How Causality Bridges the Semantic Gap
Organizations: University of California, San Diego · University of Illinois Urbana-Champaign
Abstract
Numerical measurements capture how a system behaves, but often leave the meanings of its variables unspecified. Some variables are measured but never labeled, and others are never measured at all. Existing methods assign semantics to such variables by consulting general human knowledge, but this inherits its biases where that knowledge exists and offers nothing where it does not. We bridge this gap between measurements and their meanings with causal structure instead, reading a variable's semantics from how it acts on other variables. We formalize this as structure-constrained semantic alignment, in which the embedding of each unnamed variable is solved under the dependence relations implied by the causal graph, with the embeddings of a few known names as anchors. Accordingly, we build CausalBridge, a framework that discovers the causal graph from the measurements, latent variables included, solves for the embeddings under those relations, and expresses them as names through a language model. The causal structure reflects the mechanism that generated the measurements and is recovered from the measurements alone, which may make it the one source of information free of bias from human knowledge. We evaluate CausalBridge on five questionnaires and three robotics scenarios, with 20 to 90% of the variable names masked. It recovers the semantics of observed and latent variables more accurately than existing methods that rely on association, and its lead widens as less of the system is documented. The graph it discovers names variables as accurately as the documented one, and a new system is named in minutes and at a fraction of the cost of sampling methods. Once the semantic gap is bridged faithfully, machines can understand the world and take actions causally.
Figures & tables
Appendix figures & tables60 assets
Supplementary material from the paper’s appendix.
Appendix
| symbol | meaning |
|---|---|
| Setting and causal structure | |
| the variables, observed and latent | |
| , | the causal mechanism of in Eq. 1 , and its noise term |
| , | the measurement matrix over the observed variables, and the number of samples |
| the true naming map, from a variable to its text | |
| , | the space of text, and the name written for an unnamed variable |
| Causal neighbors given to the model |
| - EFFECT: it causes the item ”I experienced breathing difficulty (eg, excessively rapid breathing, breathlessness in the absence of physical exertion).” |
| - EFFECT: it causes the item ”(label hidden)” |
| - EFFECT: it causes the item ”(label hidden)” |
| - EFFECT: it causes the item ”I experienced trembling (eg, in the hands).” |
| Structural evidence given to the model |
| a factor with 4 items (2 hidden), visible items: ”I experienced breathing difficulty (eg, excessively rapid breathing, breathlessness in the absence of physical exertion).”, ”I experienced trembling (eg, in the hands).”. its factor score correlates +0.73 with the factor of ”I found myself in situations that made me so anxious I was most relieved when they ended.” / ”I had a feeling of faintness.”, +0.68 with the factor of ”I found it difficult to relax.” / ”I found it hard to wind down.”, +0.52 with the factor of ”I felt down-hearted and blue.” / ”I was unable to become enthusiastic about anything.”. cue phrases decoded from its data: feeling nervous, nervousness. in the constrained embedding its vector lies closest to ”I experienced trembling (eg, in the hands).” (cos 0.94), ”I felt that I was using a lot of nervous energy.” (cos 0.92). its hidden items read from the data as: feeling nervous, trembling; feeling nervous, nervousness. |
| set | members | number | channels | steps |
|---|---|---|---|---|
| simulated arms | Panda (lift), Sawyer, IIWA, UR5e, Kinova3, xArm7 | 6 | 32 to 44 | 1,200 |
| real logs | UTokyo xArm, Stanford HYDRA, ALOHA cup | 3 | 13, 14, 28 | 1,200 |
| vehicle drives | comma2k19 drives | 10 | 12 | 2,400, one drive 1,199 |
| scale | instrument | items | latent variables | respondents | source | role |
| DASS | Depression Anxiety Stress Scales ( Lovibond & Lovibond, 1995 ) | 42 | 3 | 5,000 | ( OSP, 2018b ) | evaluation |
| HEXACO | IPIP-HEXACO scales ( Ashton et al., 2007 ) | 240 | 6 domains, 24 facets | 5,000 | ( OSP, 2014b ) | evaluation |
| KIMS | Kentucky Inventory of Mindfulness Skills ( Baer et al., 2004 ) | 39 | 4 | 521 | ( OSP, 2012c ) | evaluation |
| RIASEC | Holland occupational interest types ( Holland, 1997 ) | 48 | 6 | 5,000 | ( OSP, 2018d ) | evaluation |
| WVS | World Values Survey, Welzel indices ( Welzel, 2013 ) | 21 | 2 indices, 7 sub-indices | 5,000 | ( Haerpfer et al., 2024 ) | evaluation |
| 16PF | IPIP scales for Cattell’s sixteen personality factors ( Cattell et al., 1970 ; Goldberg et al., 2006 ) | 162 | 16 | 5,000 | ( OSP, 2014a ) | training |
| trained part | training data | size |
|---|---|---|
| optimization, questionnaires (operator, weight network, encoder fine-tuning) | the sixteen public scales with their published keys (Table 4 ) | 16 scales |
| optimization, robots (operator, weight network) | generated arms and vehicles | 20 |
| encoder fine-tuning, robots | generated arms and vehicles, warm-started from the questionnaire one, 20,000 general words held fixed | 300 |
| semantic negation map | WordNet antonym pairs and pole pairs from the sixteen training scales | — |
| adapter and low-rank update, questionnaires | synthetic scales, after the leakage filter | 600 scales, 33,073 examples |
| adapter and low-rank update, robots | generated arms and vehicles, each under its true graph and under a degraded edge set | , 391,352 examples |
| arm, log or drive | supplied | found | shared |
|---|---|---|---|
| Panda | 113 | 148 | 29 |
| Sawyer | 108 | 100 | 27 |
| IIWA | 122 | 106 | 31 |
| UR5e | 106 | 117 | 34 |
| Kinova3 | 121 | 109 | 24 |
| xArm7 | 119 | 92 | 28 |
| scale | published latent variables | discovered latent variables | latent to latent edges | items reached | purity |
| DASS | 3 | 9 | 2 | 40 / 42 | 0.86 |
| HEXACO | 24 | 25 | 5 | 64 / 240 | 0.80 |
| KIMS | 4 | 11 | 5 | 29 / 39 | 0.88 |
| RIASEC | 6 | 13 | 8 | 28 / 48 | 0.95 |
| WVS | 7 | 12 | 14 | 21 / 21 | 0.53 |
| all five | 44 | 70 | 34 | 182 / 390 | — |
| NRR@1 | MRR | identification | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| simulated arms | CausalBridge | .083 | .140 | .137 | .046 | .224 | .286 | .278 | .194 | .106 | .203 | .208 | .116 |
| CLIP-Dissect-e5 | .083 | .058 | .027 | .027 | .185 | .186 | .116 | .120 | .062 | .050 | .033 | .060 | |
| AutoInterp | .000 | .008 | .011 | .005 | .078 | .095 | .095 | .086 | .000 | .033 | .039 | .033 | |
| Delphi | .000 | .025 | .016 | .005 | .079 | .120 | .119 | .083 | .062 | .034 | .072 | .028 | |
| SASC-style | .021 | .058 | .027 | .018 | .112 | .162 | .130 | .118 | .042 | .074 | .060 | .028 | |
| NRR@1 | MRR | SDA | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| simulated arms | CausalBridge | .083 | .140 | .137 | .046 | .224 | .286 | .278 | .194 | .128 | .190 | .153 | .164 |
| CLIP-Dissect-e5 | .083 | .058 | .027 | .027 | .185 | .186 | .116 | .120 | .234 | .155 | .142 | .169 | |
| AutoInterp | .000 | .008 | .011 | .005 | .078 | .095 | .095 | .086 | .255 | .207 | .165 | .155 | |
| Delphi | .000 | .025 | .016 | .005 | .079 | .120 | .119 | .083 | .043 | .241 | .193 | .197 | |
| SASC-style | .021 | .058 | .027 | .018 | .112 | .162 | .130 | .118 | .170 | .147 | .165 | .183 | |
| NRR@1 | MRR | SDA | identification | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| questionnaire items | CausalBridge | .121 | .098 | .059 | .028 | .253 | .216 | .164 | .105 | .226 | .189 | .164 | .147 | .356 | .364 | .283 | .217 |
| CLIP-Dissect-e5 | .028 | .023 | .022 | .014 | .096 | .095 | .099 | .071 | .097 | .112 | .112 | .137 | .163 | .179 | .183 | .153 | |
| AutoInterp | .010 | .012 | .008 | .007 | .058 | .055 | .054 | .054 | .118 | .124 | .109 | .109 | .085 | .103 | .101 | .099 | |
| Delphi | .008 | .010 | .013 | .011 | .060 | .055 | .060 | .063 | .108 | .113 | .121 | .110 | .141 | .122 | .133 | .113 | |
| SASC-style | .079 | .062 | .035 | .021 | .211 | .175 | .128 | .087 | .169 | .164 | .164 | .136 | .356 | .342 | .303 | .219 | |
| NRR@1 | MRR | identification | naming quality | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| latent variables | CausalBridge | .540 | .486 | .386 | .240 | .660 | .623 | .560 | .424 | .531 | .511 | .441 | .254 | .446 | .426 | .390 | .217 |
| CLIP-Dissect-e5 | .073 | .119 | .127 | .142 | .257 | .288 | .298 | .292 | .128 | .120 | .151 | .121 | .116 | .112 | .135 | .105 | |
| AutoInterp | .096 | .100 | .108 | .088 | .258 | .259 | .270 | .252 | .160 | .140 | .170 | .139 | .160 | .140 | .170 | .139 | |
| Delphi | .123 | .108 | .085 | .069 | .266 | .269 | .251 | .235 | .138 | .108 | .100 | .115 | .138 | .108 | .100 | .115 | |
| SASC-style | .369 | .315 | .204 | .115 | .523 | .479 | .393 | .291 | .502 | .424 | .319 | .204 | .502 | .424 | .319 | .204 | |
| NRR@1 | MRR | SDA | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | CausalBridge | .146 | .198 | .181 | .055 | .317 | .341 | .354 | .225 | .170 | .259 | .222 | .117 |
| CLIP-Dissect-e5 † | .083 | .058 | .027 | .027 | .185 | .186 | .116 | .120 | .234 | .155 | .142 | .169 | ||
| AutoInterp † | .000 | .008 | .011 | .005 | .078 | .095 | .095 | .086 | .255 | .207 | .165 | .155 | ||
| Delphi † | .000 | .025 | .016 | .005 | .079 | .120 | .119 | .083 | .043 | .241 | .193 | .197 | ||
| SASC-style † | .021 | .058 | .027 | .018 | .112 | .162 | .130 | .118 | .170 | .147 | .165 | .183 | ||
| identification | type acc | coord acc | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | CausalBridge | .167 | .252 | .242 | .106 | .542 | .612 | .703 | .525 | .149 | .233 | .216 | .132 |
| CLIP-Dissect-e5 † | .062 | .050 | .033 | .060 | .271 | .215 | .137 | .105 | .085 | .026 | .023 | .009 | ||
| AutoInterp † | .000 | .033 | .039 | .033 | .000 | .107 | .126 | .114 | .000 | .009 | .034 | .000 | ||
| Delphi † | .062 | .034 | .072 | .028 | .104 | .141 | .170 | .132 | .021 | .052 | .051 | .014 | ||
| SASC-style † | .042 | .074 | .060 | .028 | .208 | .281 | .203 | .173 | .043 | .060 | .040 | .014 | ||
| NRR@1 | MRR | SDA | identification | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | CausalBridge | .126 | .097 | .064 | .038 | .254 | .220 | .179 | .121 | .200 | .176 | .147 | .129 | .351 | .314 | .304 | .227 |
| CLIP-Dissect-e5 † | .028 | .023 | .022 | .014 | .096 | .095 | .099 | .071 | .097 | .112 | .112 | .137 | .163 | .179 | .183 | .153 | |
| AutoInterp † | .010 | .012 | .008 | .007 | .058 | .055 | .054 | .054 | .118 | .124 | .109 | .109 | .085 | .103 | .101 | .099 | |
| Delphi † | .008 | .010 | .013 | .011 | .060 | .055 | .060 | .063 | .108 | .113 | .121 | .110 | .141 | .122 | .133 | .113 | |
| SASC-style † | .079 | .062 | .035 | .021 | .211 | .175 | .128 | .087 | .169 | .164 | .164 | .136 | .356 | .342 | .303 | .219 | |
| NRR@1 | MRR | identification | naming quality | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | CausalBridge | .485 | .415 | .415 | .238 | .624 | .560 | .551 | .400 | .627 | .537 | .535 | .351 | .596 | .518 | .500 | .332 |
| CLIP-Dissect-e5 | .158 | .146 | .135 | .181 | .333 | .314 | .315 | .337 | .243 | .203 | .188 | .186 | .243 | .203 | .188 | .186 | |
| AutoInterp | .108 | .108 | .112 | .096 | .262 | .267 | .275 | .260 | .139 | .202 | .135 | .142 | .139 | .202 | .135 | .142 | |
| Delphi | .088 | .123 | .135 | .088 | .250 | .287 | .283 | .257 | .169 | .174 | .192 | .173 | .169 | .174 | .192 | .173 | |
| SASC-style † | .369 | .315 | .204 | .115 | .523 | .479 | .393 | .291 | .502 | .424 | .319 | .204 | .502 | .424 | .319 | .204 | |
| NRR@1 | MRR | identification | type acc | coord acc | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | discovery | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| simulated arms | time only | .083 | .140 | .137 | .046 | .224 | .286 | .278 | .194 | .106 | .203 | .208 | .116 | .396 | .537 | .577 | .420 | .106 | .181 | .159 | .145 |
| with the physical law | .104 | .157 | .132 | .068 | .286 | .316 | .299 | .213 | .167 | .229 | .187 | .144 | .583 | .587 | .654 | .466 | .106 | .198 | .153 | .174 | |
| vehicle CAN | time only | .800 | .367 | .244 | .218 | .859 | .570 | .412 | .397 | .800 | .400 | .300 | .282 | .900 | .683 | .356 | .391 | .800 | .367 | .500 | .367 |
| with the physical law | .950 | .483 | .222 | .209 | .955 | .632 | .379 | .394 | .950 | .500 | .278 | .282 | .950 | .800 | .333 | .427 | 1.000 | .333 | .500 | .200 | |
| variables | metric | 20 | 50 | 75 | 90 |
|---|---|---|---|---|---|
| simulated arms | NRR@1 | .019 .067 (2/6) C | +.079 .040 (4/6) S | +.109 .022 (6/6) S | +.014 .017 (3/6) V |
| MRR | +.026 .058 (5/6) C | +.097 .030 (6/6) C | +.145 .026 (6/6) V | +.069 .017 (6/6) C | |
| identification | +.042 .024 (3/6) D | +.130 .022 (6/6) S | +.135 .031 (6/6) D | +.054 .023 (4/6) C | |
| real logs | NRR@1 | +.167 .167 (1/3) C | +.238 .133 (3/3) S | +.132 .034 (3/3) D | .002 .046 (1/3) D |
| MRR | +.090 .182 (1/3) C | +.177 .090 (3/3) C | +.104 .008 (3/3) D | +.021 .062 (2/3) D | |
| identification | +.111 .111 (1/3) D | +.234 .135 (3/3) D | +.163 .121 (2/3) C | +.000 – (0/1) V |
| variables | metric | 20 | 50 | 75 | 90 |
| simulated arms | NRR@1 | +.037 .084 (3/6) C | +.121 .033 (6/6) B | +.149 .016 (6/6) B | +.027 .021 (3/6) V |
| MRR | +.107 .093 (5/6) C | +.151 .029 (6/6) B | +.220 .020 (6/6) B | +.083 .031 (6/6) B | |
| identification | +.041 .055 (3/6) B | +.058 .038 (4/6) B | +.164 .024 (6/6) B | +.022 .019 (3/6) B | |
| real logs | NRR@1 | +.278 .147 (2/3) B | +.190 .156 (2/3) B | +.098 .002 (3/3) B | +.041 .024 (2/3) D |
| MRR | +.115 .133 (2/3) B | +.098 .133 (2/3) B | +.095 .007 (3/3) B | +.057 .018 (3/3) D | |
| identification | +.167 .096 (2/3) B | +.032 .159 (2/3) B | +.143 .030 (3/3) B | +.115 .071 (3/3) B |
| NRR@1 | MRR | identification | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| simulated arms | Correlation kNN | .000 | .000 | .000 | .000 | .181 | .173 | .159 | .117 | .106 | .067 | .068 | .051 |
| Feature Propagation | .000 | .000 | .000 | .000 | .189 | .157 | .168 | .118 | .128 | .067 | .074 | .052 | |
| real logs | Correlation kNN | .000 | .000 | .000 | .000 | .262 | .218 | .179 | .142 | .083 | .222 | .098 | .040 |
| Feature Propagation | .000 | .000 | .000 | .000 | .210 | .209 | .174 | .136 | .167 | .259 | .122 | .020 | |
| vehicle CAN | Correlation kNN | .000 | .000 | .000 | .000 | .228 | .251 | .181 | .191 | .000 | .083 | .012 | .000 |
| NRR@1 | MRR | identification | naming quality | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| EFA loading naming | .500 | .458 | .381 | .254 | .643 | .611 | .543 | .431 | .608 | .600 | .550 | .402 | .000 | .000 | .000 | .000 |
| Feature Propagation + EFA | .454 | .400 | .358 | .235 | .616 | .570 | .519 | .413 | .631 | .585 | .519 | .342 | .408 | .373 | .308 | .196 |
| NRR@1 | MRR | identification | naming quality | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | scale | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| discovered graph | DASS | .756 | .800 | .622 | .400 | .859 | .881 | .789 | .648 | .689 | .689 | .511 | .222 | .667 | .622 | .511 | .156 |
| HEXACO | .408 | .320 | .304 | .104 | .516 | .462 | .461 | .247 | .512 | .496 | .504 | .248 | .384 | .432 | .456 | .192 | |
| KIMS | .691 | .655 | .418 | .400 | .814 | .803 | .633 | .605 | .382 | .382 | .273 | .164 | .382 | .345 | .255 | .164 | |
| RIASEC | .692 | .585 | .508 | .262 | .793 | .726 | .655 | .473 | .800 | .662 | .562 | .369 | .615 | .446 | .406 | .323 | |
| WVS | .350 | .333 | .217 | .233 | .524 | .488 | .427 | .409 | .300 | .367 | .283 | .250 | .283 | .317 | .267 | .250 | |
| NRR@1 | MRR | identification | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| items | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| CausalBridge | .071 | .067 | .056 | .021 | .192 | .184 | .173 | .101 | .286 | .219 | .176 | .105 |
| CLIP-Dissect-e5 | .000 | .010 | .013 | .011 | .078 | .093 | .115 | .094 | .029 | .107 | .088 | .079 |
| AutoInterp | .024 | .019 | .019 | .016 | .103 | .095 | .103 | .104 | .048 | .105 | .113 | .111 |
| Delphi | .000 | .029 | .013 | .005 | .092 | .093 | .093 | .089 | .143 | .086 | .157 | .074 |
| SASC-style | .071 | .048 | .025 | .016 | .218 | .162 | .130 | .091 | .310 | .143 | .125 | .053 |
| NRR@1 | MRR | identification | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| items | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| CausalBridge | .138 | .113 | .059 | .026 | .249 | .209 | .141 | .080 | .442 | .438 | .348 | .279 |
| CLIP-Dissect-e5 | .025 | .022 | .017 | .013 | .068 | .074 | .068 | .051 | .204 | .209 | .204 | .190 |
| AutoInterp | .004 | .005 | .004 | .000 | .027 | .027 | .027 | .020 | .083 | .114 | .103 | .108 |
| Delphi | .000 | .003 | .004 | .004 | .023 | .026 | .027 | .030 | .167 | .149 | .146 | .133 |
| SASC-style | .087 | .060 | .039 | .016 | .199 | .160 | .117 | .063 | .421 | .438 | .402 | .290 |
| NRR@1 | MRR | identification | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| items | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| CausalBridge | .179 | .050 | .069 | .074 | .370 | .237 | .236 | .198 | .179 | .310 | .214 | .143 |
| CLIP-Dissect-e5 | .026 | .010 | .041 | .017 | .147 | .127 | .165 | .118 | .184 | .140 | .148 | .093 |
| AutoInterp | .026 | .010 | .014 | .011 | .096 | .092 | .099 | .100 | .077 | .051 | .083 | .069 |
| Delphi | .026 | .040 | .041 | .034 | .117 | .126 | .136 | .124 | .154 | .090 | .083 | .069 |
| SASC-style | .077 | .120 | .055 | .057 | .273 | .270 | .203 | .175 | .333 | .242 | .193 | .190 |
| NRR@1 | MRR | identification | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| items | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| CausalBridge | .062 | .042 | .050 | .009 | .220 | .198 | .194 | .124 | .271 | .258 | .200 | .116 |
| CLIP-Dissect-e5 | .042 | .050 | .028 | .014 | .148 | .153 | .147 | .074 | .083 | .167 | .194 | .079 |
| AutoInterp | .021 | .025 | .011 | .023 | .108 | .085 | .075 | .102 | .125 | .117 | .133 | .088 |
| Delphi | .021 | .008 | .022 | .023 | .122 | .085 | .089 | .105 | .042 | .100 | .106 | .102 |
| SASC-style | .062 | .050 | .022 | .014 | .201 | .179 | .119 | .102 | .167 | .217 | .172 | .112 |
| NRR@1 | MRR | identification | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| items | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| CausalBridge | .048 | .220 | .075 | .032 | .269 | .372 | .210 | .184 | .048 | .140 | .075 | .095 |
| CLIP-Dissect-e5 | .095 | .020 | .050 | .032 | .234 | .140 | .188 | .165 | .048 | .060 | .138 | .129 |
| AutoInterp | .000 | .060 | .013 | .032 | .139 | .171 | .127 | .144 | .095 | .040 | .025 | .063 |
| Delphi | .048 | .000 | .037 | .042 | .165 | .116 | .162 | .171 | .048 | .000 | .087 | .063 |
| SASC-style | .048 | .020 | .000 | .032 | .246 | .181 | .127 | .164 | .190 | .100 | .037 | .042 |
| discovered graph | supplied graph | |||||||
|---|---|---|---|---|---|---|---|---|
| arm or log | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| Panda | .167 (6) | .250 (16) | .227 (22) | .138 (29) | .000 (6) | .188 (16) | .208 (24) | .207 (29) |
| Sawyer | .143 (7) | .167 (18) | .154 (26) | .125 (32) | .286 (7) | .278 (18) | .333 (27) | .161 (31) |
| IIWA | .000 (9) | .238 (21) | .152 (33) | .125 (40) | .222 (9) | .300 (20) | .242 (33) | .075 (40) |
| UR5e | .125 (8) | .190 (21) | .258 (31) | .079 (38) | .125 (8) | .190 (21) | .188 (32) | .079 (38) |
| Kinova3 | .111 (9) | .227 (22) | .242 (33) | .128 (39) | .111 (9) | .273 (22) | .182 (33) | .075 (40) |
| NRR@1 | MRR | SDA | identification | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variant | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | CausalBridge | .126 | .097 | .064 | .038 | .254 | .220 | .179 | .121 | .200 | .176 | .147 | .129 | .351 | .314 | .304 | .227 |
| evidence | .067 | .056 | .042 | .025 | .177 | .161 | .130 | .092 | .092 | .092 | .081 | .087 | .190 | .218 | .174 | .131 | |
| prefix | .074 | .053 | .050 | .018 | .217 | .184 | .165 | .101 | .123 | .103 | .122 | .109 | .344 | .314 | .286 | .227 | |
| prefix low-rank update | .074 | .051 | .051 | .017 | .219 | .182 | .166 | .100 | .126 | .102 | .119 | .109 | .338 | .309 | .280 | .228 | |
| discovered graph | CausalBridge | .121 | .098 | .059 | .028 | .253 | .216 | .164 | .105 | .226 | .189 | .164 | .147 | .356 | .364 | .283 | .217 |
| NRR@1 | MRR | identification | naming quality | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variant | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | CausalBridge | .485 | .415 | .415 | .238 | .624 | .560 | .551 | .400 | .627 | .537 | .535 | .351 | .596 | .518 | .500 | .332 |
| evidence | .446 | .450 | .381 | .262 | .579 | .566 | .507 | .396 | .539 | .479 | .496 | .290 | .535 | .475 | .485 | .278 | |
| prefix | .462 | .404 | .319 | .208 | .600 | .550 | .475 | .371 | .496 | .465 | .465 | .281 | .496 | .465 | .462 | .273 | |
| prefix low-rank update | .477 | .419 | .331 | .212 | .614 | .560 | .480 | .376 | .512 | .492 | .454 | .285 | .512 | .492 | .450 | .277 | |
| discovered graph | CausalBridge | .540 | .486 | .386 | .240 | .660 | .623 | .560 | .424 | .531 | .511 | .441 | .254 | .446 | .426 | .390 | .217 |
| NRR@1 | MRR | SDA | identification | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | model | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | Qwen3-4B | .126 | .097 | .064 | .038 | .254 | .220 | .179 | .121 | .200 | .176 | .147 | .129 | .351 | .314 | .304 | .227 |
| Qwen3-4B base model | .074 | .051 | .051 | .017 | .219 | .182 | .166 | .100 | .126 | .102 | .119 | .109 | .338 | .309 | .280 | .228 | |
| Qwen3-8B | .105 | .079 | .056 | .032 | .222 | .199 | .158 | .113 | .182 | .151 | .137 | .132 | .346 | .294 | .260 | .214 | |
| Qwen3-8B base model | .069 | .053 | .036 | .012 | .206 | .180 | .146 | .095 | .136 | .107 | .119 | .115 | .321 | .296 | .264 | .223 | |
| Llama-3.2-3B | .067 | .071 | .062 | .033 | .188 | .181 | .162 | .107 | .113 | .116 | .119 | .120 | .282 | .254 | .258 | .180 | |
| NRR@1 | MRR | SDA | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | variant | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | CausalBridge | .146 | .198 | .181 | .055 | .317 | .341 | .354 | .225 | .170 | .259 | .222 | .117 |
| evidence | .104 | .140 | .099 | .055 | .240 | .350 | .277 | .216 | .149 | .164 | .131 | .150 | ||
| prefix | .333 | .198 | .088 | .018 | .402 | .288 | .206 | .122 | .447 | .293 | .250 | .183 | ||
| prefix low-rank update | .021 | .083 | .033 | .023 | .164 | .193 | .135 | .148 | .255 | .293 | .205 | .211 | ||
| supplied graph | real logs | CausalBridge | .500 | .333 | .244 | .160 | .566 | .451 | .369 | .276 | .545 | .440 | .333 | .298 |
| NRR@1 | MRR | identification | naming quality | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | model | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | Qwen3-4B | .485 | .415 | .415 | .238 | .624 | .560 | .551 | .400 | .627 | .537 | .535 | .351 | .596 | .518 | .500 | .332 |
| Qwen3-4B base model | .477 | .419 | .331 | .212 | .614 | .560 | .480 | .376 | .512 | .492 | .454 | .285 | .512 | .492 | .450 | .277 | |
| Qwen3-8B | .454 | .404 | .346 | .235 | .582 | .552 | .512 | .405 | .573 | .537 | .504 | .377 | .569 | .537 | .492 | .369 | |
| Qwen3-8B base model | .385 | .323 | .338 | .219 | .539 | .490 | .488 | .381 | .486 | .469 | .462 | .279 | .486 | .454 | .435 | .244 | |
| Llama-3.2-3B | .535 | .454 | .373 | .273 | .646 | .588 | .528 | .423 | .558 | .560 | .523 | .350 | .558 | .560 | .515 | .350 | |
| NRR@1 | MRR | SDA | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | model | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | Qwen3-4B | .146 | .198 | .181 | .055 | .317 | .341 | .354 | .225 | .170 | .259 | .222 | .117 |
| Qwen3-4B base model | .021 | .083 | .033 | .023 | .164 | .193 | .135 | .148 | .255 | .293 | .205 | .211 | ||
| Qwen3-8B | .167 | .182 | .170 | .119 | .326 | .329 | .348 | .265 | .213 | .259 | .216 | .197 | ||
| Qwen3-8B base model | .083 | .058 | .027 | .046 | .221 | .168 | .141 | .165 | .255 | .233 | .210 | .207 | ||
| Llama-3.2-3B | .271 | .157 | .154 | .105 | .393 | .300 | .304 | .251 | .319 | .259 | .182 | .225 | ||
| identification | type acc | coord acc | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | model | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | Qwen3-4B | .167 | .252 | .242 | .106 | .542 | .612 | .703 | .525 | .149 | .233 | .216 | .132 |
| Qwen3-4B base model | .109 | .190 | .078 | .084 | .375 | .281 | .214 | .288 | .043 | .172 | .074 | .061 | ||
| Qwen3-8B | .229 | .267 | .222 | .188 | .604 | .612 | .692 | .516 | .170 | .267 | .222 | .183 | ||
| Qwen3-8B base model | .085 | .137 | .084 | .083 | .458 | .281 | .220 | .251 | .043 | .103 | .074 | .070 | ||
| Llama-3.2-3B | .312 | .264 | .228 | .165 | .583 | .488 | .588 | .498 | .298 | .241 | .188 | .174 | ||
| NRR@1 | MRR | SDA | identification | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | CausalBridge | .126 | .097 | .064 | .038 | .254 | .220 | .179 | .121 | .200 | .176 | .147 | .129 | .351 | .314 | .304 | .227 |
| CausalBridge with CMI | .123 | .101 | .072 | .039 | .256 | .223 | .183 | .119 | .195 | .178 | .154 | .138 | .362 | .324 | .309 | .208 | |
| discovered graph | CausalBridge | .121 | .098 | .059 | .028 | .253 | .216 | .164 | .105 | .226 | .189 | .164 | .147 | .356 | .364 | .283 | .217 |
| CausalBridge with CMI | .133 | .094 | .057 | .036 | .265 | .218 | .166 | .113 | .231 | .193 | .164 | .153 | .367 | .359 | .301 | .209 | |
| NRR@1 | MRR | SDA | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| structure | variables | method | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 |
| supplied graph | simulated arms | CausalBridge | .146 | .198 | .181 | .055 | .317 | .341 | .354 | .225 | .170 | .259 | .222 | .117 |
| CausalBridge with CMI | .146 | .215 | .187 | .064 | .301 | .372 | .361 | .227 | .170 | .250 | .199 | .169 | ||
| supplied graph | real logs | CausalBridge | .500 | .333 | .244 | .160 | .566 | .451 | .369 | .276 | .545 | .440 | .333 | .298 |
| CausalBridge with CMI | .500 | .333 | .268 | .160 | .593 | .451 | .386 | .300 | .545 | .440 | .359 | .255 | ||
| supplied graph | vehicle CAN | CausalBridge | .750 | .300 | .156 | .145 | .775 | .553 | .317 | .378 | 1.000 | .300 | .400 | .133 |
| supplied graph | discovered graph | |||||||||
| variables | metric | 20 | 50 | 75 | 90 | 20 | 50 | 75 | 90 | mean |
| items | NRR@1 | .003 | +.004 | +.008 | +.001 | +.012 | .004 | .002 | +.008 | +.003 |
| MRR | +.002 | +.003 | +.004 | .002 | +.012 | +.002 | +.002 | +.008 | +.004 | |
| SDA | .005 | +.002 | +.007 | +.009 | +.005 | +.004 | .000 | +.006 | +.004 | |
| identification | +.011 | +.010 | +.005 | .019 | +.011 | .005 | +.018 | .008 | +.003 | |
| latent variables | NRR@1 | +.003 | +.023 | +.008 | +.012 | .020 | .000 | .012 | +.003 | +.002 |
| Causal structure learning, robot and vehicle channels | |
|---|---|
| first difference | every state channel of a simulated arm, and a channel of a real log or a drive when its lag-one autocorrelation exceeds .95 |
| input edge added | partial correlation , simulated arms only |
| edge dropped | partial correlation given the other parents and the inputs |
| Constrained embedding optimization | |
| term weights | , with on the pairs above the .7 quantile of dependence, |
| regularizer weights | , , |
| questionnaire latent variables | simulated arms | real logs | vehicle CAN | |
|---|---|---|---|---|
| CausalBridge (1 call) | 458 | 276 | 236 | 210 |
| SASC-style (6 calls) | 1,175 † | 1,125 † | 1,000 † | 774 † |
| Automated Interpretability (2 calls) | 10,482 † | 8,903 | 6,409 | 4,117 |
| Delphi (3 calls) | 25,918 † | 21,878 | 15,665 | 9,960 |
Semantic Mapping
Semantic mapping links observations and data to meaningful concepts, categories, entities, and relations for machine reasoning and action.
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