Squeeze-and-Excitation & ConvNeXt 10. Transfer Learning & Vision Fine-Tuning with Torchvision Pretrained Models

Module 4: Recurrent Architectures: RNNs, LSTMs & GRUs for Sequential Data

11. Sequential Modeling: Vanilla RNNs & The Vanishing / Exploding Gradient Problem 12. Long Short-Term Memory (LSTM) Networks: Forget Gate, Input Gate, Candidate State & Output Gate Math 13. Gated Recurrent Units (GRUs) & Bidirectional Sequence Processing in PyTorch

Module 5: Modern Transformer Architecture from Scratch in PyTorch

14. Scaled Dot-Product Attention: Query, Key, Value Matrices & Attention Softmax Calculation 15. Multi-Head Attention (MHA) & Causal Masking Implementation from Scratch in Pure PyTorch 16. Building a Complete GPT-Style Decoder-Only Transformer Language Model from Scratch

Module 6: PyTorch Distributed (DDP), Mixed Precision (AMP) & Model Checkpointing

17. Automatic Mixed Precision (torch.cuda.amp.autocast & GradScaler) for 2x Faster GPU Training 18. Distributed Data Parallel (DDP) Architecture: Multi-GPU Synchronization with torch.distributed 19. Robust Checkpointing: Saving State Dicts, Resuming Training & Early Stopping Callbacks 20. Model Export & Production Serialization: TorchScript (JIT Tracing), ONNX & TensorRT Compilation

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# 11. Sequential Modeling: Vanilla RNNs & The Vanishing / Exploding Gradient Problem

> Deep Learning & PyTorch Notes by Rishabh - Topic 11

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### 1. Vanilla Recurrent Neural Network (RNN) Architecture 🔄

Time step $t$ par hidden state update:
$$h_t = \tanh(W_{hh} h_{t-1} + W_{xh} x_t + b_h)$$
$$\hat{y}_t = \text{Softmax}(W_{hy} h_t + b_y)$$

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### 2. Backpropagation Through Time (BPTT) & Gradient Vanishing 📉

Time step $T$ se time step 1 tak gradient propagate karte waqt:
$$\frac{\partial L_T}{\partial h_1} = \frac{\partial L_T}{\partial h_T} \prod_{j=2}^T \frac{\partial h_j}{\partial h_{j-1}} = \frac{\partial L_T}{\partial h_T} \prod_{j=2}^T \text{diag}(1 - \tanh^2(\cdot)) W_{hh}^T$$

*   Agar $W_{hh}$ ki largest eigenvalue $\lambda < 1$: Gradient **exponentially $0$ ho jata hai** (Cannot remember tokens from 10 steps ago!).
*   Agar $\lambda > 1$: Gradient **exponentially explode $\infty$** ho jata hai!

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### 3. Interview Ke 3 Sawal Is Topic Se

1. **Truncated BPTT kya hota hai?** -> Long sequences ko $k_1$ steps ke chunks me break karke gradients ko maximum $k_2$ steps tak piche propagate karna (Saves GPU memory).
2. **Gradient Clipping exploding gradients ko kaise fix karta hai?** -> `torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)` call karke gradient norm ko cap karna.
3. **Vanilla RNNs modern NLP me obsolete kyu ho gaye?** -> Sequential nature ki wajah se GPU parallelization impossible tha aur 20 tokens se lambe contexts me vanishing gradients ki wajah se fail ho jate the.

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**Next Topic:** 12. Long Short-Term Memory (LSTM) Networks: Forget Gate, Input Gate, Candidate State & Output Gate Math

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