---
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-Models]] · [[Sequence-to-Sequence-Models]]
- 변형: [[Mamba-2]] · [[S4]] · [[Hyena]] · [[RWKV]]
- 응용: [[Long-Context-LLM]] · [[Genomic-Models]]
- Adjacent: [[Transformer]] · [[Linear-Attention]]

## 🤖 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 |