’Consider, for example, the fact that unsupervised machine translation is possible (Lample et al., 2018a, b; Park et al., 2021). Unsupervised machine translation works by first aligning vector spaces induced by monolingual language models in the source and target languages (Søgaard et al., 2019). This is possible because such vector spaces are often near-isomorphic (Vulic et al., 2020). If weak supervision is available, we can use techniques such as Procrustes Analysis (Gower, 1975) or Iterative Closest Point (Besl & McKay, 1992), but aligments can be obtained in the absence of any supervision using adversarial learning (Li et al., 2019; Søgaard et al., 2019) or distributional evidence alone. If the vector spaces induced by language models exhibit high degrees of isomorphism to the physical world or human perceptions thereof, we have reason to think that similar techniques could provide us with sufficient grounding in the absence of supervision.
Unsupervised machine translation show that language model representations of different vocabularies of different languages are often isomorphic. Some researchers have also explored cross-modality alignment: (Chung et al., 2018) showed that unsupervised alignment of speech and written language is possible using the same techniques, for example. This also suggests unsupervised grounding should be possible.
Is there any direct evidence that language model vector spaces are isomorphic to (representations of) the physical world? There is certainly evidence that language models learn isomorphic representations of parts of vocabularies. Abdou et al. (2021), for example, present evidence that language models encode color in a way that is near-isomorphic to conceptual models of how color is perceived, in spite of known reporting biases (Paik et al., 2021). Patel and Pavlick (2022) present similar results for color terms and directionals. Liétard et al. (2021) show that the larger models are, the more isomorphic their representations of geographical place names are to maps of their physical location.′
‘Unsupervised machine translation and unsupervised bilingual dictionary induction are evaluated over the full vocabulary, often with more than 85% precision. This indicates language models learn to represent concepts in ways that are not very language-specific. There is also evidence for near-isomorphisms with brain activity, across less constrained subsets of the vocabulary: (Wu et al., 2021), for example, show how brain activity patterns of individual words are encoded in a way that facilitates analogical reasoning. Such a property would in the limit entail that brain encodings are isomorphic to language model representations (Peng et al., 2020). Other research articles that seem to suggest that language model representations are generally isomorphic to brain activity patterns include (Mitchell et al., 2008; Søgaard, 2016; Wehbe et al., 2014; Pereira et al., 2018; Gauthier & Levy, 2019; Caucheteux & King, 2022).’
Recent works from Anders Søgaard might be relevant, e.g. Grounding the Vector Space of an Octopus: Word Meaning from Raw Text, Understanding models understanding language, Implications of the Convergence of Language and Vision Model Geometries.
E.g. from Grounding the Vector Space of an Octopus: Word Meaning from Raw Text on the success of unsupervised machine translation (and more):
’Consider, for example, the fact that unsupervised machine translation is possible (Lample et al., 2018a, b; Park et al., 2021). Unsupervised machine translation works by first aligning vector spaces induced by monolingual language models in the source and target languages (Søgaard et al., 2019). This is possible because such vector spaces are often near-isomorphic (Vulic et al., 2020). If weak supervision is available, we can use techniques such as Procrustes Analysis (Gower, 1975) or Iterative Closest Point (Besl & McKay, 1992), but aligments can be obtained in the absence of any supervision using adversarial learning (Li et al., 2019; Søgaard et al., 2019) or distributional evidence alone. If the vector spaces induced by language models exhibit high degrees of isomorphism to the physical world or human perceptions thereof, we have reason to think that similar techniques could provide us with sufficient grounding in the absence of supervision.
Unsupervised machine translation show that language model representations of different vocabularies of different languages are often isomorphic. Some researchers have also explored cross-modality alignment: (Chung et al., 2018) showed that unsupervised alignment of speech and written language is possible using the same techniques, for example. This also suggests unsupervised grounding should be possible.
Is there any direct evidence that language model vector spaces are isomorphic to (representations of) the physical world? There is certainly evidence that language models learn isomorphic representations of parts of vocabularies. Abdou et al. (2021), for example, present evidence that language models encode color in a way that is near-isomorphic to conceptual models of how color is perceived, in spite of known reporting biases (Paik et al., 2021). Patel and Pavlick (2022) present similar results for color terms and directionals. Liétard et al. (2021) show that the larger models are, the more isomorphic their representations of geographical place names are to maps of their physical location.′
‘Unsupervised machine translation and unsupervised bilingual dictionary induction are evaluated over the full vocabulary, often with more than 85% precision. This indicates language models learn to represent concepts in ways that are not very language-specific. There is also evidence for near-isomorphisms with brain activity, across less constrained subsets of the vocabulary: (Wu et al., 2021), for example, show how brain activity patterns of individual words are encoded in a way that facilitates analogical reasoning. Such a property would in the limit entail that brain encodings are isomorphic to language model representations (Peng et al., 2020). Other research articles that seem to suggest that language model representations are generally isomorphic to brain activity patterns include (Mitchell et al., 2008; Søgaard, 2016; Wehbe et al., 2014; Pereira et al., 2018; Gauthier & Levy, 2019; Caucheteux & King, 2022).’
I’ll probably write more about this soon.