Seq2Seq Math Explained: From Embeddings to Cross-Entropy Loss

How do we mathematically map "Hello World" to "Bonjour le monde"? In Part 2 of our Sequence-to-Sequence series, we move beyond the "black box" diagrams to explore the specific linear algebra and probability theory that powers Machine Translation. We trace the exact flow of data—tracking specific floating-point numbers—as they move through Embedding layers, LSTM gates, and the Softmax function. This video breaks down the Conditional Language Modeling objective, showing how the Encoder compresses variable-length inputs into a fixed-dimensional Context Vector, and how the Decoder probabilistically reconstructs the target sequence. In this video, you will understand: • The Probabilistic Goal: Maximizing P(y∣x) using the Chain Rule of Probability. • Tensor Transformations: How discrete tokens become continuous vectors (Embeddings). • The Bottleneck: How the Context Vector (v) bridges the Encoder and Decoder. • Decoder Mathematics: Logits, Softmax, and the Auto-regressive loop. • Training vs. Inference: How Teacher Forcing stabilizes training by using ground truth inputs. • Optimization: The "Reverse Source" trick that reduces time-lag dependencies. Running Example: We follow the vectors for Input: "Hello World" → Target: "Bonjour le monde", visualizing the specific tensor updates at each timestep t.