{"id":"a2db267f-fca2-4425-a953-5ab2ad1319c5","arxiv_id":"2608.07353","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A new concept-centric GeoQA benchmark probes LLMs on abstraction, compositionality, and grounding of direction, distance, and topology, finding good abstraction, weak grounding, and a Mistral-family deficit.","lead":"This paper builds a question-answering benchmark to test whether large language models understand spatial concepts such as direction, distance, and topology through abstraction, compositionality, and grounding. In experiments across eight open models, the authors find that most models encode these concepts internally but fail to ground them in numerical facts, and the Mistral family underperforms the others.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The abstraction result is confounded by lexical surface form: probes read concept words from the question text, and no control removes word identity or template; the claim that LLMs 'clearly recognize concepts' is not yet established.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern: no baseline removes word identity, question template, or lexical overlap between composite and atomic questions. I agree that this is the central gap. The random-split probe accuracy is essentially a sanity check for a trivially separable lexical feature, and the OOD token splits are tests of generalization in embedding space, not of abstraction from surface form. The manuscript gives independent credit for a novel benchmark and careful negative findings on grounding, but the proof of concept abstraction in Section 6.1 needs a control that rules out the word-identity explanation. Since the reader already assigned CONDITIONAL with this issue central, my stress test does not move the verdict. I would not reject the paper: the concern is addressable with additional experiments, and the Mistral-family deficit and weak grounding results are interesting even if the abstraction claim remains tentative.","tokens_in":24011,"tokens_out":5622,"duration_ms":58350,"concrete_test":"Retrain the abstraction probe on each model's layer-0 input embeddings using the exact same splits and labels as in Table 9, and compare against the best internal-layer accuracy. If the layer-0 probe already achieves near-perfect random-split accuracy and comparable token-OOD accuracy (>=75%), then the internal-layer results add no evidence beyond lexical token identity, confirming that the reported abstraction numbers reflect surface word features rather than concept abstraction. As a complementary check within the same experiment, replace each concept word with a matched pseudoword and repeat the token-OOD split; if pseudoword OOD accuracy also remains high, template statistics alone explain the result.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central positive claim that most models 'clearly recognize concepts via their latent representations' (Section 6.1, Table 9) rests on linear probes trained on the average token embedding of the full question. Because the question text itself contains the concept word (e.g., 'Is X north of Y?'), a probe can achieve near-perfect random-split accuracy by learning to associate the token 'north' with the 'direction' label. The token-level OOD splits in Table 8 do not remove this confound: training on {N,S} and testing on {E,W} tests whether the probe can extrapolate along an axis of pretrained word embeddings, which may reflect lexical semantics rather than LLM concept abstraction. No reported baseline strips the concept word, masks it, uses input-layer embeddings only, or trains on control tokens. Without such a control, the 99.95-99.98% random-split and 75-83% OOD accuracies cannot distinguish concept-level abstraction from predictive surface features. The Mistral-family deficit may still be real, but the positive abstraction claim is not supported by the current experimental design.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a concept-centric probing benchmark for geo-spatial concepts (direction, distance, topology, and their conjunctions) in text-only LLMs. It evaluates eight LLMs through binary and multiple-choice QA tasks and layer-wise linear probing, measuring three concept properties: abstraction, compositionality, and grounding. The central claims are that most models encode concepts almost perfectly in random splits (99.95–99.98%) and generalize to OOD splits (75–83%), that high compositional logit correlations (≥0.85) accompany higher QA accuracy, and that grounding is weak, with accuracy near chance when numerical context is provided. The Mistral family is reported to underperform on all abstraction and compositionality tests.","tokens_in":24263,"tokens_out":5219,"duration_ms":47898,"significance":"If the findings were fully supported, the paper would provide a reusable, controlled benchmark for testing concept properties in LLMs, a layer-wise analysis across model families and scales, and a clear negative result on grounding. The authors also introduce useful consistency metrics and a revealed-threshold analysis for the distance concept, and they explicitly separate task performance from representation-level probing. However, the central positive claims rest on linear probes over average token embeddings of full questions, a design that is highly vulnerable to lexical surface-form confounds, and the grounding test is partially tautological. With additional control conditions, the benchmark and results could become valuable to the community, but as presented the evidence for the abstraction and compositionality conclusions is not yet convincing.","major_comments":[{"comment":"The abstraction results are confounded by surface lexical cues. The probe input is the average token embedding of the full question h=f_l(q), and the question templates in Table 3 and Figure 2 explicitly contain the concept word (north/south/east/west, close/far, within/borders). A linear probe can achieve near-perfect random-split accuracy by reading word identity, and the token-level OOD splits in Table 8 (e.g., train {N,S}, test {E,W}) test extrapolation along pretrained lexical-embedding axes rather than abstraction from linguistic tokens to a semantic type. The paper does not report any control that masks or removes the concept word, compares against a bag-of-words lexical probe, or evaluates on templates with random placeholders. Without such a control, the claim that 'most models clearly recognize concepts via their latent representations' (end of §6.1) is not established; the Mistral deficit may be real, but the positive abstraction claim is unsupported.","section":"§6.1, Table 9"},{"comment":"The compositionality metrics are subject to the same lexical-overlap problem. Cosine similarity between L(q) and L_add = L(q1)+L(q2) is high whenever q and its subquestions share surface tokens, and the logit/embedding/probability correlations use a classifier trained on the same average-token-embedding representation, so they can reflect template and word overlap rather than compositional structure. The claim that models with logit correlations above 0.85 have better QA accuracy is therefore not a clean test of compositionality. I recommend adding baselines with non-compositional control phrases (e.g., composed embeddings of unrelated atomic pairs, or of atomics whose words are permuted) and reporting whether the observed correlations exceed those baselines.","section":"§6.2.2, Table 10"},{"comment":"The grounding test is operationally circular. The context provides the exact distance N, the threshold T0, and the rule 'X and Y are considered close if d(X,Y) ≤ T0', while the ground-truth labels were generated by the same phi_d,th with the same T0 in §4.2. A model that performs the arithmetic comparison should be at ceiling; near-chance accuracy therefore conflates failure to ground the concept with failure in numerical comparison or instruction following under a long context. The conclusion that 'concepts are not naturally grounded' is not supported unless control tasks isolate numerical comparison (e.g., direct comparison questions without the words close/far) or the threshold is varied across contexts. The revealed-threshold analysis in §5.2 also uses T0-derived labels, so the estimated T* is not an independent measure of the model's own closeness notion.","section":"§6.3, grounding"},{"comment":"The revealed-threshold estimation is fitted to the model's predictions on data whose labels were generated from T0, so the KDE intersection can reflect the labeling scheme rather than a model-intrinsic boundary. Furthermore, the reported deltas (e.g., +7.6, +14.5, +30.8) are given without variance, confidence intervals, or significance testing, making it difficult to assess whether the differences between T* and T0 are meaningful. At minimum, the authors should report bootstrap or per-region variability and clarify that T* is a data-dependent estimate, not a free model parameter.","section":"§5.2, Table 6"}],"minor_comments":[{"comment":"The threshold is described as the mean in §4.2 ('setting th as the mean of the distribution, resulting in th=47.76km') but as the pairwise distance median in §5.2 ('a fixed threshold T0 set to the pairwise distance median'). Please clarify which statistic generated the labels and whether the two thresholds differ.","section":"§4.2 and §5.2"},{"comment":"The composition example 'Is X far from Y and close to Y?' is logically contradictory, since far and close are negations of each other in Table 2; this appears to be a typo and should be corrected.","section":"Table 3"},{"comment":"In lines 8–10, the variable x is used both for the correct target ward and for a sampled negative ward; the notation x ∼ {z∈W | (z,y)∈¬R} is undefined because x was already fixed. Please use distinct symbols and define the sampling distribution.","section":"Algorithm 2"},{"comment":"The abbreviation CGA is used both for the per-question compositional accuracy and for the aggregate Compositional Gap Accuracy; these should be renamed to avoid ambiguity.","section":"§6.2.1"},{"comment":"The layer numbers are inconsistent: Table 9 reports final-layer indices L=36, 32, 28, while Table 10 lists '# layers' as 33 or 37. Please clarify which layer index is used for the final-layer results and whether the two tables refer to the same depth.","section":"Tables 9 and 10"},{"comment":"The abstract uses the term 'groundness'; the standard term used throughout the paper is 'grounding'. Please correct this.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a worthwhile question and builds a substantial synthetic benchmark, but the central abstraction/compositionality claims are currently undercut by the absence of lexical-control baselines. I believe the manuscript could become acceptable after the authors add controls that remove or neutralize surface concept words in the probe inputs, and after the grounding test is redesigned to separate numerical comparison from concept grounding. I would not recommend rejection, because the issues are addressable within the scope of a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The benchmark is the real contribution: a systematic, concept-centric generator for geo-spatial triplets (direction, distance, topology, and conjunctions) with binary QA and MCQ tasks, plus probing protocols for three concept properties. The distance-threshold analysis (KDE-revealed T*) is a nice idea, and the grounding experiments with explicit numerical context are a good corrective to over-optimistic claims about spatial reasoning. The Mistral-family deficit is consistent across splits, layers, and tasks; I would bet on it surviving added controls.\n\nThat said, the central positive claim — that most models “clearly recognize concepts via their latent representations” — is not yet supported. The probes train on the average token embedding of the full question, and the question text contains the concept word. A linear probe can hit 99.98% on the random split by learning to associate “north” with the direction class; the OOD splits (train N/S, test E/W) partly test whether the probe extrapolates along an axis of pretrained word embeddings, which is lexical semantics, not necessarily concept abstraction. No baseline strips or masks the concept token, uses input-layer embeddings, or trains on control tokens. The authors need one of these before the abstraction claim can stand.\n\nOther weaker spots: the correlation analyses in Section 6.2.2 use only eight model points with no significance testing, so the “compositionality is key” conclusion is suggestive, not established. The paper has small internal inconsistencies: the distance threshold is called the mean in Section 4.2 but the median in Section 5.2, and the CGA metric in Section 6.2.1 is defined per-question as 1−Acc(q) and then aggregated as a proportion, which does not line up. Code and data are promised but not released, which hurts reproducibility.\n\nThe soft spots are addressable. The benchmark itself is reusable, the Mistral deficit is empirically solid, and the grounding result is a genuine negative finding. This deserves a serious referee: send it to review, but the authors should be pushed to add surface-form controls, fix the metric definitions, and release the code and data alongside the revision.","headline":"A genuinely useful new benchmark and a robust-looking Mistral deficit, but the central abstraction claim is confounded by surface word identity until the authors add the obvious control experiments.","tokens_in":24746,"tokens_out":1831,"would_cite":true,"duration_ms":18558,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that concept understanding in LLMs should be measured through abstraction, compositionality, and grounding in internal representations, and reports that most tested LLMs show abstraction and partial compositionality but…","keywords":["concept probing","large language models","geo-spatial reasoning","abstraction","compositionality","grounding","linear probing","out-of-distribution generalization"],"falsifier":"Train the same linear probes on questions whose concept words (for example, 'north', 'far', 'bordering') are replaced by arbitrary placeholder tokens while preserving the underlying relation structure; if out-of-distribution accuracy stays near the 75–99% range, the conclusion that LLMs represent concepts abstractly would be corroborated, whereas a collapse to chance would show the probes were reading lexical templates rather than concepts.","tokens_in":23778,"feed_emoji":"🧭","tokens_out":5991,"duration_ms":52052,"temperature":0.7,"pith_summary":"This paper tries to establish that the question 'do LLMs understand concepts?' can be answered by probing three core concept properties—abstraction, compositionality, and grounding—inside the models' internal representations, rather than by looking only at question-answering accuracy. Using a generated benchmark of geo-spatial questions about direction, distance, and topology between UK wards, the authors report that layer-wise linear probes classify concept types with 99.95–99.98% accuracy on a random split and keep 75–83% accuracy under out-of-distribution token and geographic splits for most models. The Mistral-family models are a clear exception, staying near chance on these splits. The paper also reports that compositional structure in the representations (logit correlations above 0.85) goes with stronger QA performance, and that grounding—answering the same questions when all coordinates and distances are given in the prompt—remains near chance. The overall point is that current LLMs show genuine abstraction and partial compositionality of geo-spatial concepts in their latent spaces while lacking a solid connection to real-world numeric referents.","feed_headline":"Probes show LLMs abstract geo-concepts, yet fail to ground them","feed_subtitle":"Most models classify spatial concepts at ~99.98% and generalize to new tokens and regions; Mistral lags and grounding is weak.","key_machinery":"The load-bearing mechanism is a layer-wise linear probe applied to the average token embedding of a question: for each layer, a softmax classifier predicts one of seven concept classes (direction, distance, topology, and their conjunctions). The benchmark supplies the controlled variation: relational triplets between UK wards generated from geometric measurements, question templates in binary and MCQ form, and deliberately constructed splits—token-level OOD (train on north/south, test on east/west), compositional OOD (unseen conjunction combinations), and geographic OOD (train on middle region, test on upper region). The same testbed supports compositionality checks through cosine similarity between composite and summed atomic embeddings and through correlations among logits, embedding sums, and probability averages, plus grounding tests that insert coordinates, distances, and bearings into the prompt.","core_discovery":"The central claim is that, judged by internal-representation probes, most text-only LLMs encode geo-spatial concepts as abstract, generalizable types, compose those types approximately additively, but fail to ground them. Concretely, linear probes trained on the average token embedding of a question reach 99.95–99.98% accuracy in classifying the underlying concept type on random splits, 75–83% on a geographic out-of-distribution split, and above 99% on compositional token-level splits, for Llama and Qwen models; Mistral models stay at 52.8–58.0% (random), 37.8–42.2% (geographic), and 22.5–29.4% (single token-level). The paper interprets this as evidence that most models clearly recognize concepts via their latent representations. For compositionality, cosine similarity between composite-question embeddings and sums of atomic embeddings is high for the successful models, and their logit correlations are ≳0.85, whereas Mistral models show weak, layer-unstable correlations. For grounding, accuracy in a binary task with explicit coordinates and distances hovers around chance (≈50%), and even the best MCQ grounding (66.7% on distance) comes with low consistency, so the paper concludes that concepts are not naturally grounded in current LLMs.","pith_inferences":["A natural extension is to ask whether the near-perfect random-split probe scores partly reflect lexical template identity; replacing concept words with abstract symbols while preserving relational structure would separate surface encoding from genuine abstraction.","The same triplet-based test could be transferred to non-spatial concepts such as relevance, truth, or clinical attributes, giving information retrieval and healthcare a property-level audit of what LLMs represent.","The finding that MCQ distance answers re-calibrate to the option scale suggests geo-QA benchmarks should report consistency and threshold-revealed measures alongside accuracy to avoid overstating spatial understanding.","If the Mistral deficit is architectural rather than scale-dependent, testing intermediate-size variants or changing positional/attention schemes could pinpoint which design choice blocks concept abstraction."],"forward_implications":["QA accuracy alone is not a reliable proxy for concept understanding: even moderate MCQ accuracy coexists with low consistency, and the distance-threshold analysis shows MCQ answers track the anchor options rather than the model's own perception of closeness.","Most current LLMs (Llama, Qwen) store geo-spatial concepts as abstract, generalizable representations that survive out-of-distribution token and region shifts; Mistral-family architectures appear to lack this property.","Compositional structure in latent representations is associated with better question answering: models with logit correlations ≳0.85 across layers outperform models whose logits lose correlation, such as the Mistral family.","Explicit thinking/reasoning modes do not repair conceptual understanding and often degrade accuracy and consistency, so the deficit is representational rather than a decoding artifact.","Because grounding remains weak even when all numerical information is supplied in context, improving conceptual understanding in LLMs likely requires external grounding mechanisms rather than more training data in the same format."],"supporting_citations":[{"why":"Supplies the unit-testing approach and the three concept properties (abstraction, compositionality, grounding) that organize the probing design.","marker":"[24]"},{"why":"Provides the cognitive-science definition of concepts and links abstraction to systematicity, which the OOD splits are designed to test.","marker":"[10]"},{"why":"Establishes the linear probing methodology used to test whether internal representations encode concept types.","marker":"[4]"},{"why":"Earlier finding that LLMs represent space and time in early layers; used as the comparison point for the abstraction result.","marker":"[15]"},{"why":"Provides the approximate-additivity view of compositionality that the cosine-similarity and embedding-sum tests implement.","marker":"[44]"},{"why":"Baseline definition of compositional gap which the paper adapts from multi-hop reasoning to conjunctive concept composition.","marker":"[39]"},{"why":"Prior text-only grounding study that the paper's grounding test extends and compares against.","marker":"[34]"},{"why":"Supplies the AND/composition operation on embeddings used to build composite concept instances.","marker":"[31]"}],"fun_headline_variants":["LLMs abstract geo-concepts but fail to ground them","Geo-concept probes: abstract and compose, but not grounded","Mistral lags in geo-concept abstraction; all lack grounding","High abstraction, low grounding in LLM geo-concept probes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The abstraction and compositionality results rest on the assumption that a linear classifier trained on the averaged token embedding of a full question measures the concept representation rather than the surface wording of the question; the experiments include no control that removes word identity or question-template overlap between composite and atomic items.","fun_headline_variants_meta":{"raw":{"variants":["LLMs abstract geo-concepts but fail to ground them","Geo-concept probes: abstract and compose, but not grounded","Mistral lags in geo-concept abstraction; all lack grounding","High abstraction, low grounding in LLM geo-concept probes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00018,"raw_usage":{"total_tokens":1345,"prompt_tokens":1027,"completion_tokens":318,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":643,"completion_tokens_details":{"reasoning_tokens":249}},"tokens_in":643,"tokens_out":318,"duration_ms":3578,"temperature":1.0,"reasoning_tokens":249,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T05:42:39.459072+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same linear probes on questions whose concept words (for example, 'north', 'far', 'bordering') are replaced by arbitrary placeholder tokens while preserving the underlying relation structure; if out-of-distribution accuracy stays near the 75–99% range, the conclusion that LLMs represent concepts abstractly would be corroborated, whereas a collapse to chance would show the probes were reading lexical templates rather than concepts.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the AND/composition operation on embeddings used to build composite concept instances."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the unit-testing approach and the three concept properties (abstraction, compositionality, grounding) that organize the probing design."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier finding that LLMs represent space and time in early layers; used as the comparison point for the abstraction result."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the approximate-additivity view of compositionality that the cosine-similarity and embedding-sum tests implement."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior text-only grounding study that the paper's grounding test extends and compares against."}],"review_version":1}