Extracting Conceptual Spaces from LLM s Using Prototype Embeddings (2025)

Abstract: Conceptual spaces represent entities and concepts using cognitively meaningful dimensions, typically referring to perceptual features. Such representations are widely used in cognitive science and have the potential to serve as a cornerstone for explainable AI. Unfortunately, they have proven notoriously difficult to learn, although recent LLMs appear to capture the required perceptual features to a remarkable extent. Nonetheless, practical methods for extracting the corresponding conceptual spaces are currently still lacking. While various methods exist for extracting embeddings from LLMs, extracting conceptual spaces also requires us to encode the underlying features. In this paper, we propose a strategy in which features (e.g. sweetness) are encoded by embedding the description of a corresponding prototype (e.g. a very sweet food). To improve this strategy, we fine-tune the LLM to align the prototype embeddings with the corresponding conceptual space dimensions. Our empirical analysis finds this approach to be highly effective.

## introduction conceptual spaces @xcite are geometric representations of meaning, in which concrete entities are represented as vectors. different from word embeddings in nlp, the dimensions of a conceptual space (typically) correspond to perceptual features. for instance, in a colour space, entities would be represented using three dimensions, corresponding to their hue, saturation and intensity. conceptual spaces are used in cognitive science as theoretical models to explain phenomena such as analogy @xcite , non-monotonic reasoning @xcite and concept learning @xcite . within ai, the use of conceptual spaces has been advocated as an interface between neural and symbolic representations @xcite . as such, they can play an important role in explainable ai, for instance to enable interpretable classifiers @xcite @xcite ) and computational creativity @xcite . in practice, however, these applications have been hampered by the difficulty in learning conceptual spaces. within cognitive science, most work has relied on spaces that are learned from human similarity judgments, for instance to study perception of colour @xcite , music @xcite , taste @xcite or smell @xcite . clearly, however, such a solution is not scalable enough for explainable ai. a natural alternative is to try to construct conceptual spaces using nlp models, such as word embeddings or large language models (llms). in fact, even within cognitive science, researchers have looked at nlp models as a promising route to obtain conceptual spaces in a cheaper way @xcite . starting from a pre-trained embedding space, it is often indeed possible to identify directions within that space that capture meaningful ordinal properties @xcite @xcite @xcite . however, modelling perceptual features with traditional models has proven more challenging. this is intuitively due to the fact that many perceptual features are only rarely stated in text. for instance, @xcite highlighted how language models struggle with predicting colours, due to a divergence between the typical colour of an object and the distribution of co-occurring colour terms (e.g. the phrase "green banana" being more common than "yellow banana" in text). however, recent llms have proven more capable at modelling perceptual features, where promising results have been reported for colour @xcite @xcite , taste @xcite , touch @xcite , smell @xcite and sound @xcite , among others. one problem that is not addressed by these works is how to extract conceptual spaces from llms. for instance, @xcite prompt llms to make pairwise judgments (e.g. which is sweeter, banana or cucumber?), which only allows us to rank the entities along some conceptual space dimensions, without capturing how much the entities differ. using pairwise comparisons is also intractable when dealing with thousands of entities. @xcite use llms to make pairwise similarity judgments, which is again too inefficient for constructing conceptual spaces at scale. in a wider context, the problem of learning embeddings of text fragments using llms is well-studied @xcite @xcite @xcite . we therefore consider the following research question: is it possible to extract conceptual spaces directly from llm-generated embeddings? entity embeddings can straightforwardly be obtained using standard techniques. however, we also need to model the perceptual features. for instance, given an embedding emb("banana") of the word banana, how do we determine its level of sweetness? as already mentioned, previous work has shown that many features of interest can be modelled as directions in pre-trained embeddings. it is thus natural to assume that there exists a vector v sweet such that emb("banana") • v sweet reflects the degree of sweetness of a banana. one possibility is to estimate this vector v sweet from labelled examples, but such data is not readily available for most domains. another possibility is to estimate the vector from seed words, i.e. examples of entities at both extremes of the ranking, but such directions can be unreliable, being highly sensitive to choice of seeds @xcite . in this paper, we consider a simple alternative, which is to estimate the vector v f encoding some feature f as the description of a generic prototype. for instance, v sweet could be modelled as emb("a very sweet food"). unfortunately, with pre-trained llm embedding models, the performance of this approach is sub-optimal, as the embedding of such a generic prototype description lies in a different subspace than the entities themselves (see figure 1 ). we therefore propose a fine-tuning strategy, which encourages the embeddings of such descriptions to be aligned with the embeddings of the corresponding entities. we find that a small training set, synthetically generated using gpt-4o, is sufficient to achieve state-of-the-art results. ## related work the problem of learning entity embeddings using language models has received considerable attention, especially for bidirectional models of the bert family @xcite . for instance, a number of authors have proposed to represent entities by averaging the contextualised embeddings of their mentions in a corpus, using pretrained @xcite @xcite or fine-tuned @xcite language models. however, approaches that directly extract embeddings based on the name of an entity have also been studied @xcite @xcite . most relevant to our work, several authors have focused on predicting semantic and commonsense properties of concepts from their embeddings @xcite @xcite . for instance, chatterjee et al. (2023) evaluated a bert encoder that was fine-tuned to predict commonsense properties on the task of predicting taste dimensions such as sweetness, showing that their encoder was able to match the performance of gpt-3. @xcite showed that a fine-tuned llama 3 model is able to outperform bert encoders. in this paper, we build on these results, aiming to extract embeddings from models such as llama3, rather than using them for making pairwise judgments. compared to encoder-only models such as bert, it is somewhat less straightforward to use decoder-only llms for embedding text. however, in recent years, several successful strategies have been proposed for fine-tuning llms to become general-purpose text embedding models @xcite @xcite , with the massive text embedding benchmark @xcite serving as a key driver. however, the focus of this benchmark is on sentence and paragraph level tasks, and little is currently known about the quality of llm embedding models when it comes to representing entities. our analysis in this paper partially addresses this gap, by comparing the quality of the conceptual space representations that are obtained by several recent models. llms can also be used to predict embeddings without fine-tuning. @xcite suggested an explicit one word limitation (eol) prompt, of the following form, for this purpose: "this sentence: [text] means in one word:". we will also rely on prompts with this one-word limitation. ## methodology problem formulation let emb be an llmbased embedding model, where we write emb(x) ∈ r n for the encoding of a phrase x. let us furthermore assume that a set of entities e is given which all belong to some natural category. for instance, the entities in e could represent different types of food (e.g. banana, roast chicken, cake). for an entity e, we write γ(e) for the verbalization of that entity, i.e. γ(e) is a phrase that describes e. the entity e can then be represented by its embedding emb(γ(e)). we are interested in modelling semantic features of the entities based on these embeddings, where our focus is on perceptual features such as the sweetness of a food item or the intensity of an odour. let f be some real-valued feature, such that every entity @xmath0. we want to find an encoding τ f : r @xmath1. we want to find the encoding τ f without any supervision, other than a verbalization of the feature f , hence we cannot expect τ f (emb(γ(e))) = f (e), as there is typically no unique way to measure the degree to which a perceptual feature is satisfied. instead, we want the rankings induced by the functions f (.) and τ f (emb(γ(.))) to be as similar as possible. embedding entities we experiment with two types of models: standard llms such as llama-3 and pre-trained llm-based embeddings models such as e5. the latter models can directly be used to obtain an embedding of γ(e). to obtain embeddings with standard llms, we use a variant of the eol trick from @xcite . specifically, we use the following prompt: the embedding emb(γ(e)) is then defined as the normalized encoding of the llm for the last token. to verbalize the entity e, we observed that adding the name of the considered category leads to more informative embeddings for most models. for instance, we verbalize the entity banana as "food item banana" rather than "banana". this intuitively helps with resolving some ambiguities (e.g. orange as a fruit rather than a colour) and with specializing the embeddings to the domain of interest (e.g. strawberry as an odour rather than a food). modelling features a common approach for modelling semantic features based on embeddings is to fit a logistic regression model (or a linear svm) based on some training data. however, for most perceptual features, such training data is not readily available. another common approach relies on a few examples of seed words h 1 , ..., h p which are known to have a high value for the considered feature, and examples of seed words l 1 , ..., l q which are known to have a low value. we can then estimate a vector v f that models the considered feature f based on this vectors, e.g.: and τ f (e) = e • v f . in principle, v f can then be estimated from just two seeds words (i.e. @xmath2. however, several authors have pointed out that this approach can be unreliable @xcite . for instance, if we have banana as the only example of a sweet food, then the resulting vector v sweetness might capture the property of being yellow (in addition to, or instead of sweetness). we pursue a different strategy, estimating the vector v f by embedding a description γ(f ) of the feature f . @xcite trained a bert biencoder based on this idea. specifically, they finetuned two different bert models, one for encoding entities and one for encoding properties, using a large dataset of commonsense properties. with llms, this bi-encoder strategy is not practical, as it doubles the memory requirement compared to finetuning a single model. we therefore embed entities and features using the same model. however, we still need to ensure that the embeddings of entities and features are aligned, i.e. emb(γ(e))•emb(γ(f )) should reflect the extent to which e has the feature f . to this end, we verbalize f as a generic description of a prototypical entity with a high value for the feature f . for instance, we can choose: γ(sweetness) = "a very sweet food" however, as illustrated in figure 1 , the embeddings of such generic descriptions are not in the same subspace as those of the entities. we therefore add a fine-tuning step, as we explain next. ## datasets following @xcite , we evaluate our approach on the following datasets: taste: a dataset, originally created by @xcite , describing the taste of 590 food items, in terms of the following quality dimensions: sweetness, sourness, saltiness, bitterness, fattiness and umaminess. this dataset was first used for evaluating llms by @xcite , who rephrased some of the properties to make the more suitable for prompting. we use their cleaned version of the dataset. rocks: a dataset, originally created by @xcite , describing the physical appearance of 30 types of rocks, in terms of the following dimensions: lightness of colour, average grain size, roughness, shininess, organisation, variability of colour and density . tag genome: a dataset with human ratings of the extent to which a number of tags apply to different movies and books. @xcite selected 38 tags for movies and 32 tags for books which can be viewed as ordinal features, all corresponding to adjectives (e.g. scary, quirky, suspenseful). the original movie ratings were obtained by @xcite , while the book ratings were obtained by @xcite . physical properties: a dataset focused on three physical properties: mass, size and height. the data was originally created by @xcite and @xcite . it was used to evaluate llms by @xcite and subsequently cleaned by @xcite , who removed 7 items. wikidata: a dataset with 20 numerical features obtained from wikidata, collected by @xcite (e.g. the length of rivers, population of countries, and date of birth of people). we will furthermore experiment on the following datasets, which have not yet been considered for evaluating llms, to the best of our knowledge: odour: a dataset of 200 odorants collected by @xcite . a total of 103 participants rated odorants across nine dimensions. the authors reported that the following four were the most useful as normative data: familiarity, intensity, pleasantness, and irritability. we therefore also focus on these dimensions. music: a dataset of 364 music excerpts from different genres, collected by a panel of nine music experts @xcite . the 517 participants rated the excerpts based on the emotions they felt, using the following dimensions from the geneva emotion music scale (gems) @xcite : wonder, transcendence, tenderness, nostalgia, peacefulness, energy, joyful activation, sadness and tension. ## experiments we refer to our proposed approach as protosim (prototype similarity). 2 protosim is clearly more practical than prompting llms to provide pairwise judgments, especially when large numbers of entities need to be ranked. our main research question is whether or not the increased convenience of pro-tosim comes with a trade-off on performance. ## conclusions we have shown that llm embeddings can serve as conceptual space representations of perceptual features. while previous work had already shown the potential of llms for modelling perceptual features, this was based on pairwise comparison prompts, which are not practical when representations for large numbers of entities are needed. to model a given quality dimension (e.g. sweetness) we obtain an llm embedding of a corresponding prototype description (e.g. "a sweet food"). the main idea is that we can then simply compare this embedding with the embeddings of the entities of interest. however, we found this to perform poorly with pre-trained llms (including llm-based embedding models), due to the fact that the embeddings of the prototype descriptions and the entities are not aligned. to address this, we align the embeddings by fine-tuning the llm on a small synthetically generated dataset. after this alignment step, we found the proposed strategy to be highly effective, matching and often even surpassing the performance of the pairwise approach. model name hugging face url license llama3-8b meta-llama/meta-llama-3-8b llama 3 qwen3-8b qwen/qwen3-8b apache 2.0 qwen3-14b qwen/qwen3-14b apache 2.0 mistral-nemo-12b mistralai/mistral-nemo-base-2407 apache 2.0 mistral-small-24b mistralai/mistral-small-24b-base-2501 apache 2.0 olmo2-7b allenai/olmo-2-1124-7b apache 2.0 olmo2-13b allenai/olmo-2-1124-13b apache 2.0 phi4-14b microsoft/phi-4 mit e5-mistral-7b intfloat/e5-mistral-7b-instruct mit llm2vec-llama3-8b