Update README.md

README.md

@@ -56,19 +56,19 @@ Adaptive Math 2 focuses on educational mathematical reasoning rather than simple
 
 ### Characteristics
 
-✅ Structured instruction format
+ Structured instruction format
 
-✅ Educational explanations
+ Educational explanations
 
-✅ Curriculum-oriented questions
+ Curriculum-oriented questions
 
-✅ Reasoning-aware responses
+ Reasoning-aware responses
 
-✅ Clean supervised fine-tuning format
+ Clean supervised fine-tuning format
 
 ##  Example Dataset Samples
 
-### Example 1
+### Example 
 
 **Instruction**
 
@@ -86,24 +86,6 @@ x = 7
 ```
 
 ---
-
-### Example 2
-
-**Instruction**
-
-```
-A triangle has angles of 45° and 65°.
-
-Find the third angle.
-```
-
-**Expected Response**
-
-```
-180° − (45° + 65°)
-
-= 70°
-```
 ##  Educational Impact
 
 Adaptive Math 2 is intended for:
@@ -118,22 +100,143 @@ Adaptive Math 2 is intended for:
 
 The dataset emphasizes transparent reasoning instead of answer memorization.
 
-## Credit
-
-Adaptive data by Adaption.
-
-## Acknowledgement
-
-Adaptive Math 2 was developed using the **Adaption Lab AutoScientist** pipeline with **Meta Llama 4 Scout 17B** as the foundation model.
-
-Special thanks to:
-
-- **Adaption Lab** for the AutoScientist training and evaluation platform.
-- **Meta AI** for the Llama 4 Scout base model.
-- **Hugging Face** for open model hosting and distribution.
-- **Kaggle** for dataset publication and community accessibility.
+## Mathematical Training Specification
+
+model:
+  base_model: "meta-llama/Llama-4-Scout-17B-16E-Instruct"
+  approximate_model_size: "109B parameters"
+  training_method: "Supervised Fine-Tuning (SFT)"
+  adaptation_method: "LoRA"
+  data_format: "Chat"
+
+mathematical_formulation:
+
+  objective:
+    description: "The adapted model minimizes the supervised language-modeling loss over the Adaptive Math 2 dataset."
+    equation: |
+      θ* = argmin_θ L(θ)
+
+  language_model_loss:
+    equation: |
+      L(θ) = -Σᵢ log Pθ(yᵢ | xᵢ)
+
+  lora:
+    description: "Instead of updating the full model weights, LoRA learns a low-rank update."
+    equation: |
+      W' = W + ΔW
+      ΔW = (α/r)BA
+
+    parameters:
+      rank_r: 16
+      alpha: 32
+      dropout: 0
+      scaling_factor: |
+        α/r = 32/16 = 2
+
+    effective_update:
+      equation: |
+        ΔW = 2BA
+
+  optimization:
+    learning_rate: 0.00005
+    weight_decay: 0
+    max_gradient_norm: 2
+    optimizer_constraint: |
+      ||g||₂ ≤ 2
+
+  training_schedule:
+    epochs: 5
+    evaluations: 5
+    evaluation_frequency: |
+      5 evaluations / 5 epochs = 1 evaluation per epoch
+
+    scheduler:
+      type: "Linear"
+      num_cycles: 0.5
+      warmup_ratio: 0.03
+
+    warmup:
+      equation: |
+        T_warmup = 0.03T
+
+  batch:
+    batch_size: "max"
+
+  target_modules:
+    count: 10
+    modules:
+      - "k_proj"
+      - "o_proj"
+      - "q_proj"
+      - "v_proj"
+      - "shared_expert.gate"
+      - "shared_expert.up_proj"
+      - "shared_expert.down_proj"
+      - "feed_forward.gate_proj"
+      - "feed_forward.up_proj"
+      - "feed_forward.down_proj"
+
+  training_objective:
+    equation: |
+      θ_LoRA* = argmin_{A,B} L(W + (α/r)BA)
+
+  interpretation:
+    rank: "r = 16 controls the low-rank adaptation capacity."
+    scaling: "α/r = 2 controls the magnitude of the LoRA update."
+    regularization: "LoRA dropout = 0 and weight decay = 0."
+    stability: "Gradient norm is clipped at 2."
+    schedule: "Learning rate follows a linear schedule after a 3% warmup."
+
+## Training Interpretation
+
+benchmark:
+  adaptation_strategy: "Parameter-efficient fine-tuning"
+  objective: "Improve mathematical reasoning while preserving the pretrained model."
+  full_parameter_update: false
+  low_rank_update: true
+
+  key_result:
+    statement: |
+      Adaptive Math 2 applies a low-rank parameter update rather than
+      retraining the complete 109B-parameter model.
+
+  mathematical_summary: |
+    W_adapted = W_base + 2BA
+
+  meaning:
+    - "W_base represents the pretrained model."
+    - "A and B are learned low-rank matrices."
+    - "r = 16 defines the adaptation rank."
+    - "α = 32 gives a scaling factor of 2."
+    - "Only the selected target modules receive LoRA updates."
+
+## Reproducibility
+
+configuration:
+  training_method: "SFT"
+  training_type: "LoRA"
+  epochs: 5
+  learning_rate: 0.00005
+  warmup_ratio: 0.03
+  weight_decay: 0
+  max_grad_norm: 2
+  lora_rank: 16
+  lora_alpha: 32
+  lora_dropout: 0
+  scheduler: "linear"
+  scheduler_cycles: 0.5
+  evaluations: 5
+  batch_size: "max"
+
+credit:
+  adaptive_data: "Adaptive Data by Adaption Labs"
+  training_evaluation: "AutoScientist"
+
+
+
+
+Adaptive Math 2 was developed using the **Adaption Lab AutoScientist** pipe
 
-This project demonstrates how adaptive instruction datasets can improve mathematical reasoning, instruction following, and educational AI through efficient LoRA fine-tuning.
 
 ## 📊 Model Performance