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Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding

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Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding Karim Radouane

Jose G Moreno

Lynda Tamine

karim.radouane@irit.fr University of Toulouse, IRIT Toulouse, France

jose.moreno@irit.fr University of Toulouse, IRIT Toulouse, France

lynda.tamine@irit.fr University of Toulouse, IRIT Toulouse, France

arXiv:2608.07353v1 [cs.CL] 7 Aug 2026

Abstract Understanding concepts is fundamental to generalization. Despite their impressive performance on a wide range of tasks, Large Language Models (LLMs) still struggle with genuine concept understanding. Prior work has evaluated conceptual understanding in LLMs using natural-language benchmarks or narrowly scoped synthetic tasks, but these settings often conflate multiple skills or lack precise control over the underlying concepts and their properties. To support controlled probing of concepts in LLMs, we design tests on their core properties: abstraction, compositionality, and groundness. We set up a concept-centric benchmark, targeting spatial concepts such as direction, distance, topology, and their compositions, and use question answering tasks serving as a proxy. We conduct extensive experiments across multiple LLM architectures and training regimes to analyze how model scale and design impact conceptual understanding. The results reveal clear limitations in current LLMs and provide insights into the factors shaping their ability to acquire and compose structured concepts. Our findings shed light on how concept-based LLMs can be redesigned for improved information access and knowledge management. The code will be available at https://github.com/rd20karim/concept-probing.

CCS Concepts • Information systems → Retrieval models and ranking.

Keywords Large Language Models, Probing, Geography, Concepts.

Introduction

Large Language Models (LLMs) exhibit a wide range of capabilities, but the question of whether they can be models of human language understanding is still an open philosophical and scientific debate that impacts cognitive science, machine learning (ML), and natural language processing (NLP), and information research disciplines [13, 35, 52], to cite but a few. One major subject of debate is the source of their capabilities: do they behave as statistical parrots, or are they able to organize symbolic, structured representations of concepts that they manipulate in the generation process? The question is key since concepts are the cornerstone of intelligence, allowing better generalization, and interpretability [36]. Recent work has developed probing and learning techniques for concepts in LLMs. Probing can focus on factual knowledge through downstream task evaluation [9, 17, 28, 54] or on their internal representations to explain their predictions (e.g., mechanistic interpretability [33, 49]). Concept learning refers to the learning of concept representations and their explicit utilization in the internal layers of models, such as concept bottleneck models [20].

Given the open-ended nature of concepts across tasks and domains, other works evaluated whether concept properties acknowledged in the literature [10, 22, 24, 44] (e.g., compositionality [22, 44]), can be represented or even learned in LLMs. Evaluation of concept property provides a more fine-grained insight into the concept understanding of LLMs, enabling better control over both concept probing and learning. Research gap. Recently, there has been growing interest in studying LLMs’ understanding of concepts such as truth [2], time and space [15], patient gender [1], and gender bias [53]. Other works addressed the study of concept properties such as complexity [18], compositionality [22, 44], and grounding [23, 32]. However, while previous work provides insights on the abilities of LLMs to succeed in (cross-modal) tasks through task performance involving concepts of interest, they do not systematically assess concepts per se for the following reasons: (i) they mostly consider multi-modal LLMs (text and image) and concept probing is addressed through representation sharing between modalities (e.g., [23]); (ii) the few works that considered text-only LLMs covered only one core property of concepts (e.g., abstraction [15], grounding [35]) limiting the scope of concept probing; (iii) the design of probes is not guided by the concepts per se, but instead by downstream tasks, thereby confounding conclusions about both LLMs’ concept understanding and task skills (e.g., [41, 51]). Goal and research questions. In this work, we seek to fill the above research gap by investigating whether LLMs can build, from only the text modality, concept representations of world models using a controlled concept-centric benchmark. Inspired by previous work [24], we approach this challenge by framing it as a set of probing tests about each of the core properties of conceptual representations: abstraction, compositionality, and grounding. Under this perspective, our main goal can be formalized as: How can we translate abstraction, compositionality, and grounding into testable hypotheses and develop the empirical probing tests allowing us to quantify the extent to which LLMs align with? We choose three popular spatial concepts—direction, distance, and topology—which are particularly challenging for dealing with spatial commonsense since they are rarely expressed in texts, though our probing methodology is designed to generalize across spatial concepts and extend to other concepts, tasks, and domains. Specifically, we address the following research questions: (RQ1) Are LLMs’ performances on a geo-spatial question-answering task sufficient to assess their actual ability to understand underlying concepts?

Karim Radouane, Jose G Moreno, and Lynda Tamine

(RQ2) Do LLMs encode abstract geo-spatial concept representations? Are concept representations generalizable across linguistic tokens and geographic regions? (RQ3) Are LLMs able to compose geo-spatial concepts? Can LLMs’ predictions be explained by composing concept representations? (RQ4) Can concept representations be grounded in real-world knowledge? We build a concept-centric benchmark and probe popular text-only LLMs (Llama-8B, Mistral-7B/8B, Qwen-0.6B, 1.7B, 4B, 8B) through binary and multi-choice question-answering (MCQ) tasks to analyze their internal representations across layers and concepts. Main findings. • For RQ1, we assess LLM performance on our benchmark as a preliminary proxy for concept understanding. We find moderate MCQ accuracy coexists with low consistency under Binary-QA, exposing unstable concept understanding. This limitation is most analytically tractable for the distance concept. These findings clearly motivate moving beyond geo-spatial QA performance toward targeted probing of core conceptual properties. • For RQ2, we measure the extent to which concepts are explicitly encoded in LLMs, and their instances represent types as an abstraction across tokens and regions. Our findings indicate that most models encode concepts with a good level of generalization across instances, except the Mistral family models wich consistently underperform across generalization splits and layers. • For RQ3, compositionality is assessed through: the compositionality gap, the additivity of latent representations, and the extent to which predictions can be explained by the composition of latent embeddings and/or atomic predictions. We find that most LLM variants exhibit a compositional structure from a cosine similarity perspective, except for the Mistral models. The correlation analyses using different proposed approaches reveal that compositionality is a key factor for successful concept understanding. In particular, models that preserve correlation across layers perform well, whereas the Mistral family models fail to meet these criteria. • For RQ4, despite enriching concept-based questions with real-world factual information, such as geometrical measurements, it does not improve related QA-task performance in LLMs even with an explicit distance threshold definition. This limitation highlights a persistent gap in the LLMs models’ ability to ground geo-spatial concepts, revealing a misalignment between representations in linguistic space and their corresponding numerical representations.

Related Work

The primary objective of this work is to investigate LLMs’ understanding of concepts through abstraction, compositionality, and grounding. As a use case, we consider geography-related concepts and use performance on question-answering and probing tasks as a proxy. Therefore, we review previous work on (i) concepts in LLMs; (ii) probing LLMs on geography knowledge, and (iii) geo-spatial

question-answering. Table 1 compares prior close work on probing LLMs’ concepts with ours.

2.1

Concepts in LLMs

The definition of concept, which has recently gained renewed attention in explainable artificial intelligence (XAI), remains elusive and varies across disciplinary boundaries (e.g., cognitive science, ML [10, 36, 43]). In cognitive science, a concept is a fundamental unit of structured knowledge representing an interpretable abstraction of entities (e.g., shape, color) that functions like a symbol used for problem-solving, reasoning, or organizing information [10, 14, 50]. In ML, a concept is an abstract representation that captures a meaningful class, attribute, or feature within a model’s learned space that correlates with high-level semantic [11, 37, 44]. Across these disciplines, a conceptual representation is generally assumed to require three core properties [10, 22, 24, 44]: (i) abstraction1 : different instances of a concept evaluate to the same semantic type. This property is strongly related to the ability of concept representations to tackle out-of-distribution generalization [12, 24]; (ii) compositionality: a concept can be atomic or composed of a set of concepts. A composite concept is a function of its constituents. Previous work addressed the compositionality of LLMs from two sides. Compositional reasoning is the ability to process reasoning chains [16, 21, 39, 42] while conjunctive compositionality is the ability to disentangle and combine the concept constituents (e.g., via logical AND [31]) to recall or understand the composite concept [29, 31]; and (iii) grounding: universally refers to the fact that concepts are assumed to apply to situational context reflecting physical things in the real-world [10, 23, 51]. Grounding tests [3] generally rely on multimodal mapping between concept modalities, where a “modality” could be either a sensor (e.g., text vs. image) or a mode (e.g., plain text and a textual description of a grid [32]). The question of whether LLMs can give rise to complex conceptual representations has led to a large body of work that falls in the mechanistic interpretability [12, 30, 33]. It has been shown that concepts such as truth [2], time and space [15], patient gender [1], and gender bias [53] can be localized in LLM representations. In their recent work [18], Jian et al. categorized the complexity of concepts based on their level of abstraction and showed that tasks requiring complex concepts require deeper layers for an accurate understanding. Other works studied, particularly, whether concept properties such as compositionality [22, 39, 44] and grounding [23, 32, 51] hold in LLMs through multi-modal downstream tasks (i.e., using texts and images). In this work, we probe LLMs from a concept-centric perspective that explicitly models concepts and their three core properties—abstraction, grounding, and compositionality—and, unlike prior work, introduce a concept-guided probing benchmark to evaluate LLMs’ internal concept representations and the sensitivity of natural language question-answering performance to the presence of these concepts along with their three core properties.

2.2

Probing LLMs for geo-spatial knowledge

Probing LLMs for geo-spatial knowledge offers a lens into two categories of work. The first category aims to evaluate the capabilities 1 Abstraction is also referred to as systematicity. [10]

Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding Related Work Ramrakhiyani et al. [41] Patel and Pavlick [34] Manvi et al. [28] Gurnee and Tegmark [15] Park et al. [32] Yamada et al. [51] Our work

Dir ✓ ✓ ✓ ✓

Concepts Dis Top Other Location Color Location Time ✓ ✓ -

Abst. ✓ ✓

Properties Comp. Ground ✓ ✓ ✓ ✓

Probing Tests Knowledge Repr. ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

Table 1: Related work on concept probing in LLMs with a focus on text modality. The table summarizes investigated concepts and properties, and categorizes probing tests by whether they target knowledge or/and internal representations.

of LLMs to recall geographic facts using downstream tasks’ performance as a proxy [17, 28, 47, 54]. For instance, Manvi et al. [28] demonstrated that LLMs are highly sensitive to prompt formats but that fine-tuning using map data from OpenStreetMap enhances the accuracy and robustness of these models. However, it has been shown that fine-tuning LLMs on specific datasets introduces bias against geographic areas with lower socio-economic conditions [27]. The second category of work [15, 34] aims to examine the association between internal representations and extrinsic properties of geo-spatial knowledge. Gurnee and Tegmark [15] showed that LLMs internally store concepts like latitude, longitude, and time in the early layers, and they can predict a location map. The work developed by Patel and Pavlick [34] represents a notable conceptual advancement in understanding the capabilities of LLMs to ground the learned conceptual representation –built upon a linguistic world– with real-world representation based on a few in-context examples. They showed that large-size models exhibit high-level capabilities for grounding and generalization, indicating that they can learn a latent structure of the world.

2.3

Geospatial question-answering

Geospatial question answering (GeoQA) aims to enable generation or retrieval models to answer questions involving geographic entities or concepts and that require spatial operations [26]. Mai et al. [26] report many challenges in GeoQA systems, among which are the vagueness of geographic concepts invoked in the questions, the difficulty in identifying the correct spatial relations between the entities involved in the questions, and the difficulty in encoding spatial entities. With the advancement of LLMs, a large body of work examined their capabilities to address these challenges, by covering a wide range of GeoQA tasks, including place retrieval [25], and spatial reasoning on topological relations [6–8, 17]. The main limitations of LLMs that arise from this literature are: (i) LLMs are not spatially replicable over the globe, nor efficiently robust across tasks; (ii) LLMs are not efficiently transferable to tasks handling different spatial scales; and (iii) LLMs’ do not generalise the “neighbourhood” relationship. The challenges mentioned above motivate us to: (i) target spatial concepts as a use case for our probing study, but without loss of generality; and (ii) design a question-answering benchmark test built upon these concepts.

3 Background, Terminology and Notations 3.1 Definitions Concept. Across disciplines, a concept 𝐶 is a high-level and human-interpretable unit of information. Specifically, we adopt a definition rooted in knowledge representation [5] and widely used in Information Retrieval (IR) and NLP, where a concept is an abstract category or class that defines a set of object entities sharing common properties and roles (e.g., concept of direction). Concepts are interpreted as unary predicates, and roles as binary relations between object entities. Concept instance. A concept instance 𝑐 is a concrete exemplar of a concept, representing a specific real-world entity that belongs to the extension of that concept. In IR and NLP, a concept is approximated by a finite vocabulary of representative lexical words 𝑐 that represent its instances (e.g., east, west are instances of concept direction). We note I (𝐶) the finite representative set of instances of concept 𝐶. For the sake of simplicity, we consider in practice 𝐶 = I (𝐶). Concept instance representation. We consider symbolic concept instance representations using binary relational predicates that express facts. A fact is represented as a positive triplet ⟨𝑥, 𝑟, 𝑦⟩, where 𝑥 is the subject entity, 𝑟 is the core relation (predicate) expressing the concept instance 𝑐, and 𝑦 is the object entity (e.g., ⟨Prescot, west_of, Todmorden⟩ represents west, an instance of concept direction viewed as a the binary relation west_of between Prescot and Todmorden object entities). We also consider the negated triplet ⟨𝑥, ¬𝑟, 𝑦⟩ which embeds a fact with an opposite relation to 𝑟 (e.g., ¬west_of is east_of ). Concept properties. Following [10, 24], we consider three core properties of concepts: • Abstraction: a concept 𝐶 is assumed to be the abstraction of its instances I (𝐶). Therefore, I (𝐶) form the semantic type of 𝐶. • Compositionality: following compositional distributional semantics models [39, 44, 46], we focus on compositionality through conjunctive (i.e., logical AND) concept composition [31]. The composition of atomic concepts 𝐶 1, . . . , 𝐶𝑛 yields a new composite concept 𝐶 1 × . . . × 𝐶𝑛 , whose instances are formed by composing the instances of the constituent atomic concepts (e.g., ⟨Prescot, west_of ∧far_from, Todmorden⟩). • Grounding is the awareness of concepts, expressed using natural language constructs, with the physical entities in the world they are assumed to apply to [10, 23, 51]. As done in previous work [34], we only use the text modality to represent concepts in two different modes. In our work, we specifically use numerical fact–based geometric measurements and associated questionbased formulations.

3.2

Concept probing methodology overview

To probe concept 𝐶 through the properties of abstraction, compositionality, and grounding, we build a concept-centric question-answering benchmark where questions 𝑞 ∈ Q are generated from triplets ⟨𝑥, 𝑟, 𝑦⟩ representing instances of either atomic or composite concepts (§ 4). Using this benchmark, we assess each concept property through specific tests (§ 6) by using

Karim Radouane, Jose G Moreno, and Lynda Tamine Concept 𝐶 Direction Distance Topology

Instance (𝑐) / Relation (𝑟𝑐 ) north/north_of | south/south_of east/east_of | west/west_of far/far_from | close/close_to within/is_within | borders/is_bordering

Negation (¬𝑟𝑐 ) south_of | north_of west_of | east_of close_to | far_from is_not_within | is_not_bordering

Table 2: Concepts with paired instance–relation entries and their corresponding negated relations. two proxies: - Task performance: to evaluate whether LLMs succeed on a test, we compute the accuracy and consistency metrics on the questionanswering task. Let Q𝑡 denote the question set. We define perˆ ˆ question accuracy as Acc(𝑞) = I[𝑦(𝑞) = 𝑦 (𝑞)], where 𝑦(𝑞) is the LLM’ prediction and 𝑦 (𝑞) is the ground-truth answer. Accuracy is computed as the average over all questions Q𝑡 as Acc = 1 Í 𝑞 ∈ Q𝑡 Acc(𝑞). We access consistency, regarding a concept prop| Q𝑡 | erty test, as a measure of whether a model correctly answers the ¯ that embed concept instances and their negapaired questions (𝑞, 𝑞) tion through opposite relational facts (e.g., if ⟨𝑥, east_of, 𝑦⟩ is true, then ⟨𝑥, west_of, 𝑦⟩ should be false). Consistency is computed as Í ¯ where Acc(𝑞) ¯ is the perConsist. = | Q1𝑡 | 𝑞 ∈ Q Acc(𝑞) · Acc(𝑞), question accuracy of the negated question. - Probing performance: We complement task performance evaluation with probing task evaluation [4]. The probing tasks rely on linear classifiers to test whether the internal concept instance representations L(𝑞), 𝑞 ∈ Q are aligned with the requirements of the property being tested.

4 The Concept-Centric Probing Benchmark 4.1 Benchmarking geographic concepts Without loss of generality, we investigate in this work three key spatial concepts— Direction, Topology, and Distance. Let W be a set of geographic entities. We note M the set of wards that belong to UK metropolitan districts,2 M ∈ P (W) where P denotes the power set. The distance, direction, and topology concepts can be expressed using a wide range of instances. In our work, we consider the following concept instances: 𝐶𝑑𝑖𝑟 = {north, south, east, west}, 𝐶𝑑𝑖𝑠 = {close, far},

𝐶𝑡𝑜𝑝 = {within, borders}.

(1)

Each concept 𝐶 is represented using a set of instances 𝑐 as relational triplets 𝑅𝐶 = {(𝑥, 𝑟𝑐 , 𝑦)/(𝑥, 𝑦) ∈ W ×W, 𝑐 ∈ I (𝐶)}. For the sake of simplicity, we consider 𝑅𝐶 = ∪𝑐 ∈ I (𝐶 ) 𝑅𝑐 (e.g., 𝑅𝑟𝑑𝑖𝑠 = 𝑅𝑟𝑐𝑙𝑜𝑠𝑒 ∪𝑅𝑟 𝑓 𝑎𝑟 ) To allow the evaluation of consistency, we also consider negated concept instance representations {(𝑥, ¬𝑟𝑐 , 𝑦)/(𝑥, 𝑦) ∈ W × W, 𝑐 ∈ I (𝐶)}. Table 2 presents the concepts, their instances, associated relations, and their negations.

4.2

GeoQA dataset Generation

Concept instance generation. We focus on the UK metropolitan district wards2 as location entities, which form three discontinuous regions (upper, middle, and lower). Concept instances in the form of triplets ⟨𝑥, 𝑟, 𝑦⟩ are generated from the middle continuous region W, while the upper region is reserved for out-of-distribution (OOD) generalization. Specifically, using geometric measurements

from GraphDB3 and YAGO2GEO4 , we compute bearings, pairwise distances, and topological relations between wards associated with direction, distance, and topology concepts, respectively. For any 𝑥, 𝑦 ∈ W, we denote their distance and bearing by 𝑑 (𝑥, 𝑦) and 𝜃 (𝑥, 𝑦), respectively, and map these measurements to relation concept instances ⟨𝑥, 𝑟, 𝑦⟩ via the functions 𝜙𝑑,th and 𝜙𝜃 , defined as follows:  E,     S,  𝜙𝜃 (𝑥, 𝑦) =  W,    N, 

𝜃 ∈ [45◦ , 135◦ [, 𝜃 ∈ [135◦ , 225◦ [, 𝜃 ∈ [225◦ , 315◦ [, otherwise.

close, 𝑑 (𝑥, 𝑦) ≤ th, far,

𝑑 (𝑥, 𝑦) > th.

Figure 1: Direction function 𝜙𝜃 mapping angles to cardinal directions. Distance threshold function 𝜙𝑑,th mapping distances to ‘close’ or ‘far’. For example, 𝜙𝜃 (𝑥, 𝑦) = E yields the triplet (𝑥, east_of, 𝑦), while 𝜙𝑑,th (𝑥, 𝑦) = close yields (𝑥, close_to, 𝑦); analogous triplets are generated for all remaining atomic distance and direction relations. We select the distance threshold based on the pairwise distance distribution of geometric wards, setting 𝑡ℎ as the mean of the distribution, resulting in 𝑡ℎ = 47.76 km. Since our goal is to investigate the internal LLM perception of distance, this threshold is not provided in the question context; its impact is further analyzed in Section 5.2. For topological relations, following YAGO2geo, the relations is_within and is_bordering between spatial entities are derived by applying GeoSPARQL/OGC topological predicates over their geometries. The generation of all such atomic spatial triplets is described in Part 1 of Algorithm 1(lines 4-16). We further construct higher-level concept instances through conjunctive composition, by systematically combining atomic relations that share the same subject and object. Given two atomic triplets (𝑥, 𝑟 1, 𝑦) and (𝑥, 𝑟 2, 𝑦), where 𝑟 1 and 𝑟 2 belong to different relational families (e.g., distance and direction), we generate a composite triplet (𝑥, 𝑟 1 ∧ 𝑟 2, 𝑦) and proceed analogously for three relations. This composition process exhaustively covers all valid pairwise combinations of atomic relations, and is further extended to higher-order compositions (i.e., triplets of relations) whenever applicable. By explicitly generating atomic, pairwise, and higher-order composed relations, the benchmark enables controlled evaluations of abstraction and compositional generalization. The compositional generation procedure is detailed in Part 2 of Algorithm 1(lines 17-22). Question generation. We generate Binary-QA (Yes/No) and MCQ (3-options) from each concept instance represented as triplets generated by Algorithm 1. Given the resulting set of positive triplets 𝑇 + , we construct negative triplets 𝑇 − by negating each relation 𝑟 (Table 2), yielding the complete set T = 𝑇 + ∪ 𝑇 − . We then apply a predefined set of templates to each triplet 𝑡 ∈ T , illustrated in Table 3. The prompt templates used for binary and MCQ tasks are defined are presented in Figure 2. Ground-truth answer generation. Ground-truth answers for both, Binary-QA and MCQ tasks, are generated using Algorithm 2. 3 https://graphdb.ontotext.com/

2 Metropolitan boroughs on Wikipedia: en.wikipedia.org/wiki/Metropolitan_borough.

( 𝜙𝑑,th (𝑥, 𝑦) =

4 https://yago2geo.di.uoa.gr/

Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding

Binary-QA Task: Answer the following geography question on UK metropolitan district wards. Respond only with yes or no. MCQ Task: Answer the following geography question on UK metropolitan district wards. Respond only with the correct option A, B, or C. Figure 2: Prompt templates for Binary-QA and MCQ tasks. Algorithm 1 Triplet Generation 1: Inputs: wards W, metropolitan districts M 2: Output: 𝑇 + (atomic and compositional positive triplets) 3: Initialize 𝑅𝑟𝑑𝑖𝑠 , 𝑅𝑟𝑑𝑖𝑟 , 𝑅𝑟𝑡𝑜𝑝 , 𝑅𝑖𝑠_𝑤𝑖𝑡ℎ𝑖𝑛 ,𝑇 + ← ∅ 4: for all 𝑥, 𝑦 ∈ W do

⊲ Part 1: Atomic triplet 𝑑 ← 𝑑 (𝑥, 𝑦), 𝜃 ← 𝜃 (𝑥, 𝑦) ⊲ compute distance and angle 6: 𝑟𝑑𝑖𝑠 ← 𝜙𝑑 (𝑥, 𝑦), 𝑟𝑑𝑖𝑟 ← 𝜙𝜃 (𝑥, 𝑦) ⊲ dis. and dir. relation 7: 𝑅𝑟𝑑𝑖𝑠 ← 𝑅𝑟𝑑𝑖𝑠 ∪ {(𝑥, 𝑦)}; 𝑅𝑟𝑑𝑖𝑟 ← 𝑅𝑟𝑑𝑖𝑟 ∪ {(𝑥, 𝑦)} 8: if border(𝑥, 𝑦) then ⊲ Using YAGO2GEO 9: 𝑟𝑡𝑜𝑝 ← 𝑖𝑠_𝑏𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 10: 𝑅𝑟𝑡𝑜𝑝 ← 𝑅𝑟𝑡𝑜𝑝 ∪ {(𝑥, 𝑦)} 11: end if 12: 𝑟𝑡𝑜𝑝 ← 𝑖𝑠_𝑤𝑖𝑡ℎ𝑖𝑛 13: Find 𝑧 ∈ M, such that (𝑥, 𝑟𝑡𝑜𝑝 , 𝑧) ⊲ Using YAGO2GEO 14: 𝑅𝑟𝑡𝑜𝑝 ← 𝑅𝑟𝑡𝑜𝑝 ∪ {(𝑥, 𝑧)} 15: 𝑇 + ← 𝑇 + ∪ {(𝑥, 𝑟, 𝑦) ∀𝑟 ∈ {𝑟𝑑𝑖𝑟 , 𝑟𝑑𝑖𝑠 , 𝑟𝑡𝑜𝑝 }} 16: end for 17: for all (𝑥, 𝑦) ∈ 𝑇 + do ⊲ Part 2: Compositional triplet 18: 𝑆 ← {𝑟 | (𝑥, 𝑟, 𝑦) ∈ 𝑇 + } 19: for all subsets 𝑈 ⊆ 𝑆 with |𝑈 | ≥ 2 do Ó 20: 𝑟𝑈 ← 𝑟 ∈𝑈 𝑟 ⊲ logical AND (e.g. 𝑟 1 ∧ 𝑟 2 ) + 21: 𝑇 ← 𝑇 + ∪ {(𝑥, 𝑟𝑈 , 𝑦)} 22: end for 23: end for 24: return 𝑇 + 5:

Affirmation Is 𝑋 far from 𝑌 ? Is 𝑋 close to 𝑌 ? Is 𝑋 west of 𝑌 ? Does 𝑋 border 𝑌 ? Is 𝑋 within 𝑍 ?

Negation Is 𝑋 close to 𝑌 ? Is 𝑋 far from 𝑌 ? Is 𝑋 east of 𝑌 ? Is 𝑋 not bordering 𝑌 ? Is 𝑋 not within 𝑍 ?

Composition Example Is 𝑋 far from 𝑌 and close to 𝑌 ? Is 𝑋 close to 𝑌 and far from 𝑌 ? Is 𝑋 west of 𝑌 and bordering 𝑌 ? Does 𝑋 border 𝑌 and north of 𝑌 ? Is 𝑋 within 𝑍 and close to 𝑌 ?

Table 3: Examples of binary atomic and compositional questions, for MCQ task, we use slightly different template (e.g., Which ward is close to 𝑌 ? followed by options). MCQ tasks additionally require the generation of incorrect options, which are produced using a distractor generator denoted by 𝐷𝑛 : 𝐷𝑛 (𝑅, 𝑦) = {𝑑 1, . . . , 𝑑𝑛 | 𝑑𝑖 ∼ {𝑥 ∈ W | (𝑥, 𝑦) ∉ 𝑅}}. In our case 𝑛 = 2, the procedure is to choose the target 𝑤 ∗ ∈ W as the correct answer, sample two distinct distractors 𝑤 1, 𝑤 2 ∈ W \ {𝑤 ∗ } satisfying (𝑤𝑖 , 𝑦) ∉ 𝑅, form the option set 𝑂 = {𝑤 ∗, 𝑤 1, 𝑤 2 }, and place 𝑤 ∗ at a uniformly random position 𝑖 ∗ ∈ {1, 2, 3}. QA-Dataset statistics. Let |.| denotes the cardinality measure, we have |W| = 506 wards and |M| = 25 metropolitan district. Statistics of our generated Geo-QA dataset, D𝑄𝐴 , are presented in Table 4.

Algorithm 2 Ground Truth Generation of Answers (A) 1: Inputs: 𝑘 ∈ {Binary-QA, MCQ},𝑇 + , W, 𝐷𝑛 2: Outputs: Answer set 𝐴 3: for all (𝑥, 𝑅, 𝑦) ∈ 𝑇 R++ do

⊲ Binary task answers if 𝑘 = Binary-QA then 5: 𝐴(𝑥, 𝑅, 𝑦) ← {Yes}; 𝐴(𝑥, ¬𝑅, 𝑦) ← {No} 6: else if 𝑘 = MCQ then ⊲ MCQ task answers 7: 𝐴(𝑥, 𝑅, 𝑦) ← {𝑥, 𝑑 1, 𝑑 2 } (i.e. 𝑥 ∪ 𝐷 2 (𝑅, 𝑦)) 8: 𝑥 ∼ {𝑧 ∈ W | (𝑧, 𝑦) ∈ ¬𝑅} ⊲ Sampling (∼) 9: 𝐴(𝑥, ¬𝑅, 𝑦) ← {𝑥, 𝑑 1, 𝑑 2 } (i.e. 𝑥 ∪ 𝐷 2 (¬𝑅, 𝑦)) 10: 𝐴(𝑦) ← 𝑥 11: end if 12: end for 13: return 𝐴 4:

Task(s)

Combinations

Binary-QA

1-Concept: dir, dist, top 2-Concept: dir_top, dist_top , dist_dir 3-Concept: dist_dir_top Overall Total

769,260 771,930 258,200 1,799,390

Total

MCQ

1-Concept: dir, dist, top 2-Concept: dir_top, dist_top, dist_dir 3-Concept: dist_dir_top Overall Total

4,096 70,100 41,098 115,294

Table 4: Statistics of the Geo-QA dataset (D𝑄𝐴 ) per task for Binary-QA and MCQ.

Probing LLMs on geo-spatial QA

Our key objective here is to investigate whether geo-QA task performance is a reliable and sufficient proxy to probe LLMs on their understanding of concepts.

5.1

Preliminary evaluation

Before testing LLM’s understanding of concepts on core properties, we first aim to evaluate their performance on the QA dataset of our benchmark, D𝑄𝐴 (§ Table 4). We evaluate popular text-only LLMs (Llama-8B, Mistral-7B/8B, Qwen-0.6B, 1.7B, 4B, 8B) and report the main results in Table 5. We can see that across all settings, MCQ accuracy consistently exceeds Binary-QA accuracy, confirming that structured answer choices substantially ease the task. Larger instruction-tuned models achieve the highest accuracies (e.g., Llama-3.1-8B at 71.7% MCQ and Qwen3-4B at 56.14% Binary-QA). However, consistency remains low overall, especially for Binary-QA (often < 26%), indicating unstable factual recall despite moderate accuracy. While explicit thinking is costly, we can observe that it is largely ineffective: it yields marginal gains at best and often degrades performance (e.g., LLaMA-3.1-8B MCQ accuracy drops from 71.7% to 50.6%, with consistency decreasing from 48.7% to 16.6%). Smaller models sometimes reach comparable or slightly improved accuracy under explicit thinking but still suffer noticeable consistency declines, suggesting correct answers without robust consistency. Consequently, we focus henceforth on models without explicit thinking, relying instead on their inner latent reasoning for our different tests on LLMs’ concept understanding. Focusing on concept-level analysis, Figure 3 highlights performance across concept dimensions. In particular, we can see that

Karim Radouane, Jose G Moreno, and Lynda Tamine Model/Task

Llama-3.1-8B-Inst. Mistral-2410-8B-Inst. Mistral-7B-v0.3-Inst. Mistral-7B-v0.2-Inst. Qwen3-8B Qwen3-4B-Inst. Qwen3-1.7B Qwen3-0.6B

Binary_QA Acc (%) Consist. (%) ✓ × ✓ × 61.58 54.95 40.04 25.68 61.26 53.39 38.22 22.94 51.64 51.65 22.55 18.09 55.42 51.28 27.24 17.10 62.30 47.99 41.02 10.83 62.73 56.22 39.98 20.81 56.05 49.09 30.74 0.30 53.52 50.25 19.86 0.62

MCQ Acc (%) Consist. (%) ✓ × ✓ × 50.60 71.70 16.61 48.72 49.10 56.16 23.73 30.96 51.87 55.31 21.63 31.64 58.54 52.73 22.40 32.32 47.22 53.52 15.96 24.25 50.00 56.14 22.67 25.05 46.17 54.29 19.47 28.54 49.06 49.90 21.09 22.02

Table 5: MCQ and Binary-QA performance with shared metrics. ✓indicates explicit thinking (reasoning-enabled for Qwen models and CoT for the others); ✗ indicates standard prompting. the LLaMA3-8B model exhibits relatively higher accuracy across most settings compared to other models, reaching above 70% on the 𝑑𝑖𝑠𝑡_𝑑𝑖𝑟 _𝑡𝑜𝑝 composition, with broader coverage across the seven dimensions representing the full concept space. However, consistency remains comparatively lower, reaching around 60% at best on 𝑡𝑜𝑝 concept (MCQ task). Overall, models tend to perform better under standard prompting than with explicit reasoning, with compositional settings not consistently outperforming atomic ones in the MCQ task. Binary task

MCQ task

top

top dist

Accuracy

dir_top 0 15

dist dir_top

dir

dist_dir

dir

dist_dir dist_dir_top

dist_dir_top

dist_top

top

top dist

dir_top

Consistency

1 3

5 10

dist dir_top

15 05

dir

dist_dir

60 70

dir

dist_dir dist_dir_top

dist_dir_top

dist_top

Qwen3-0.6B Ministral-8B-Instruct-2410

dist_top

Models

Mistral-7B-Instruct-v0.3 Mistral-7B-Instruct-v0.2

Qwen3-4B-Instruct-2507 Qwen3-8B

Qwen3-1.7B Llama-3.1-8B-Instruct

Figure 3: Performance trends per concept type and composition from one to three concepts across Binary-QA and MCQ tasks.

5.2

Distance threshold analysis

In this part, we investigate the internal definition of the distance concept per LLMs, regions and tasks. Binary and MCQ distance labels are derived from a fixed threshold 𝑇0 set to the pairwise distance median. A key question is whether 𝑇0 reflects the models’ implicit notion of closeness or imposes an external boundary misaligned with LLM perception. Moreover, to evaluate the effect of regional scale, we regenerate the data similarly as UK for the US region. For each region, and task, we estimate each model’s revealed threshold 𝑇 ∗ as the intersection of the kernel density

estimation (KDE) curves fitted to the close- and far-labelled distance distributions extracted from existing predictions. For binary questions, question polarity combined with Yes/No prediction, determines question label, for MCQ, the distance to the chosen ward is assigned with question relation (close/far). Results are summarized in Table 6. We highlight three main findings: (i) Closeness perception is systematically stricter than the dataset label. ∗ ≪ 𝑇 , treating a large In the binary task, most models yield 𝑇UK 0 fraction of close-labeled pairs as far. This compression is consistent across families, suggesting a corpus-level prior on proximity rather than a model-specific artifact. (ii) Task format re-calibrates the implicit threshold. MCQ reverses the binary pattern: all models cluster near 𝑇 ∗ /𝑇0 ≈0.92–0.94 (UK), closely tracking 𝑇0 . The three named candidate wards act as implicit distance anchors, pulling the model’s boundary toward the dataset scale, regardless of its underlying spatial prior. This re-calibration is format-induced rather than evidence of stronger spatial understanding, and cautions against interpreting MCQ accuracy as a reliable proxy for absolute closeness concept strength.(iii) Distance concept understanding degrades at continental scale. Smaller Qwen models (0.6B, 1.7B) show nearchance US binary accuracy (≈ 50%) with negligible Δ, indicating no close/far discrimination at the 1,637 km scale, whereas larger models maintain meaningful gains (Qwen3-4B: Acc +6.1, Cons +5.3; Qwen3-8B: Acc +5.7)—suggesting continental-scale distance concepts are capacity-dependent. The same small models yield nontrivial improvements in UK binary (Qwen3-4B: Acc +3.2, Cons +4.8), confirming the collapse is scale-induced rather than a general model limitation. This degradation manifests differently in MCQ: nearly all models yield negative accuracy deltas at 𝑇 ∗ across both regions (e.g. Qwen3-1.7B US: −2.1, Qwen3-4B UK: −0.5), meaning the fixed label 𝑇0 already outperforms the model’s own revealed boundary in the anchored-option setting—further evidence that MCQ performance reflects format calibration rather than intrinsic spatial understanding. To sum up. QA-based evaluation has inherent limitations as a proxy for concept understanding: surface-level accuracy does not reliably reflect robust understanding across tasks and regions, particularly for challenging concepts such as distance. Consequently, a more targeted probing approach is required to analyze the core properties of concepts in depth, which is the central focus of the following Section 6.

Concept Probing

To evaluate concept abstraction, compositionality, and grounding, we construct a dedicated probing dataset D𝑃𝐵 by subsampling 1,000 binary and 1,000 ternary representative compositional questions from our Geo-QA corpus D𝑄𝐴 and including all corresponding atomic decompositions and their negations, resulting in 2 × 7,000 = 14,000 QA instances. Particularly for the MCQ task, we ensure that each compositional question and its atomics share the same options, this is mandatory for consistent decomposition. Statistics of D𝑃𝐵 are presented in Table 7.

6.1

Testing concept abstraction

To test LLMs on the property of abstraction, we answer two core questions tightly related to semantic type representativeness and generalizability: (i) Are concept instances explicitly encoded in the

Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding UK (𝑇0 = 47.76 km) Binary Model Llama-3.1-8B Ministral-8B Mistral-7B-v0.2 Mistral-7B-v0.3 Qwen3-0.6B Qwen3-1.7B Qwen3-4B Qwen3-8B

US (𝑇0 = 1636.66 km) MCQ

Binary

MCQ

𝑇∗

Acc (%)

Cons (%)

𝑇∗

Acc (%)

Cons (%)

𝑇∗

Acc (%)

Cons (%)

𝑇∗

Acc (%)

Cons (%)

16.80 20.88 20.78 19.70 47.37 7.54 30.86 31.74

70.0 (+7.6) 60.3 (+9.0) 65.3 (+14.5) 64.4 (+14.0) 50.0 (+0.0) 50.1 (+0.0) 55.9 (+0.9) 57.1 (+2.9)

48.3 (+7.6) 38.8 (+9.0) 41.5 (+14.5) 38.3 (+14.0) 0.1 (+0.0) 1.3 (+0.0) 21.6 (+0.9) 18.1 (+2.9)

43.22 43.99 56.36 28.05 45.09 44.43 43.65 44.89

41.0 (+2.7) 39.8 (+2.4) 67.6 (+17.0) 44.2 (-1.0) 35.9 (+2.4) 35.5 (+1.8) 35.6 (+2.7) 36.8 (+1.9)

13.4 (+3.0) 16.0 (+1.6) 22.2 (+11.1) 16.8 (-2.0) 11.9 (+0.2) 11.9 (+2.0) 14.3 (+1.2) 11.6 (+0.6)

1824.39 1225.86 1034.62 344.80 1293.36 1724.44 1055.08 1582.63

48.8 (-2.9) 58.5 (+8.4) 64.2 (+13.4) 80.0 (+30.8) 50.1 (+0.1) 50.3 (-0.4) 60.0 (+9.5) 52.8 (+0.9)

25.4 (-2.9) 38.0 (+8.4) 47.2 (+13.5) 63.6 (+30.8) 2.0 (+0.1) 10.7 (-0.4) 32.1 (+9.5) 28.0 (+0.9)

1365.79 1570.75 1495.82 1486.11 1508.52 1604.81 1503.55 1453.31

43.4 (+1.7) 31.6 (+0.5) 35.9 (-2.8) 32.5 (+0.0) 32.9 (+0.7) 24.7 (-0.3) 36.9 (+2.8) 37.5 (+1.1)

0.0 (+0.0) 0.0 (+0.0) 14.3 (+0.0) 14.3 (+4.8) 0.0 (+0.0) 0.0 (+0.0) 15.6 (+0.0) 0.0 (+0.0)

Table 6: Revealed threshold 𝑇 ∗ (km) and performance relative to the GT label 𝑇0 . Acc (%) and Cons (%) are evaluated at 𝑇 ∗ ; deltas in parentheses show gain over evaluation at 𝑇0 (+ = improvement, − = degradation).

dir 1541

dist 1523

Probing Data (D𝑃𝐵 ): Concept types dist_dir_top top dir_top dist_top 1000 844 374 354

dist_dir 272

Table 7: Positive counts for each combination in the probing data with uniform sampling per number of concepts.

Split Type

Train

Test

Token-Level Split (Atomic-Based) Direction Distance Topology

{N, S} {C} {Wi}

{E, W} {F} {B}

Combination-Based

hidden layer and reliably classified as concept types? (ii) Do learned concept representations generalize to unseen instances or novel combined instances? Experimental design. To investigate whether frozen LLMs encode geographical concepts at different depths, we employ a layer-wise linear probing approach. For each layer 𝑙 of a pre-trained model, we extract the average token embedding for a question 𝑞, producing a layer-specific representation ℎ = 𝑓𝑙 (𝑞). A probe classifier trained on ℎ predicts one of seven conceptual classes 𝐶 (e.g., directional, topological, distance, or their compositions). Specifically, for each 𝑞, the probe outputs 𝑦ˆ = softmax(𝑊𝑙 ℎ + 𝑏𝑙 ) where 𝑐𝑞 ∈ 𝐶 is the predicted label and 𝑊𝑙 , 𝑏𝑙 are layer-specific parameters. To evaluate the generalizability of LLM representations, we construct several data splits: a standard random train/test split to probe concept encoding (question (i)), and two OOD settings, to probe generalization and systematicity [10] (question (ii)): the region-based OOD uses QA pairs from the upper-region, while the token-based OOD withholds specific concept combinations. All splits are summarized in Table 8. Results. Table 9 and Figure 4 show that most evaluated LLMs achieve near-perfect performance on the standard random split (99.95−99.98% accuracy) and generalize well to OOD settings, reaching 75−83% on the Geo-Level split, 80−83% on the single Tokenlevel split, and over 99% on the compositional Token-level split. In contrast, the Mistral-family models exhibit substantially lower accuracy across all splits –random split 52.8−58.0%, Geo-Level split 37.8−42.2%, single Token-level split 22.5−29.4%, and compositional Token-level split 48.5−55.4%– indicating significantly weaker concept encoding and generalization under comparable experimental settings. To sum up: Most models clearly recognize concepts via their latent representations, which is a consistent finding with previous work that has shown the ability of LLMs to represent the space through the geographic entity location task [15]. However, the Mistral family consistently underperforms across all splits and layers, suggesting limited concept abstraction capacity in its architecture compared to the other tested LLMs.

Atomics Dis×Dir Dis×Top Dir×Top Dis×Dir×Top

50% per token {C, F}×{N, S} {C×Wi, F×B} {N×Wi, S×B} {C, F}×{N, S}×{Wi, B}

50% per token {C, F}×{E, W} {C×B, F×Wi} {E×Wi, W×B} {C, F}×{E, W}×{Wi, B}

Geo-Level Split2 Geo-OOD

{mid-region}

{upper-region}

Table 8: Atomic-based token-level and combination-based compositional OOD splits, followed by geographic OOD evaluation. Token abbreviations: N=North, S=South, E=East, W=West, C=Close, F=Far, Wi=Within, B=Borders.

Figure 4: Binary Task: Concepts classification accuracy per LLM layer (depth) for Geo-Level split. The other splits shows similar trends for both tasks.

6.2

Testing concept compositionality

To test the compositionality of LLMs, we proceed in two stages: first, we measure the compositionality gap (§6.2.1), then we test the compositionality of the representations and the predictions (§6.2.2).

Karim Radouane, Jose G Moreno, and Lynda Tamine

38.6

10.9%

29.6

20.0%

27.3%

14.1%

27.5

14.1%

2.8

3.3

24 1

0_8

7b .3_

18.3 46.1%

2.7

str

al_

al_ str

v0 mi

al_

(a) Binary-QA Task.

2.4

.2_

_4b

1.3

18.9%

3_8 b

3.1 100.0% 0.0

19.1

50.6%

26.8

2.6

18.2

_8b

3.2

str

7.8

18.7 25.4%

18.0

lla

33.6%

en 3

14.8

12.2%

15.9

15.1

17.6%

18.7 14.5

en 3

10.7 4.5%

Models

10.9%

21.3

3_8 b ma

34.2 2.6%

4.4

lla

_8b

b 0_8

.3_ al_

str

v0 al_ str

81.2% 0.5

43.5

_1. 7b

3.6

43.4%

48.0 38.3

en 3

3.0

16.4

4.5

20.7

25.9

Performance and Gap (%)

70.8%

25.4%

.2_

_4b en 3 mi

en 3 qw

17.1

50.4%

0.0

en 3 qw

_0. 6b

0.0

1.0

20.4

15.9

24 1

0.1 100.0%

0.5 100.0%

27.1

29.8

en 3

44.4%

38.0

38.7%

27.0%

_0. 6b

32.2

28.2 24.5

17.5%

54.5

54.3

Accuracy Consistency Compos Atomic

en 3

13.0%

49.7

18.9%

al_

Accuracy Consistency Compos Atomic

51.1

str

40 30

15.4%

45.9

54.8

52.8

51.4

49.9

49.4 33.5%

_1. 7b

Performance and Gap (%)

50.0 50.2%

59.7

Models

(b) MCQ Task.

Figure 5: Compositional gap analysis (in blue rectangle), highlighting differences between composite and atomic question performance w.r.t accuracy of compositional questions and their atomics. The arrow points from compositional to atomics, illustrating the gap. Token-Level Test

Geo-Level Test

Model

Random

Single-Based

Combination-Based

Geo

qwen3_4b qwen3_8b llama3_8b qwen3_1.7b mistral_2410_8b mistral_v0.3_7b mistral_v0.2_7b qwen3_0.6b

36 36 32 28 36 32 32 28

99.98 99.98 99.95 99.98 53.05 52.83 58.02 99.95

81.65 80.76 82.85 80.43 22.47 24.17 29.40 80.87

99.45 99.61 99.90 99.10 48.47 49.15 55.37 99.33

75.86 75.83 75.69 75.81 37.76 38.88 42.17 75.81

Table 9: Final-layer probe results across evaluation settings. Single-Based and Combination-Based correspond to atomic and compositional token-level OOD tests, respectively. GeoLevel Test evaluates geographic generalization. 6.2.1 Measuring the compositionality gap. Instead of following [39] that measures the cases where a model correctly answers all constituent subquestions but fails on the corresponding compositional question to test multi-hop or relational chaining as compositional gap, we probe LLMs through QA tasks with conjunctive concept compositions. For each compositional question 𝑞 ∈ Q, let S(𝑞) denote its set of sub-questions. Let Q𝑡𝑐 = {𝑞 ∈ Q𝑡 /𝑆𝑢𝑏𝐴𝑐𝑐 (𝑞) = 1} be the set of compositional questions for a given task 𝑡 that h has its subquestions icorrectly ˆ = 𝑦(𝑠) . answered, where SubAcc(𝑞) = I ∀𝑠 ∈ S(𝑞) : 𝑦(𝑠)

Evaluation metrics. To measure the compositionality gap, we define the following metrics: • Per-question CGA. We define the per-question compositional accuracy as: CGA(𝑞) = 1 − Acc(𝑞) = 1 − I 𝑦ˆ (𝑞) = 𝑦 (𝑞) ∀𝑞 ∈ Q𝑡𝑐 ¯ S(𝑞) denotes where 𝑞¯ denote the negative version of question 𝑞, ˆ the set of subquestions of 𝑞, 𝑦(𝑞) is the model prediction, and 𝑦 (𝑞) is the ground truth answer. • Compositional Gap Accuracy (CGA). The proportion of compositional questions answered incorrectly for which all corresponding subquestions were answered correctly: 1 ∑︁ CGA = 𝑐 CGA(𝑞) |Q𝑡 | 𝑐 𝑞 ∈ Q𝑡

• Compositional Gap Consistency (CGC). We define a consistencybased compositional gap using paired positive (𝑞) and negative ¯ of each question, which decouples true performance versions (𝑞) from random chance. CGC measures the proportion of compositional questions answered incorrectly for which all corresponding sub-questions where answered consistently correct: CGC =

1 ∑︁ ¯ CGA(𝑞) · CGA(𝑞) |Q𝑡𝑐 | 𝑐 𝑞 ∈ Q𝑡

Results. The main results are reported in Figure 5. Unlike [39], in conjunctive-based compositionality, LLMs perform better on compositional questions than on atomic ones. Notably, for the Binary-QA task, Mistral-v0.3-7B shows the smallest compositional gap in accuracy (13%), suggesting relatively better compositional generalization. However, this does not translate into strong consistency: its rate is 17.1%, slightly above Mistral-v0.2-7B (15.9%), while both remain far from ideal. This advantage in gap size should be interpreted alongside absolute performance, which is higher for Qwen3-4B (59.7%). Unsurprisingly, smaller models show the largest compositional and consistency gaps. For the MCQ task, the llama3-8B model has the highest compositional accuracy (54.5%) but with a higher compositional gap compared to small-size models. Interestingly, smaller models on this task show lower gaps than in the binary task, yet overall compositional accuracy remains very low (< 39%). 6.2.2 Measuring compositionality. Here, we attempt to answer two core questions: (i) Are concept representations compositional? (ii) Can LLMs’ predictions be explained through compositional representations? Experimental design. To investigate whether internal representations learned by selected LLMs exhibit compositional structure (i.e., question (i)), we follow previous work [44], by testing compositionality as approximate additivity. We analyze cosine similarity scores between L(𝑞) and Ladd = L(𝑞 1 ) + L(𝑞 2 ), enabling systematic comparison of compositional behavior across models. We then

Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding

Figure 6: Binary-QA Task: Cosine similarity per layer between each compositional question embedding 𝑞 and its decomposition, considering 2-Concepts (𝑞 1 + 𝑞 2 ) and 3-Concepts (𝑞 1 + 𝑞 2 + 𝑞 3 ). For MCQ task, we observe similar curves trend. Qwen models have very similar trend as llama3_8b for both tasks. 1.0

0.75

0.6

0.70 0.65 0.60

1.0 0.42 0.8 0.40

0.4

Avg correlation

0.8

Avg correlation

0.80

0.38

0.2 0.36

0.0

0.6 0.4 0.2

0.2

0.55

0.34 0.0

0.4

0.50 0

mistral_2410_8b

Layer

mistral_v0.3_7b

mistral_v0.2_7b

0.32 0

qwen3_4b

qwen3_8b

Layer

qwen3_0.6b

qwen3_1.7b

llama3_8b

(a) Binary Task. Mistral models lose logits correlation across layers, directly explaining performance gap compared to the other LLMs.

mistral_2410_8b

Layer

mistral_v0.3_7b

mistral_v0.2_7b

qwen3_4b

qwen3_8b

Layer

qwen3_0.6b

qwen3_1.7b

llama3_8b

(b) MCQ Task. Mistral models again exhibit weaker compositionality between atomics and composite questions compared to other models..

Figure 7: Logits-based Pearson correlation coefficient across LLM layers for both tasks. compute a cosine similarity score 𝑠 ∈ [−1, 1] as: 𝑠 = sim L(𝑞), Ladd =

L(𝑞) ⊤ Ladd . ∥L(𝑞)∥ ∥Ladd ∥

The score 𝑠 measures how well the additive approximation by atomics matches the model’s composite representation. To test prediction compositionality (i.e., question (ii)), we train multinomial logistic regression probes on frozen LLM layer representations rather than relying on the model’s native logits of the final layer only. This layer-wise probing framework enables analysis across all layers, revealing where compositional structure is encoded. By decoupling evaluation from LLMs’ output-formatting artifacts of auto-regressive generation and focusing on fixed embeddings, the approach isolates representational content and yields a more robust assessment of how internal model features support compositional predictions. Probes are trained on a subset of factual items and evaluated on held-out facts, assessing not fact inference but the consistency of factual and compositional encoding within the model’s representational space and whether it emerges across LLMs from its frozen representation, and explain compositional prediction by its atomic predictions. To test the level of prediction compositionality, we measure correlations between predictions from the full composite representation L(𝑞) and the combination of atomic representations 𝐿add . This is performed using logits and embeddings, and probabilitybased methods. Let vcomp denote the embedding of a composite question, v𝑖 the embeddings of its 𝑛 atomic sub-questions, 𝑓 the trained classifier, and L (𝑓 (v)) the logit for the true answer class:

• Logit Additivity: Correlation between L (𝑓 (vcomp )) and Í𝑛 𝑖=1 L (𝑓 (v𝑖 )), testing whether logit values compose linearly. • Embedding Summation: Correlation between 𝑃 (𝑓 (vcomp )) Í and 𝑃 (𝑓 ( 𝑛𝑖=1 v𝑖 )), evaluating whether summed embeddings predict the same class probabilities as composite embeddings. • Probability Averaging: Correlation between 𝑃 (𝑓 (vcomp )) and 1 Í𝑛 𝑖=1 𝑃 (𝑓 (v𝑖 )), testing whether individual atomic predictions 𝑛 aggregate to composite predictions. Each metric probes a distinct compositionality hypothesis: decision-boundary linearity, embedding-space compositionality, and compositional confidence. Results. From an embedding-based perspective, Figure 6 reports cosine similarity between compositional questions and their sub-questions across LLM layers. In both Binary-QA and MCQ tasks, Mistral models exhibit the lowest and most variable compositionality correlation. In both settings, 2-Concept compositions consistently show higher compositionality than 3-Concept ones. From a prediction-based perspective, Mistral achieves moderate Binary-QA accuracy (∼65%) with weak compositional correlations (logit correlations ∼0.4), and lower MCQ accuracy (∼35%). In contrast, Qwen and LLaMA attain higher Binary-QA accuracy (∼80%) and comparable MCQ performance (∼35–39%), while maintaining consistently strong correlations across settings (logits ≳0.85, probabilities ≳0.7), indicating a substantially stronger alignment between compositional structure and predictive behavior (cf. Table 10). To sum up. Across experiments, LLMs exhibit a compositional consistency gap in QA tasks. In contrast, probing latent representations across layers reveals that predictive compositionality has a clear impact on performance: models with compositional embeddings

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MCQ (grounding ref) -0.16 +3.63 -1.02 +1.05 +2.95 +1.89 -0.37 +1.14 +0.00 +5.81 +0.60 +2.10 +5.60 +3.55 -0.79 +2.41 +0.42 +1.66 +0.10 +1.58 -0.05 +0.00 +0.45 +0.59 +1.27 +1.66 -0.99 -1.05 -0.60 -2.37 +0.00 -0.30 +0.03 -0.72 -0.07 -0.53 -0.10 +0.12 -0.40 -0.24 +0.00 -1.46 -0.26 -1.05 -0.30 +0.23 -0.79 -0.52 -0.35 +0.72 +0.43 +1.05 +0.25 +0.00 -0.34 +0.25 -0.70 +0.41 +0.60 +0.00 +1.00 -2.36 -0.31 -0.19 -0.63 +0.52 -0.17 +2.11 +0.95 +0.59 -0.11 +0.47 -0.70 +0.21 -0.06 +2.11 +1.50 +0.24 +0.11 +0.49 +0.44 +1.14 +0.33 +1.58 -1.00 -0.82 -0.68 +0.14 +0.95 +1.03 +0.92 +0.00 -1.00 -1.19 -0.73 -0.00 +0.79 +0.52 +0.52 +0.00 -0.55 -0.23 +0.84 +0.27 +0.45 +0.42 +0.20 -2.11 -1.30 -0.71 +0.42 -0.38 -0.61 -0.11 +0.75 +0.00 -0.35 +0.12 -0.32 -0.07 -0.06 -0.21 +0.39 +2.10 -0.40 +0.47 -0.90 +0.20

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76.0 57.5 63.2 39.2 51.5 3.1 63.7 39.5 59.5 32.9 56.1 29.3 54.7 26.7 50.1 23.6

Binary (grounding ref) -0.17 +5.21 -2.01 +0.37 +3.15 +1.70 +5.27 +1.93 llama3_8b +3.77 +5.08 -4.59 +1.83 +3.20 +3.67 +8.06 +3.00 +0.35 +0.27 -0.63 -0.56 +1.65 +0.28 +2.37 +0.53 79.8 mistral_2410_8b 66.7 +0.78 -2.67 -3.02 -1.84 +1.60 -3.67 +2.60 -0.89 63.6 44.7 75 -0.68 +0.00 +0.13 +3.49 +0.15 +0.00 -0.23 +0.41 64.8 mistral_v0.2_7b 58.4 +0.00 +1.87 +0.00 +4.78 +0.40 -0.56 -0.12 +0.91 41.8 33.6 70 54.5 mistral_v0.3_7b 52.3 +0.04 -0.27 -0.13 +0.00 +0.35 +0.43 -0.35 +0.01 65 8.9 4.6 +0.39 -0.80 -0.14 +0.00 +0.60 +0.00 -0.71 -0.09 65.9 60.1qwen3_4b -0.59 +1.07 -0.59 -2.02 -1.15 +1.27 -0.06 -0.30 60 43.3 32.6 -0.45 +2.14 -0.66 -1.83 -1.40 +1.70 -0.24 -0.11 68.1 58.5qwen3_8b +0.26 -0.27 -0.26 +0.37 -0.85 -0.14 +0.30 -0.08 55 44.6 30.6 +0.52 +0.00 -0.13 +0.00 -0.90 -0.28 +0.59 -0.03 60.7 56.1 -0.03 +0.27 -0.07 -0.37 +0.10 +0.42 +0.94 +0.18 50 qwen3_1.7b 34.9 28.2 +0.13 +0.00 -0.32 -0.74 +0.00 +0.00 +0.00 -0.13 45 60.4 54.6 +0.00 +0.00 +0.07 +0.56 -0.05 +0.00 +0.00 +0.08 qwen3_0.6b 33.4 27.5 +0.00 +0.27 +0.00 +0.00 -0.10 -0.28 +0.00 -0.02 40 50.7 50.7 23.7 24.1

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MCQ 53.2 76.3 24.2 58.7 55.3 62.0 27.4 37.1 50.0 53.5 0.0 7.0 50.0 68.7 16.8 47.0 56.3 60.6 27.4 33.3 54.2 57.5 20.0 31.1 57.9 54.9 29.5 28.4 47.4 50.7 24.2 24.0

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llama3_8b 49.6 11.8 mistral_2410_8b 51.4 20.8 mistral_v0.2_7b 50.9 14.7 mistral_v0.3_7b 51.4 14.9 qwen3_4b 49.2 4.3 qwen3_8b 50.3 4.5 qwen3_1.7b 49.9 0.5 qwen3_0.6b 50.0 0.0

Binary 52.8 56.6 16.5 29.7 51.6 53.6 18.8 18.5 51.6 54.0 19.5 19.7 50.5 50.5 13.2 18.7 54.2 58.8 16.2 21.9 52.9 54.8 14.3 25.4 50.0 49.6 0.0 0.0 49.8 50.0 0.0 0.0

Karim Radouane, Jose G Moreno, and Lynda Tamine

(b) Performance changes in grounding (improvement/ degradation).

(a) Per-concept and overall grounding performance.

Figure 8: Effect of grounding information on model performance compared to settings without grounding information per concept type. Consistency is reported below accuracy in each cell of the heatmaps, the final column shows the overall and average results. Mistral

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Llama

Method

7b_v0.2

7b_v0.3

8b_2410

0.6b

1.7b

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67.03

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64.88

35.39

65.75

33.89

80.89

35.48

81.27

35.22

81.18

36.02

81.36

35.66

81.32

39.01

logits embed. proba.

0.53 0.23 0.24

0.60 0.51 0.59

0.37 0.05 0.12

0.55 0.44 0.55

0.33 0.08 0.10

0.57 0.45 0.56

0.98 0.80 0.73

0.86 0.83 0.85

0.99 0.73 0.66

0.86 0.81 0.85

0.99 0.76 0.70

0.88 0.86 0.88

0.99 0.78 0.70

0.88 0.84 0.88

0.99 0.58 0.74

0.85 0.72 0.84

Table 10: Average correlations and accuracies for Binary/MCQ. preserve prediction consistency and achieve more robust results, unlike Mistral-like architectures.

6.3

Testing concept grounding

We test contextual grounding via QA performance on tasks defined in a numerically explicit spatial context using coordinates, distances, and bearing angles, where all relevant real-world information is provided in context to LLMs as follows: Context_Binary: 𝑋 at (𝑎𝑋 , 𝑏𝑋 ), 𝑌 at (𝑎𝑌 , 𝑏𝑌 ), distance 𝑑 (𝑋 , 𝑌 ) = 𝑁 km, bearing 𝛽𝑌 →𝑋 = 𝜃 ◦ , X and Y are considered close if 𝑑 (𝑋 , 𝑌 ) ≤ 𝑇0 , and far otherwise. Context_MCQ: 𝑌 at (𝑎𝑌 , 𝑏𝑌 ), {𝑋𝑖 at (𝑎𝑖 , 𝑏𝑖 ), 𝑑 (𝑌 , 𝑋𝑖 ) = 3 𝑁𝑖 km, 𝛽𝑌 →𝑋𝑖 = 𝜃𝑖◦ }𝑖=1 (𝑋𝑖 ward option 𝑖), X and Y are considered close if 𝑑 (𝑋 , 𝑌 ) ≤ 𝑇0 , and far otherwise.

Grounding. In our context is defined by the ability to map linguistic concepts to their numerical meaning. If an LLM fully achieves grounding, it is expected to successfully answer the corresponding questions. In practice, answer quality provides a continuous measure of grounding. Direction- and distance-based concepts can be precisely tested in coordinate-based contexts, where all quantitative information is explicit. In contrast, topology-based concepts require a larger number of points, often leading to noisy contextual expansions and making practical evaluation challenging. Experimental design. In this test, the LLM context is augmented with relevant geographical measurements and then asked to answer a corresponding related question. This protocol aims to evaluate LLMs’ ability to ground concepts appearing in a given question to equivalent numerical representations. Results. As shown in Figure 8, topology-independent spatial grounding performance in LLMs varies substantially across both task formulations and model architectures. In the MCQ setting, several models surpass the random baseline (33%), with Qwen38B achieving the strongest results (66.7% accuracy and 44.7% consistency on the distance concept). However, overall consistency

remains limited, indicating only weak grounding ability. In the Binary-QA setting, accuracy largely concentrates around chance level (∼50%) and is consistently paired with low consistency, revealing significant instability in concept grounding (e.g., Mistral-8B at ≈ 52%). Across geographical concept-mapping tasks, LLMs demonstrate weak and inconsistent grounding, with no systematic advantage for direction- or distance-based concepts over topological ones. In several cases, performance degrades below that of simple factual recall, with only marginal improvement in some instances, achieving at best an average improvement of 1.93% accuracy and 3% consistency (Fig. 8b). To sum up. Concepts are not naturally grounded in the evaluated LLMs; instead, the results indicate a reliance on in-context concept memorization rather than true numerical meaning grounding. This aligns with prior findings showing that text-only small LMs struggle to map linguistic concepts to non-linguistic referents [34].

Conclusion

We investigated geo-spatial concept understanding in LLMs through the lens of abstraction, grounding, and compositionality. Our results show that while LLMs encode and partially compose concepts, factual consistency and real-world grounding remain critical bottlenecks. The core of our probing concept-centric QA benchmark (i.e., questions and ground truth) is based on a task-agnostic generation and filtering of relational facts in the form of triplets (§ Algorithm 1, 2). Such a widely adopted knowledge representation form inherently eases the extendability and reuse of our probing methodology to the study of abstraction, compositionality, and grounding of other concepts (e.g., truth [2]) even in other domains (e.g., gender bias in healthcare [1]). However, while providing valuable insights, our study has some limitations. First, our experiments rely only on two real-world geographic regions. Second, the studied concepts may not fully capture the complexity of other real-world concepts. Third, our probing experiments are limited to linear classifiers. Our work has potential implications for information and knowledge management, including the following: (i) Information access and retrieval: our findings reveal that LLMs generally have a good level of performance in recognizing OOD concept instances, indicating a significant ability of abstraction. Based

Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding

on this finding, new paths moving from the current designs of LLMs for relevance ranking [19, 38, 55] toward new approaches of axiomatic IR [48] or mechanistic interpretability for IR [33] are worth investigation by testing the concept of relevance through its core properties that constrain words, documents, and queries; (ii) Mining multimodal content: the limited grounding of concepts in current LLMs provides concrete evidence of why multi-modal (e.g. language and vision) models must go beyond traditional two-tower models [40]. Our findings argue for externally grounded models that complement LLMs with parametric mechanisms for explicit grounding in the same line as parametric retrieval augmented generation [45]; (iii) Evaluation: our findings reveal a critical limited ability of downstream task evaluation to actually probe LLMs on their understanding of conceptual knowledge. This result calls for the design of new benchmarks suited to concept probing, annotated with core properties, standardized metrics, and reference concepts, configurations with published baselines.

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