Residual Streams Read, Recurrent States Remember: The Global Workspace in Mamba Models
Organizations: Fin AI Research
Abstract
Can the global-workspace account of transformer representations extend to state-space language models? We fit Jacobian lenses to the residual streams and recurrent states of Mamba-1, Mamba-2 and Mamba-3, using the original 1000-prompt recipe. Joint residual--state readouts improve recovery of known intermediate concepts over the residual lens on at least five of six task families in every tested Mamba checkpoint. On Mamba-2, state alone exceeds residual and logit lenses on all six families; a normalised joint readout improves on both components on five. Temporal maps and word-list experiments show earlier content remaining state-readable as residual visibility changes. We also propose sign-guarded steering, which improves target top-five success over coordinate exchange on matched verbal-report trials in five models. Recurrent state alone supports this verbal access. These gains do not extend consistently to relational answers: guarded edits often output the edited concept itself, and Mamba-3's joint edits can disrupt successful state-only redirection. Recurrent state thus provides a complementary carrier of workspace content, whose recovery, persistence and causal uses require separate measurements.
Figures & tables
| Model | Params. | Blocks | State blocks | Role | |
|---|---|---|---|---|---|
| Mamba-1 | 2.8B | 64 | 2560 | 63 | recurrent comparison |
| Mamba-2 | 2.7B | 64 | 2560 | 63 | principal model |
| Mamba-3 SISO | 1.5B | 24 | 2048 | 23 | recurrent comparison |
| Mamba-3 MIMO | 1.5B | 24 | 2048 | 23 | readout comparison |
| Pythia | 2.8B | 32 | 2560 | – | transformer control |
| Nemotron-3.5 | 30B/3B active | 52 | 2688 | 23 | hybrid control |
| Task | Edited concept (example) | Scored output |
|---|---|---|
| Verbal report | Category answer: Canada to Brazil | Brazil in next-token top five |
| Two-hop reasoning | Implicit intermediate: Brazil to Mexico | Spanish, the new intermediate’s answer |
| Flexible generalisation | Explicit argument: France to Canada | Ottawa, the function’s new answer |
| Model | Best state residual | Plain joint residual | State coverage |
|---|---|---|---|
| Mamba-1 2.8B | 5/6 | 6/6 | 63 source blocks |
| Mamba-2 2.7B | 6/6 | 6/6 | 63 source blocks |
| Mamba-3 SISO 1.5B | 5/6 | 5/6 | 23 source blocks |
| Mamba-3 MIMO 1.5B | 4/6 | 5/6 | 23 source blocks |
| Task | Residual | State | Joint normalised | Permuted-state joint |
|---|---|---|---|---|
| Multihop | 0.475 | 0.557 | 0.679 | 0.431 |
| Multilingual | 0.362 | 0.615 | 0.647 | 0.312 |
| Order of ops. | 0.460 | 0.795 | 0.807 | 0.515 |
| Poetry | 0.029 | 0.101 | 0.114 | 0.092 |
| Association | 0.058 | 0.237 | 0.231 | 0.117 |
| Typo | 0.303 | 0.706 | 0.714 | 0.350 |
| Mamba-1 | Mamba-2 | |
|---|---|---|
| Rank words held@5 | 7.5 | 6.7 |
| Transported-state pursuit words | 18.7 | 18.6 |
| Transformers | SSMs | Hybrid | ||||
|---|---|---|---|---|---|---|
| Measurement | Qwen3.6 27B † | Pythia 2.8B | Mamba-1 2.8B | Mamba-2 2.7B | Mamba-3 SISO 1.5B | Nemotron 3.5 |
| Verbal report Target top-5 | 85/124 | 242/399 | 85/446 | 114/335 | 207/728 | 130/621 |
| Two-hop reasoning Requested answer | 47/90 | 5/90 | 6/90 | 7/90 | 6/90 | 15/90 |
| Flexible generalisation Requested answer | 80/192 | 13/192 | 30/192 | 12/192 | 23/192 | 29/192 |
| Introspection Injected token top-1 | 0/101 | 2/99 | : 0/99 : 0/99 | : 0/99 : 4/99 | : 6/101 : 49/101 | : 0/99 : 93/99 |
| Directed modulation Focus / control / suppress hit@5 | .38/.07/.07 | .04/.07/.04 | : .01/.05/.04 : .15/.15/.13 | : .01/.05/.04 : .15/.20/.17 | : .00/.00/.01 : .07/.09/.10 | : .02/.02/.02 : .03/.05/.02 |
| Transformers | SSMs | Hybrid | ||||
|---|---|---|---|---|---|---|
| Intervention | Qwen3.6 27B † | Pythia 2.8B | Mamba-1 2.8B | Mamba-2 2.7B | Mamba-3 SISO 1.5B | Nemotron 3.5 |
| Table 6 result Coordinate exchange in this study | 85/124 | 242/399 | 85/446 | 114/335 | 207/728 | 130/621 |
| Sign-guarded steering | – | 298/399 | 426/446 | 333/335 | 677/728 | 621/621 |
Appendix figures & tables27 assets
Supplementary material from the paper’s appendix.
Appendix
| Any block (0–62) | Band (16–48) | |||
|---|---|---|---|---|
| Task | State | Residual | State | Residual |
| Multihop | 0.557 | 0.475 | 0.444 | 0.313 |
| Multilingual | 0.615 | 0.362 | 0.601 | 0.276 |
| Order of ops. | 0.795 | 0.460 | 0.589 | 0.266 |
| Poetry | 0.101 | 0.029 | 0.078 | 0.014 |
| Association | 0.237 | 0.058 | 0.196 | 0.051 |
| Task | State | Logit | Tuned | Permuted state |
|---|---|---|---|---|
| Multihop | 0.557 | 0.379 | 0.441 | 0.021 |
| Multilingual | 0.615 | 0.449 | 0.446 | 0.056 |
| Order of ops. | 0.795 | 0.647 | 0.666 | 0.164 |
| Poetry | 0.101 | 0.049 | 0.036 | 0.049 |
| Association | 0.237 | 0.027 | 0.036 | 0.022 |
| Typo | 0.706 | 0.292 | 0.279 | 0.040 |
| Task | WikiText J-lens | Old Pile J-lens | Logit | Tuned |
|---|---|---|---|---|
| Multihop | 0.470 | 0.474 | 0.296 | 0.353 |
| Multilingual | 0.324 | 0.333 | 0.214 | 0.217 |
| Order of ops. | 0.736 | 0.748 | 0.583 | 0.674 |
| Poetry | 0.063 | 0.078 | 0.018 | 0.031 |
| Association | 0.008 | 0.014 | 0.001 | 0.002 |
| Typo | 0.377 | 0.369 | 0.287 | 0.239 |
| Task | Original | Row zeroed | Change |
|---|---|---|---|
| Multihop | 0.475 | 0.443 | |
| Multilingual | 0.362 | 0.335 | |
| Order of ops. | 0.460 | 0.417 | |
| Poetry | 0.029 | 0.045 | |
| Association | 0.058 | 0.056 | |
| Typo | 0.303 | 0.304 |
| Model | Band blocks | Clean | ||
| Mamba-1 | 33 | 1 [0.2, 6.0] | 7 [3.8, 15.2] | 20 |
| Mamba-2 | 33 | 1 [0.2, 6.0] | – | 25 |
| Mamba-2, sparse | 12 | 1 [0.2, 6.0] | 1 [0.2, 6.0] | 25 |
| Mamba-3 SISO | 13 | 12 [7.8, 21.9] | 19 [14.0, 30.6] | 27 |
| Random / shuffled | matched | 1 [0.2, 6.0] per run | – | |
| Construction / outcome | Count | 95% interval (%) |
|---|---|---|
| Residual exchange, all scorable | 10/80 | [6.9, 21.5] |
| Residual exchange, given clean correct | 7/23 | [15.6, 50.9] |
| Original pursuit, retained | 22/37 | [43.5, 73.7] |
| Row-zeroed pursuit, retained | 12/37 | [19.6, 48.5] |
| Coordinates 2–11, retained | 22/37 | [43.5, 73.7] |
| Random coordinates 2–21, retained | 26/37 | [54.2, 82.5] |
| Construction | State, all | State, clean correct | Both, all |
|---|---|---|---|
| exchange | 1/84 [0.2, 6.4] | 0/29 [0.0, 11.7] | 6/84 [3.3, 14.7] |
| clamp | 22/84 [18.0, 36.5] | 14/29 [31.4, 65.6] | 15/84 [11.1, 27.4] |
| clamp | 13/84 [9.3, 24.7] | 8/29 [14.7, 45.7] | 14/84 [10.2, 26.1] |
| Model | Residual only | State only | Both |
|---|---|---|---|
| Mamba-1 | 10/90 | 1/90 | 11/90 |
| Mamba-2 | 1/90 | 1/90 | 1/90 |
| Mamba-3 | 3/90 | 12/90 | 14/90 |
| Condition | Target rank | Top-1 word | Top-5 success |
|---|---|---|---|
| Clean | 20 | Canada | No |
| Residual clamp | 1 | Brazil | Yes |
| State clamp | 16 | France | No |
| Simultaneous clamps | 1 | Brazil | Yes |
| Matched random residual | 23 | Canada | No |
| Matched random state | 20 | Canada | No |
| Model | Evaluation prompts | Valid clean prompts | Eligible target swaps |
|---|---|---|---|
| Mamba-1 2.8B | 140 | 110 | 446 |
| Mamba-2 2.7B | 140 | 99 | 335 |
| Mamba-3 SISO 1.5B | 140 | 124 | 728 |
| Nemotron-3.5 hybrid | 140 | 134 | 621 |
| Pythia-2.8B | 140 | 107 | 399 |
| Model | Site | C | U | Rw | ctrl | U ctrl | Rw ctrl | |||
|---|---|---|---|---|---|---|---|---|---|---|
| Mamba-1 | R | 446 | 0 | 446 | 417 | 87 | 90 | 5/4/3 | 2/1/0 | 2/1/0 |
| Mamba-1 | S | 446 | 0 | 32 | 290 | 31 | 27 | 0/0/0 | 0/0/0 | 0/0/0 |
| Mamba-1 | RS | 446 | 0 | 446 | 426 | 85 | 87 | 7/6/5 | 2/0/1 | 2/0/1 |
| Mamba-2 | R | 335 | 0 | 44 | 291 | 120 | 121 | 0/0/0 | 0/1/1 | 3/2/4 |
| Mamba-2 | S | 335 | 0 | 0 | 258 | 1 | 1 | 0/0/0 | 0/0/0 | 0/0/0 |
| Mamba-2 | RS | 335 | 0 | 47 | 333 | 114 | 117 | 1/4/0 | 0/1/0 | 4/2/5 |
| Model | Site | Interval | Interval | ||
|---|---|---|---|---|---|
| Mamba-1 | R | +0.740 | [+0.628, +0.844] | +0.733 | [+0.620, +0.835] |
| Mamba-1 | S | +0.581 | [+0.499, +0.654] | +0.590 | [+0.510, +0.662] |
| Mamba-1 | RS | +0.765 | [+0.672, +0.857] | +0.760 | [+0.674, +0.847] |
| Mamba-2 | R | +0.510 | [+0.402, +0.617] | +0.507 | [+0.392, +0.616] |
| Mamba-2 | S | +0.767 | [+0.704, +0.829] | +0.767 | [+0.704, +0.831] |
| Mamba-2 | RS | +0.654 | [+0.547, +0.757] | +0.645 | [+0.533, +0.750] |
| Model | Site | |||||
|---|---|---|---|---|---|---|
| Mamba-1 | R | 446 | 436 | 376 | 34 | 28 |
| Mamba-1 | S | 446 | 2 | 202 | 1 | 3 |
| Mamba-1 | RS | 446 | 442 | 401 | 19 | 17 |
| Mamba-2 | R | 335 | 26 | 258 | 74 | 77 |
| Mamba-2 | S | 335 | 0 | 203 | 0 | 0 |
| Mamba-2 | RS | 335 | 27 | 314 | 69 | 74 |
| Model | Site | C | U | Rw | ctrl | U ctrl | Rw ctrl | |||
|---|---|---|---|---|---|---|---|---|---|---|
| Mamba-1 | R | 90 | 1 | 10 | 5 | 7 | 7 | 1/1/3 | 1/1/1 | 1/1/1 |
| Mamba-1 | S | 90 | 1 | 1 | 1 | 1 | 1 | 1/1/1 | 1/1/1 | 1/1/1 |
| Mamba-1 | RS | 90 | 1 | 11 | 4 | 6 | 6 | 1/2/3 | 1/1/1 | 1/1/1 |
| Mamba-2 | R | 90 | 1 | 1 | 12 | 7 | 7 | 1/1/1 | 1/2/1 | 0/2/1 |
| Mamba-2 | S | 90 | 1 | 1 | 2 | 1 | 1 | 1/1/1 | 1/1/1 | 1/1/1 |
| Mamba-2 | RS | 90 | 1 | 1 | 6 | 7 | 5 | 1/1/1 | 1/2/1 | 0/3/1 |
| Model | Site | Interval | Interval | ||
|---|---|---|---|---|---|
| Mamba-1 | R | -0.022 | [-0.089, +0.056] | -0.022 | [-0.089, +0.056] |
| Mamba-1 | S | +0.000 | [+0.000, +0.000] | +0.000 | [+0.000, +0.000] |
| Mamba-1 | RS | -0.022 | [-0.089, +0.044] | -0.022 | [-0.089, +0.044] |
| Mamba-2 | R | +0.056 | [-0.033, +0.144] | +0.056 | [-0.011, +0.133] |
| Mamba-2 | S | +0.011 | [+0.000, +0.044] | +0.011 | [+0.000, +0.044] |
| Mamba-2 | RS | -0.011 | [-0.100, +0.067] | +0.011 | [-0.067, +0.078] |
| Model | Site | C | U | Rw | ctrl | U ctrl | Rw ctrl | |||
|---|---|---|---|---|---|---|---|---|---|---|
| Mamba-1 | R | 192 | 4 | 37 | 18 | 32 | 33 | 2/2/3 | 6/4/3 | 6/4/3 |
| Mamba-1 | S | 192 | 4 | 3 | 3 | 3 | 3 | 4/4/4 | 4/4/3 | 4/4/3 |
| Mamba-1 | RS | 192 | 4 | 37 | 18 | 30 | 31 | 2/2/3 | 6/4/3 | 6/4/3 |
| Mamba-2 | R | 192 | 2 | 2 | 8 | 12 | 12 | 0/0/0 | 2/1/3 | 2/2/3 |
| Mamba-2 | S | 192 | 2 | 3 | 2 | 3 | 3 | 2/2/2 | 2/2/2 | 2/2/2 |
| Mamba-2 | RS | 192 | 2 | 2 | 23 | 12 | 11 | 0/0/0 | 2/1/3 | 2/2/3 |
| Model | Site | Interval | Interval | ||
|---|---|---|---|---|---|
| Mamba-1 | R | -0.073 | [-0.188, +0.047] | -0.078 | [-0.193, +0.042] |
| Mamba-1 | S | +0.000 | [+0.000, +0.000] | +0.000 | [+0.000, +0.000] |
| Mamba-1 | RS | -0.062 | [-0.172, +0.052] | -0.068 | [-0.177, +0.052] |
| Mamba-2 | R | -0.021 | [-0.120, +0.078] | -0.021 | [-0.115, +0.078] |
| Mamba-2 | S | -0.005 | [-0.026, +0.000] | -0.005 | [-0.026, +0.000] |
| Mamba-2 | RS | +0.057 | [-0.036, +0.146] | +0.062 | [-0.016, +0.141] |
| Exchange failures | Edited-intermediate outputs | |||
| Model | Total | Retain clean first token | Coordinate exchange | Sign-guarded steering |
| Mamba-1 | 84 | 73 | 1 | 55 |
| Mamba-2 | 83 | 69 | 2 | 37 |
| Mamba-3 SISO | 84 | 59 | 2 | 74 |
| Nemotron | 75 | 60 | 1 | 73 |
| Pythia | 85 | 72 | 3 | 72 |
| Model | Edit | A | I | O | S | C | D | |
|---|---|---|---|---|---|---|---|---|
| Mamba-1 | Xunit | 90 | 6 | 1 | 11 | 1 | 61 | 10 |
| Mamba-1 | G | 90 | 4 | 55 | 0 | 0 | 7 | 24 |
| Mamba-1 | N | 90 | 11 | 12 | 2 | 0 | 48 | 17 |
| Mamba-1 | Xraw | 90 | 6 | 1 | 12 | 1 | 59 | 11 |
| Mamba-2 | Xunit | 90 | 7 | 2 | 12 | 2 | 55 | 12 |
| Mamba-2 | G | 90 | 6 | 37 | 0 | 0 | 21 | 26 |
| Model | Edit | A | I | O | S | C | D | |
|---|---|---|---|---|---|---|---|---|
| Mamba-1 | Xunit | 20 | 3 | 1 | 11 | 0 | 0 | 5 |
| Mamba-1 | G | 20 | 3 | 12 | 0 | 0 | 0 | 5 |
| Mamba-1 | N | 20 | 6 | 6 | 2 | 0 | 0 | 6 |
| Mamba-1 | Xraw | 20 | 3 | 1 | 12 | 0 | 0 | 4 |
| Mamba-2 | Xunit | 25 | 5 | 1 | 12 | 0 | 0 | 7 |
| Mamba-2 | G | 25 | 4 | 10 | 0 | 0 | 0 | 11 |
| Model | Site | Edit | A | I | O | S | C | D |
|---|---|---|---|---|---|---|---|---|
| Mamba-1 | R | N | 10 | 12 | 2 | 0 | 48 | 18 |
| Mamba-1 | R | G | 5 | 53 | 0 | 0 | 9 | 23 |
| Mamba-1 | R | Xunit | 7 | 1 | 10 | 1 | 62 | 9 |
| Mamba-1 | R | Xraw | 7 | 1 | 10 | 1 | 64 | 7 |
| Mamba-1 | S | N | 1 | 0 | 20 | 1 | 64 | 4 |
| Mamba-1 | S | G | 1 | 0 | 20 | 1 | 64 | 4 |
| Model | Alignment | Own overlap | Residual energy | State energy | Random |
|---|---|---|---|---|---|
| Mamba-1 | 0.887 | 0.500 | 0.381 | 0.752 | 0.0062 |
| Mamba-2 | 0.882 | 0.504 | 0.554 | 0.659 | 0.0063 |
| Mamba-3 SISO | 0.894 | 0.593 | 0.400 | 0.619 | 0.0079 |
| Model | Task | Full | Shared | Complement | Own | Random |
|---|---|---|---|---|---|---|
| Mamba-1 | Multihop | 0.554 | 0.204 | 0.534 | 0.211 | 0.019 |
| Multilingual | 0.710 | 0.106 | 0.666 | 0.100 | 0.042 | |
| Order of ops. | 0.801 | 0.389 | 0.807 | 0.722 | 0.106 | |
| Poetry | 0.115 | 0.039 | 0.113 | 0.043 | 0.058 | |
| Association | 0.337 | 0.116 | 0.274 | 0.073 | 0.038 | |
| Typo | 0.712 | 0.150 | 0.853 | 0.079 | 0.066 |
| Analysis checked | Assertions |
|---|---|
| State and joint readouts | 974 |
| Held-out residual Jacobian geometry | 752 |
| Held-out state Jacobian geometry | 4077 |
| Readout protocols and intervention controls | 2214 |
| Direction and fixed-budget controls | 508 |
| Coordinate exchange and numerical cross-checks | 1234 |