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10_Wiki/Topics/Topic_Programming/AI_and_ML/Selective State Space Models (Mamba).md

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+---
+id: wiki-2026-0508-selective-state-space-models-mam
+title: Selective State Space Models (Mamba)
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [Mamba, S6, Selective SSM, State Space Model]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [architecture, ssm, sequence-modeling, llm]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: python
+  framework: PyTorch / mamba-ssm
+---
+
+# Selective State Space Models (Mamba)
+
+## 매 한 줄
+> **"매 hidden state 가 input 에 따라 selectively update"**. 매 Gu & Dao (2023) 의 Mamba — S4 의 시간-불변 한계를 깬 selective scan (S6). 매 linear-time sequence modeling, Transformer 와 경쟁 가능한 long-context 효율. 매 2026: Mamba-2, hybrid Transformer-Mamba (Jamba, Zamba2) 가 prod 진입.
+
+## 매 핵심
+
+### 매 SSM 기초
+- Continuous: x'(t) = Ax(t) + Bu(t), y(t) = Cx(t).
+- Discretized (zero-order hold): xₖ = Āxₖ₋₁ + B̄uₖ.
+- S4: A는 HiPPO-init, time-invariant → 매 efficient FFT convolution.
+
+### 매 Selective (S6)
+- B, C, Δ를 input-dependent function. 매 매 token마다 dynamic.
+- FFT 못 씀 → 매 hardware-aware parallel scan (kernel fusion, SRAM).
+- Benefit: 매 selective recall, copying, induction 가능 (S4 못함).
+
+### 매 vs Transformer
+- Compute: O(L) vs O(L²). 매 long context 큰 advantage.
+- Memory: constant state vs KV cache. 매 inference 매우 cheap.
+- Quality: 7B scale 비슷, 14B+ Transformer slight edge — 매 hybrid 가 sweet spot.
+
+### 매 응용
+1. Long-context LLM (Codestral Mamba, Jamba 1.5, Zamba2).
+2. Genomic sequence (HyenaDNA → Caduceus → Evo).
+3. Audio / time series.
+4. State tracking, retrieval (induction heads).
+
+## 💻 패턴
+
+### Mamba block 사용 (mamba-ssm)
+```python
+from mamba_ssm import Mamba
+import torch
+
+block = Mamba(d_model=1024, d_state=16, d_conv=4, expand=2).cuda()
+x = torch.randn(2, 4096, 1024).cuda()
+y = block(x)  # (2, 4096, 1024), O(L)
+```
+
+### Selective scan (toy)
+```python
+def selective_scan(u, delta, A, B, C):
+    # u:(B,L,D), delta:(B,L,D), A:(D,N), B,C:(B,L,N)
+    dA = torch.exp(delta.unsqueeze(-1) * A)        # discretize
+    dB = delta.unsqueeze(-1) * B.unsqueeze(2)
+    x = torch.zeros(u.shape[0], u.shape[2], A.shape[1], device=u.device)
+    ys = []
+    for t in range(u.shape[1]):
+        x = dA[:, t] * x + dB[:, t] * u[:, t].unsqueeze(-1)
+        ys.append((x * C[:, t].unsqueeze(1)).sum(-1))
+    return torch.stack(ys, dim=1)
+```
+
+### Mamba-2 block (SSD)
+```python
+from mamba_ssm import Mamba2
+b = Mamba2(d_model=2048, d_state=128, d_conv=4, expand=2, headdim=64).cuda()
+```
+
+### Hybrid stack (Jamba-style)
+```python
+class HybridLayer(nn.Module):
+    def __init__(self, d, attn_every=4, idx=0):
+        super().__init__()
+        self.use_attn = (idx % attn_every) == 0
+        self.mix = nn.MultiheadAttention(d, 8, batch_first=True) if self.use_attn else Mamba(d_model=d)
+        self.ffn = SwiGLU(d)
+    def forward(self, x):
+        h = self.mix(x, x, x)[0] if self.use_attn else self.mix(x)
+        return self.ffn(x + h)
+```
+
+### 1M context inference
+```python
+# Mamba: KV cache 없음 → constant memory
+model.eval()
+with torch.no_grad():
+    state = None
+    for chunk in chunks_of_1M_tokens:
+        out, state = model.step(chunk, state)
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Long context (>32k) inference cost critical | Mamba / Jamba |
+| Need strong in-context reasoning | Transformer or Hybrid |
+| Genomic / audio million-length | Mamba family |
+| Standard chat 8k context | Transformer (matured tooling) |
+| Edge device, low memory | Mamba (no KV cache) |
+
+**기본값**: Hybrid (Jamba/Zamba2) — 매 best of both.
+
+## 🔗 Graph
+- 부모: [[State-Space|State-Space-Models]] · [[Sequence-to-Sequence-Models]]
+- 변형: [[S4]]
+- Adjacent: [[Transformer]]
+
+## 🤖 LLM 활용
+**언제**: 매우 긴 context, streaming, 매 inference 비용 critical. Genomic / audio.
+**언제 X**: 매 strong needle-in-haystack recall — pure Mamba 약함, hybrid 필요.
+
+## ❌ 안티패턴
+- **Pure Mamba for retrieval**: induction OK 지만 exact recall 매 약함.
+- **Naive scan implementation**: SRAM-aware kernel 없으면 매 felt slower than attention.
+- **S4 (non-selective)** for LLM: 매 obsoleted by S6/Mamba.
+
+## 🧪 검증 / 중복
+- Verified (Gu & Dao 2023 "Mamba", Mamba-2 2024, Jamba 2024).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — Mamba/Mamba-2/hybrid 2026 state |