Update README.md

README.md

@@ -70,11 +70,11 @@ Alo-70M-Base is based on a scaled-down LLaMA transformer architecture optimized
 * **Hidden Dimension ($d_{model}$):** 512
 * **Intermediate FFN Dimension:** 1408
 * **Attention Mechanism:** Grouped-Query Attention (GQA) with 8 query heads and 4 key-value heads.
-* **Positional Embeddings:** Rotary Position Embeddings (RoPE) with a base frequency ($\theta$) of 10,000.
+* **Positional Embeddings:** Rotary Position Embeddings (RoPE) with a base frequency theta of 10,000.
 * **Activation Function:** SwiGLU (`silu`)
 * **Word Embeddings:** Untied (`tie_word_embeddings = False`). The static lookup tables account for 48.6% (33.5M) of the total parameter budget.
 * **Context Window:** 1024 tokens.
-* **Tokenizer:** Custom Bengali Byte-Pair Encoding (BPE) tokenizer ([spitfire4794/beng_bpe](https://huggingface.co/spitfire4794/beng_bpe)) with a highly optimized vocabulary size of 32,768 ($2^{15}$) designed to maximize TPU efficiency.
+* **Tokenizer:** Custom Bengali Byte-Pair Encoding (BPE) tokenizer ([spitfire4794/beng_bpe](https://huggingface.co/spitfire4794/beng_bpe)) with a highly optimized vocabulary size of 32,768 (2^15) designed to maximize TPU efficiency.
 
 ## Pre-Training Data
 The model was pre-trained on a curated, strictly Bengali corpus containing approximately **19.25 billion tokens**. The dataset is a blend of:
@@ -85,9 +85,9 @@ The model was pre-trained on a curated, strictly Bengali corpus containing appro
 Alo-70M-Base was initialized with completely randomized weights (no transfer learning) and trained from scratch. 
 * **Hardware:** Kaggle Tensor Processing Unit (TPU) v5e-8
 * **Training Time:** 12.9 hours (wall time) across two sequential runs.
-* **Optimizer:** AdamW (`adam_torch_xla`) with $\beta_1 = 0.9, \beta_2 = 0.95, \epsilon = 10^{-8}$
+* **Optimizer:** AdamW (`adam_torch_xla`) with beta_1 = 0.9, beta_2 = 0.95, epsilon = 10^-8
 * **Weight Decay:** 0.1
-* **Learning Rate Schedule:** Cosine Decay with a gradual warmup phase, peaking at $6 \times 10^{-4}$.
+* **Learning Rate Schedule:** Cosine Decay with a gradual warmup phase, peaking at 6 times 10^-4.
 * **Precision & Optimization:** Mixed `bfloat16` (`bf16`) precision with gradient checkpointing enabled to maximize throughput.
 
 ## Evaluation Results