A framework for auditing grounding claims
Organizations: Center for Possible Minds Indiana University Bloomington Bloomington, IN 47408 · Eruditis Milwaukee, WI 53207
Abstract
The symbol grounding problem asks how a token such as cat can be about cats. We propose a framework for auditing grounding claims against a declared semantic standard. The audit reports measurements and evidence, with overall verdicts conditional on explicit acceptance criteria. Its profiles assess accuracy, robustness, and composition alongside evidence about how the system acquired its mechanisms, how they contribute to performance, and why they were retained. In a toy gridworld, an agent interprets individual symbols accurately but fails a withheld combination. Composing its interpretations by the declared rule would succeed. This comparison identifies a departure from the composition rule within the observed failure. Both this audit and a pilot on pretrained word vectors provide evidence that a designated mechanism contributes to present performance. Whether that contribution explains its retention remains uncertified. The framework evaluates the evidence for grounding claims; candidate accounts remain responsible for explaining how meaning emerges.
Figures & tables
| Clause | Question | Comparison |
| G0 authenticity | Do the mechanisms that carry symbols to meanings belong to the system, and did its own learning or evolution produce them? | inspection of provenance for each component relied upon, relative to the declared boundary and history: membership, then acquisition |
| G1 preservation | Does each atom mean what the standard says it means? | the realized meaning of each atom against its target, aggregated over the atoms |
| G2a correlational faithfulness | Does each composite mean what the standard says it means? | the realized meaning of each composite against its target, aggregated over the composites |
| G2b etiological faithfulness | Does the designated mechanism contribute to success now, and was it retained for that contribution? | success with the mechanism on against success with it off, on the decoupled distribution; historical controls for the retention |
| G3 robustness | How far does realized meaning move under a declared perturbation? | the realized meaning of an item against the realized meaning of its perturbed self, as a curve over scales |
| G4 compositionality | Does a composite mean what the algebra makes of the system’s own parts, and do withheld combinations pass? | the realized composite against the algebra applied to the realized atoms; the pass rate over withheld composites |
| Clause | Measurement | Declarations and assessment | Acceptance |
| G0 | component membership and acquisition records | declare system boundary, history , and components relied upon; inspect their provenance. Record instrument components separately | weak: system membership; strong: own learning or evolution |
| G1 | atomic discrepancy | declare target, metric, atomic population, and aggregate (maximum or quantile) | |
| G2a | composite discrepancy | declare target, metric, composite population, and aggregate (maximum or quantile). | |
| G2b | causal effect and historical certification status | declare succ , , on/off intervention, and construction of from ; assess retention using stated historical controls and selection assumptions. | and historical requirement satisfied |
| G3 | robustness curve : -quantile over of worst-case semantic change at scale | declare metric, population , perturbation location ( or ), threat family, scales, and coverage ; report supremum or approximation used; sampled perturbation quantiles estimate the worst case from below | over declared range |
| G4 | compositional deviation and withheld-composite accuracy | declare metric, grammar, algebra, constructor applications, and deviation aggregate; for , declare targets, withheld population, its overlap with G2a, and item tolerance . | and |
| Clause | Result | Population or scope |
| G0 | strong: system components acquired through training | embedding, GRU, and readout |
| G1 | maximum discrepancy | six atoms |
| G2a | maximum discrepancy ; success rate | eight composites, including both withheld commands |
| G2b | ; historical status uncertified | directional integration ablated; eight composites under |
| G3 | hidden-state supremum ; sampled directional mean | radius ; mean over sampled directions |
| G4: deviation | maximum on trained pairs; on withheld pairs | six trained and two withheld constructor applications |
| Format or coupling | Representative realization | Audit | Questions for measurement |
| Symbolic | discrete expressions with lookup or rule-based interpretation; simplest case, and | logical context, inferential meanings, surface-edit threats | atomic and composite accuracy; agreement with semantic algebra; sensitivity to edits; acquisition and retention of rules |
| Vectorial | with declared metric, an encoder , readout | linguistic or visual contexts, with threats specified at input or representation level | target agreement, geometric alignment where declared, perturbation sensitivity, composition on novel combinations |
| Relational | typed nodes, edges, or axioms, with graph metric and readout based on roles or rule closure | inferential meanings under edits to relations, types, or axioms | agreement with target relations; propagation of edits through inference; composition across typed structures |
| Referential coupling | sensorimotor representations connected to world or task states through perception and action | extensional meanings in embodied context, under declared environmental perturbations | accuracy of world-directed interpretation, causal dependence on coupling, evidence of retention for task success |
| Clause | Stipulated formal interpreter | Human language use |
| G0 | weak when designed interpretation is implemented within declared system | strong where audited mechanisms were acquired within a history including evolution and development |
| G1 | zero discrepancy on atoms in interpretation’s domain | agreement depends on context, sense resolution, and declared standard |
| G2a | zero discrepancy on well-typed composites interpreted by same semantic algebra | agreement must be assessed across declared constructions and communicative situations |
| G2b | historical requirement fails in stipulated case, whose construction excludes selection for task success | acquisition and communicative feedback motivate selection hypotheses; certification requires mechanism- and task-specific evidence |
| G3 | every edit below minimum spacing is trivial; behavior at larger scales depends on interpretation and treatment of malformed inputs | tolerance of benign variation is expected locally; its extent depends on threat and population |
| G4 | zero compositional deviation; any nonempty valid withheld set has where | productive interpretation motivates systematicity tests; idioms and coercion require an appropriate grammar and algebra |
| G2b certified | G2b uncertified | G2b failed | |
| G2a passes | target agreement with etiological support | target agreement; etiology unresolved | target agreement despite established etiological deficit |
| G2a fails | target error despite etiological support | target error; etiology unresolved | target error and established etiological deficit |
| Pattern | Profile | Diagnostic question |
| Exact composition, inaccurate atoms | G1 fails while . Composite accuracy and require separate assessment | Does changing the atomic interpretation improve target agreement while preserving composition? Atomic errors may cancel or accumulate. |
| Accurate composites, divergent composition | G2a passes while on evaluated applications. | Is the declared algebra appropriate? If so, what mechanism supports accuracy despite departure from it? |
| Familiar accuracy, withheld failure | G2a passes on familiar composites, but on strict withheld population. | Does failure involve inaccurate constituents, departure from the algebra, or both? Memorization is one hypothesis among several. |
| Accuracy with perturbation sensitivity | G2a passes on clean composites while G3 fails under declared threat and bound. | Where does the perturbation enter, and which mechanism amplifies its effect? Front-end correction and readout control address different sources. |
| Instrument-dependent agreement | Accuracy is measured through an auditor-supplied readout or composer, recorded as instrument under G0. | Does the system implement a corresponding interpretation or operation? Accuracy measured through an adapter is credited to the instrument. |
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
| Clause | Instrument | Quantity | Value |
| G0 | inspection | atomic : system, own learning | strong |
| composite extension; readout | instrument | ||
| G1 | MEN, evaluation pairs | median atomic discrepancy; fraction within | ; |
| SimLex, evaluation pairs | median atomic discrepancy; fraction within | ; | |
| G2a | WordNet tiers, all adjectives | mean Kendall discrepancy; perfect-order rate | ; |
| G2b | permutation ablation, MEN | [bootstrap interval]; | ; estimate above ; history uncertified |