12. Long Short-Term Memory (LSTM) Networks: Forget Gate, Input Gate, Candidate State & Output Gate Math • Deep Learning & PyTorch Neural Networks Architecture • Rishabh Ki Kaksha

Deep Learning & PyTorch Neural Networks Architecture › 12. Long Short-Term Memory (LSTM) Networks: Forget Gate, Input Gate, Candidate State & Output Gate Math

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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

Interactive Lesson Studio

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

> Deep Learning & PyTorch Notes by Rishabh - Topic 12

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### 1. The 4 Gates of LSTM (Hochreiter & Schmidhuber 🧠)

Given input $x_t$ and previous hidden state $h_{t-1}$:

1. **Forget Gate ($f_t$):** Purani memory me se kya delete karna hai:
   $$f_t = \sigma(W_f [h_{t-1}, x_t] + b_f)$$
2. **Input Gate ($i_t$) & Candidate Cell ($\tilde{C}_t$):** Nayi memory me kya add karna hai:
   $$i_t = \sigma(W_i [h_{t-1}, x_t] + b_i), \quad \tilde{C}_t = \tanh(W_c [h_{t-1}, x_t] + b_c)$$
3. **Cell State Update ($C_t$ - The Linear Superhighway):**
   $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t$$
4. **Output Gate ($o_t$) & Hidden State ($h_t$):**
   $$o_t = \sigma(W_o [h_{t-1}, x_t] + b_o), \quad h_t = o_t \odot \tanh(C_t)$$

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### 2. Master Comparison Matrix

| Component | Function | Activation |
| :--- | :--- | :--- |
| **Forget Gate ($f_t$)** | Multiplicative mask on purani memory | Sigmoid $\in [0, 1]$ |
| **Candidate State ($\tilde{C}_t$)**| Naya information content | $\tanh \in [-1, 1]$ |
| **Cell State ($C_t$)** | **Linear additive conveyor belt (Zero vanishing gradients!)**| Linear Addition |

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

1. **Cell State update me linear addition ($C_t = f_t \odot C_{t-1} + \dots$) vanishing gradients ko kaise rokkta hai?** -> Linear additive derivative hone ki wajah se gradient bina decay huye sequence me 100+ steps piche flow kar sakta hai.
2. **Forget Gate bias $b_f$ ko start me $1.0$ ya $2.0$ par initialize kyu karte hain?** -> Taaki training ke start me model purani information ko galti se delete na kare (Default to remembering everything).
3. **Peephole Connections LSTM me kya hoti hain?** -> Gate equations me direct Cell State $C_{t-1}$ ko input feature ki tarah pass karna.

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**Next Topic:** 13. Gated Recurrent Units (GRUs) & Bidirectional Sequence Processing in PyTorch

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