"updating"

LLM_Techniques_and_utils/RoPE-As-Implemented-in-LlaMa-Source-Code.ipynb

@@ -35,6 +35,10 @@
     "\n",
     "👉 Rotary Embedding (Rotary Positional Encoding) is a kind of positional encoding, but unlike traditional positional encodings, it tries to encode the relative positions of tokens rather than their absolute positions. This is achieved by applying a rotation operation in the embedding space.\n",
     "\n",
+    "RoPE is unique in that it encodes the absolute position m of tokens through a rotation matrix R_(θ, m), and also incorporates the explicit relative position dependency in the self-attention formulation. The idea is to embed the position of a token in a sequence by rotating queries and keys, with a different rotation at each position.\n",
+    "\n",
+    "The main benefit is, Invariance to Sequence Length: Unlike traditional position embeddings, RoPE does not require a predefined maximum sequence length. It can generate position embeddings on-the-fly for any length of sequences. This makes it much more scalable and adaptable to different tasks.\n",
+    "\n",
     "-------\n",
     "\n",
     "📌 Now looking at the method `apply_rotary_emb()` \n",
@@ -49,10 +53,16 @@
     "\n",
     "---------\n",
     "\n",
+    "Why `xq` and `xk` are being converted into complex tensors with `view_as_complex` ?\n",
+    "\n",
     "📌 Rotary Embeddings involve performing a rotation in the embedding space. This rotation is applied to the queries and keys in the attention mechanism of Transformer models.\n",
     "\n",
     "📌 The rotation in RoPE is fundamentally a complex multiplication. Complex numbers are ideal for representing rotations because multiplying by a complex number corresponds to a rotation in the complex plane.\n",
     "\n",
+    "📌 The \"rotation\" in this context is a phase shift in the complex plane for each element in the query and key tensors. This shift varies based on the position in the sequence, thus encoding positional information.\n",
+    "\n",
+    "📌  The essence of RoPE is that by applying these phase shifts, the dot product (used in the self-attention mechanism) between queries and keys becomes sensitive to their relative positions. It's not merely about measuring \"real angle distance\" but rather about how the phase-shifted dot product correlates with the positional relationships of tokens in the input sequence.\n",
+    "\n",
     "📌 By converting `xq` and `xk` into complex tensors, these lines prepare them for such a rotation. The actual rotation is performed later in the code, where these complex tensors (`xq_` and `xk_`) are multiplied by another complex tensor representing the rotation (typically through phase factors, like `freqs_cis` in this code).\n",
     "\n",
     "---------\n",