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10_Wiki/Topics/Topic_Programming/AI_and_ML/Parameter.md

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+---
+id: wiki-2026-0508-parameter
+title: Parameter
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [Model Parameter, Weight, Trainable Parameter]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.95
+verification_status: applied
+tags: [parameter, weight, hyperparameter, ml-fundamentals]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: python
+  framework: pytorch
+---
+
+# Parameter
+
+## 매 한 줄
+> **"매 learned by data vs set by human"**. Parameter = model 이 training 중 학습 (weight, bias). Hyperparameter = 매 human 이 사전 설정 (lr, depth, batch size). 2026 frontier: 매 trillion-parameter models (GPT-5, Claude Opus 4.7) — 매 scale 의 dominant axis.
+
+## 매 핵심
+
+### 매 parameter vs hyperparameter
+- **Parameter (θ)**: 매 trainable, gradient descent 의 update target. Examples: W, b in `y = Wx + b`.
+- **Hyperparameter**: 매 fixed before training, 매 architecture/optim choice. Examples: learning rate, batch size, num_layers, dropout p.
+- 매 distinction 모호 case: prompt token (soft prompt 시 parameter, hard prompt 시 input).
+
+### 매 parameter types
+- **Weights**: matrix multiply coefficients (`W` in `Wx + b`).
+- **Biases**: additive offsets (`b`).
+- **Embeddings**: lookup table (vocab × dim).
+- **LayerNorm γ, β**: scale/shift learned per channel.
+- **Buffers**: 매 NOT params — running statistics (BatchNorm running_mean), moving averages.
+
+### 매 modern scale
+- BERT-base (2018): 110M.
+- GPT-3 (2020): 175B.
+- GPT-4 (2023): ~1.7T (rumored MoE).
+- Llama 3.1 405B (2024): 405B dense.
+- GPT-5 / Claude Opus 4.7 (2025-2026): trillion-scale, MoE common.
+- 매 active params (MoE) ≠ total params.
+
+### 매 응용
+1. Model size estimation (memory budget).
+2. Compute budget (Chinchilla scaling: tokens ≈ 20× params).
+3. Compression (quantization, pruning operate on params).
+4. Fine-tuning scope (full vs PEFT — see [[PEFT (Parameter-Efficient Fine-Tuning)]]).
+
+## 💻 패턴
+
+### Count parameters
+```python
+def count_params(model):
+    total = sum(p.numel() for p in model.parameters())
+    trainable = sum(p.numel() for p in model.parameters() if p.requires_grad)
+    return total, trainable
+
+total, trainable = count_params(model)
+print(f"Total: {total/1e9:.2f}B, Trainable: {trainable/1e9:.2f}B")
+```
+
+### Parameter vs buffer
+```python
+import torch.nn as nn
+
+class MyLayer(nn.Module):
+    def __init__(self):
+        super().__init__()
+        self.weight = nn.Parameter(torch.randn(10, 10))  # trainable
+        self.register_buffer("running_mean", torch.zeros(10))  # NOT trainable
+```
+
+### Freeze parameters (transfer learning)
+```python
+for p in model.encoder.parameters():
+    p.requires_grad = False  # frozen
+# Only classifier head trains
+optimizer = torch.optim.Adam(
+    [p for p in model.parameters() if p.requires_grad], lr=1e-4
+)
+```
+
+### Memory estimation
+```python
+def model_memory_gb(model, dtype_bytes=2):  # bf16
+    n = sum(p.numel() for p in model.parameters())
+    weights = n * dtype_bytes
+    gradients = n * dtype_bytes  # if training
+    optimizer = n * 8  # Adam: 2 states × fp32
+    return (weights + gradients + optimizer) / 1e9
+
+print(f"Training memory: {model_memory_gb(model):.1f} GB")
+```
+
+### Hyperparameter search (Optuna)
+```python
+import optuna
+
+def objective(trial):
+    lr = trial.suggest_float("lr", 1e-5, 1e-2, log=True)
+    bs = trial.suggest_categorical("batch_size", [32, 64, 128])
+    layers = trial.suggest_int("num_layers", 2, 8)
+    return train_and_eval(lr=lr, batch_size=bs, num_layers=layers)
+
+study = optuna.create_study(direction="maximize")
+study.optimize(objective, n_trials=50)
+```
+
+### MoE active params
+```python
+# Mixtral 8x7B: 47B total, ~13B active per token (top-2 routing)
+total = 47e9
+experts = 8
+active_per_token = 2
+shared = 13e9 - (47e9 - 13e9*experts) / experts  # rough
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Memory budget plan | Total params × dtype × (1 train, 4 with optim) |
+| Inference deployment | Total params × dtype (+ KV cache) |
+| Scaling decision | Chinchilla: tokens ≈ 20 × params |
+| Compute budget | FLOPs ≈ 6 × params × tokens |
+| Fine-tuning | PEFT if params > 1B and 1-GPU |
+
+**기본값**: 매 always report total + trainable params separately.
+
+## 🔗 Graph
+- 부모: [[Machine-Learning]]
+- 변형: [[Trainable-Parameter]]
+- 응용: [[LLM_Optimization_and_Deployment_Strategies|Model-Compression]] · [[PEFT (Parameter-Efficient Fine-Tuning)]] · [[LLM_Optimization_and_Deployment_Strategies|Quantization]]
+- Adjacent: [[Scaling-Laws]] · [[MoE]]
+
+## 🤖 LLM 활용
+**언제**: 매 model size discussion, memory planning, fine-tuning scope decision.
+**언제 X**: 매 high-level user-facing communication (use "model size" instead).
+
+## ❌ 안티패턴
+- **Confusing param ≠ hyperparam**: 매 calling `lr` a parameter.
+- **Counting frozen as trainable**: 매 reporting 70B "trainable" when only LoRA (0.5%) actually trains.
+- **Ignoring MoE active vs total**: 매 Mixtral 47B treated as 47B compute (실제 13B per token).
+- **Memory underestimation**: 매 forgetting optimizer states (8× param size for Adam fp32).
+
+## 🧪 검증 / 중복
+- Verified (PyTorch docs, Kaplan 2020 / Hoffmann 2022 scaling laws).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — parameter vs hyperparameter, modern scale, memory math |