{
  "schemaVersion": 1,
  "slug": "mamba",
  "title": "Carry context through a selective state",
  "className": "TinyMamba",
  "question": "How does the input decide what a recurrent state retains?",
  "description": "Follow a causal convolution into input-dependent state dynamics, then replay the scan and compare its fixed-size streaming state.",
  "category": "Alternative architectures",
  "tags": [
    "Mamba",
    "Selective SSM",
    "State space",
    "Scan",
    "Recurrence"
  ],
  "curator": "TensorViz",
  "attribution": "Original TensorViz teaching example. PyTorch provides the underlying operators.",
  "license": "No separate redistribution license has been declared for these project examples.",
  "limitations": "Untrained single teaching block, without token embeddings or a language head. CPU sequential loop with exact ZOH B discretization; the released fast implementation uses a simplified delta × B input term. No fused parallel scan, custom backward or measured speed claim. The static graph groups the recurrence in a Python node; the panel records its actual state history. This model does not universally replace attention.",
  "openingStep": "select",
  "provenance": {
    "capturedAt": "2026-09-17T06:55:55.075292+00:00",
    "productRevision": "cf0ab1c9c58c1dc640235b742fa032cade00b43c",
    "sourceSha256": "cc6ddffd335c7c6f37f908ea898b9826b5e199f49ca0fcc76d494fca0734bd85",
    "python": "3.13.13",
    "torch": "2.7.1",
    "execution": {
      "inputs": {
        "args": [
          {
            "shape": [
              1,
              6,
              4
            ],
            "dtype": "float32",
            "fill": "randn"
          }
        ]
      },
      "device": "cpu",
      "mode": "eval",
      "seed": 0,
      "deterministic": true
    },
    "outcome": "passed",
    "outputShape": [
      1,
      6,
      4
    ],
    "method": "TensorViz multifile projection and isolated execution worker",
    "scope": "Reduced Mamba-style block with causal convolution, input-dependent delta/B/C and diagonal ZOH scan. Causality, token streaming, closed-form recurrence and selection-gradient checks.",
    "numericalChecks": [
      "Future changes leave every earlier output unchanged",
      "Token streaming with a 16-value convolution cache and 24-value SSM state matches the full forward",
      "The recurrent state matches an independent sum of decayed past writes",
      "Negative diagonal A and positive input-dependent delta give decay factors between zero and one; selection maps receive gradients"
    ]
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  ],
  "steps": [
    {
      "id": "local",
      "target": "local_conv",
      "title": "Gather local context before the scan",
      "note": "The normalized input expands into eight content and eight gate features. A left-padded depthwise convolution reads only the current and two earlier content projections; SiLU supplies the scan input."
    },
    {
      "id": "select",
      "target": "selection.delta",
      "title": "Choose dynamics from the current input",
      "note": "Softplus makes delta positive. Separate learned maps produce B, which controls writes, and C, which controls readout. Unlike a time-invariant SSM, these quantities change across tokens."
    },
    {
      "id": "state",
      "target": "scan",
      "title": "Decay the old state and add the current write",
      "note": "For each channel, hₜ = Āₜ hₜ₋₁ + B̄ₜ uₜ. Negative diagonal A and positive delta produce decay factors between zero and one. The recorded panel exposes three state coordinates and checks an independent sum of decayed writes."
    },
    {
      "id": "read",
      "target": "project",
      "title": "Read, gate and project the state output",
      "note": "C reads the updated state, with a learned direct input path D. A separate SiLU gate modulates the result before projection and residual addition. Streaming retains 24 SSM values and 16 convolution-history values per sequence for this configuration."
    }
  ],
  "milestone": {
    "name": "Mamba selective state-space models",
    "year": 2023,
    "kind": "Architecture",
    "fidelity": "Width four, expansion eight, three state coordinates per channel, causal depthwise convolution width three. LayerNorm wrapper, SiLU gate and residual projection. Exact diagonal zero-order-hold discretization follows the paper’s Eq. 4.",
    "papers": [
      {
        "title": "Mamba: Linear-Time Sequence Modeling with Selective State Spaces",
        "url": "https://arxiv.org/abs/2312.00752"
      }
    ]
  },
  "experiment": {
    "kind": "matrices",
    "title": "Read, write and retain a recurrent state.",
    "description": "Recorded selective-state evolution in a tiny Mamba-style block. Streaming state size is fixed for this architecture; these counts do not include weights or training activations.",
    "controlLabel": "Scan checkpoint",
    "cases": [
      {
        "id": "first",
        "label": "After token 0",
        "target": "scan",
        "note": "The recurrence has processed tokens 0 through 0. This table shows channel 0’s three state coordinates; the complete state holds eight channels. Delta, B and C come from the current convolved token. Exact diagonal ZOH gives Ā = exp(ΔA) and B̄ = (exp(ΔA)−1)B/A. This is a recorded CPU loop, without the fused parallel scan or measured GPU speed.",
        "matrices": [
          {
            "label": "Channel 0 state history · processed tokens × state coordinates",
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              ]
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          },
          {
            "label": "Current full state · channels × coordinates",
            "values": [
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                0.0028182393539163413,
                -0.010537066745402683,
                -0.00784164629620153
              ],
              [
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                0.006223652277864977
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              [
                -0.0033953960241741867,
                0.010168460390130212,
                0.0065498798760998955
              ],
              [
                0.003721872691424867,
                -0.012092310160219935,
                -0.008144172107855993
              ],
              [
                0.0011967177169104992,
                -0.003539063139261009,
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              ],
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                0.005324342664576923
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              [
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              ],
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                -0.01826898899847851,
                -0.011859231269932035
              ]
            ]
          }
        ],
        "vectors": [
          {
            "label": "Current input token",
            "values": [
              1.279318052918509,
              0.3919448799126044,
              -0.4732379164518807,
              -1.0147876304600973
            ]
          },
          {
            "label": "Current delta · eight channels",
            "values": [
              0.4986526694645875,
              0.32822965324848863,
              1.2466799193608706,
              0.9244711888662873,
              1.3043497535885482,
              0.4329857006315755,
              0.9507933081053215,
              1.178194955355712
            ]
          },
          {
            "label": "Channel 0 decay factors",
            "values": [
              0.6073484077558778,
              0.36887208770291946,
              0.2240338689102113
            ]
          },
          {
            "label": "Channel 0 write contribution",
            "values": [
              0.0028182393539163413,
              -0.010537066745402683,
              -0.00784164629620153
            ]
          }
        ],
        "metrics": [
          {
            "label": "SSM state values per sequence",
            "value": 24
          },
          {
            "label": "Convolution history values per sequence",
            "value": 16
          }
        ]
      },
      {
        "id": "middle",
        "label": "After token 2",
        "target": "scan",
        "note": "The recurrence has processed tokens 0 through 2. This table shows channel 0’s three state coordinates; the complete state holds eight channels. Delta, B and C come from the current convolved token. Exact diagonal ZOH gives Ā = exp(ΔA) and B̄ = (exp(ΔA)−1)B/A. This is a recorded CPU loop, without the fused parallel scan or measured GPU speed.",
        "matrices": [
          {
            "label": "Channel 0 state history · processed tokens × state coordinates",
            "values": [
              [
                0.0028182393539163413,
                -0.010537066745402683,
                -0.00784164629620153
              ],
              [
                0.004873730432046338,
                -0.00915477022339425,
                -0.011602296275764815
              ],
              [
                -0.00301501689061632,
                -0.011337814206202949,
                -0.007509822729152433
              ]
            ]
          },
          {
            "label": "Current full state · channels × coordinates",
            "values": [
              [
                -0.00301501689061632,
                -0.011337814206202949,
                -0.007509822729152433
              ],
              [
                0.003005532147151552,
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                0.008067929216438398
              ],
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              ],
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              [
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                -0.01015187481480913,
                -0.005501725106148151
              ],
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                0.0006290388110263834,
                0.0004366245153112298
              ]
            ]
          }
        ],
        "vectors": [
          {
            "label": "Current input token",
            "values": [
              0.5777008018447466,
              0.21219867531604147,
              -1.3373748058478179,
              0.5705738667927814
            ]
          },
          {
            "label": "Current delta · eight channels",
            "values": [
              0.4846955167975028,
              0.3300814347688844,
              1.2746148110636655,
              0.9269083368444032,
              1.320065552066713,
              0.41988940541893655,
              0.962065418401713,
              1.173750458589704
            ]
          },
          {
            "label": "Channel 0 decay factors",
            "values": [
              0.6158846947620713,
              0.3793139565418216,
              0.23361365403755702
            ]
          },
          {
            "label": "Channel 0 write contribution",
            "values": [
              -0.0060166728701097965,
              -0.00786528209153602,
              -0.004799367900944675
            ]
          }
        ],
        "metrics": [
          {
            "label": "SSM state values per sequence",
            "value": 24
          },
          {
            "label": "Convolution history values per sequence",
            "value": 16
          }
        ]
      },
      {
        "id": "last",
        "label": "After token 5",
        "target": "scan",
        "note": "The recurrence has processed tokens 0 through 5. This table shows channel 0’s three state coordinates; the complete state holds eight channels. Delta, B and C come from the current convolved token. Exact diagonal ZOH gives Ā = exp(ΔA) and B̄ = (exp(ΔA)−1)B/A. This is a recorded CPU loop, without the fused parallel scan or measured GPU speed.",
        "matrices": [
          {
            "label": "Channel 0 state history · processed tokens × state coordinates",
            "values": [
              [
                0.0028182393539163413,
                -0.010537066745402683,
                -0.00784164629620153
              ],
              [
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                -0.011602296275764815
              ],
              [
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                -0.007509822729152433
              ],
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              ],
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                -0.006250632512568108
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                -0.0014739041684932782,
                -0.010938218661359047,
                -0.00941267502904927
              ]
            ]
          },
          {
            "label": "Current full state · channels × coordinates",
            "values": [
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                -0.0014739041684932782,
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                -0.00941267502904927
              ],
              [
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                0.0099463640652495
              ],
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                -0.008582505265828355
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                0.002493074789237922
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                -0.01901798503340152,
                -0.002914908392832273,
                0.0027143148163792426
              ],
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                -0.008932811578534396,
                -0.009116039782672449
              ],
              [
                -0.0025505728680483807,
                -0.004806505645996672,
                -0.00424639459714048
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            ]
          }
        ],
        "vectors": [
          {
            "label": "Current input token",
            "values": [
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              -0.8704264341806643,
              -1.6371821259053128,
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          },
          {
            "label": "Current delta · eight channels",
            "values": [
              0.49630550766785203,
              0.3285376263807963,
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              0.9248770483142744,
              1.3069623336906422,
              0.4307808885160657,
              0.9526662016947541,
              1.1774537056310086
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          },
          {
            "label": "Channel 0 decay factors",
            "values": [
              0.6087756270379251,
              0.37060776337475504,
              0.22561696729737396
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          },
          {
            "label": "Channel 0 write contribution",
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        "metrics": [
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            "label": "SSM state values per sequence",
            "value": 24
          },
          {
            "label": "Convolution history values per sequence",
            "value": 16
          }
        ]
      },
      {
        "id": "changed",
        "label": "Change token 2 · inspect final state",
        "target": "scan",
        "note": "The recurrence has processed tokens 0 through 5. This table shows channel 0’s three state coordinates; the complete state holds eight channels. Delta, B and C come from the current convolved token. Exact diagonal ZOH gives Ā = exp(ΔA) and B̄ = (exp(ΔA)−1)B/A. Token 2 changes while later input tokens stay fixed, exposing the carried influence.",
        "matrices": [
          {
            "label": "Channel 0 state history · processed tokens × state coordinates",
            "values": [
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