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2302.06555v2.pdf

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arXiv:2302.06555v2 [cs.CL] 6 Jul 2024

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2302.06555v2.pdf

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Do Vision and Language Models Share Concepts? A Vector Space Alignment Study

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2302.06555v2.pdf

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Jiaang Li † Yova Kementchedjhieva ‡ Constanza Fierro † Anders Søgaard †

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† University of Copenhagen

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‡ Mohamed bin Zayed University of Artificial Intelligence

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{jili,c.fierro,soegaard}@di.ku.dk, [email protected]

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2302.06555v2.pdf

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Abstract

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Large-scale pretrained language models (LMs) are said to "lack the ability to connect utterances to the world" (Bender and Koller, 2020), because they do not have "mental models of the world" (Mitchell and Krakauer, 2023). If so, one would expect LM representations to be unrelated to representations induced by vision models. We present an empirical evaluation across four families of LMs (BERT, GPT-2, OPT and LLaMA-2) and three vision model architectures (ResNet, SegFormer, and MAE). Our experiments show that LMs partially converge towards representations isomorphic to those of vision models, subject to dispersion, polysemy and frequency. This has important implications for both multi-modal processing and the LM understanding debate (Mitchell and Krakauer, 2023). 1

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2302.06555v2.pdf

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1 Introduction

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The debate around whether LMs can be said to understand is often portrayed as a back-and-forth between two opposing sides (Mitchell and Krakauer, 2023), but in reality, there are many positions. Some researchers have argued that LMs are 'all syntax, no semantics', i.e., that they learn form, but not meaning (Searle, 1980; Bender and Koller, 2020; Marcus et al., 2023). 2 Others have argued that LMs

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dataset:

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https://github.com/

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$^{1}$Code and jiaangli/VLCA .

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$^{2}$The idea that computers are 'all syntax, no semantics' can be traced back to German 17th century philosopher Leibniz's Mill Argument (Lodge and Bobro, 1998). The Mill Argument states that mental states cannot be reduced to physical states, so if the capacity to understand language requires mental states, this capacity cannot be instantiated, merely imitated, by machines. In 1980, Searle introduced an even more popular argument against the possibility of LM understanding, in the form of the so-called Chinese Room thought experiment (Searle, 1980). The Chinese Room presents an interlocutor with no prior knowledge of a foreign language, who

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have inferential semantics, but not referential semantics (Rapaport, 2002; Sahlgren and Carlsson, 2021; Piantadosi and Hill, 2022), 3 whereas some have posited that a form of externalist referential semantics is possible, at least for chatbots engaged in direct conversation (Cappelen and Dever, 2021; Butlin, 2021; Mollo and Millière, 2023; Mandelkern and Linzen, 2023). Most researchers agree, however, that LMs "lack the ability to connect utterances to the world" (Bender and Koller, 2020), because they do not have "mental models of the world" (Mitchell and Krakauer, 2023).

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This study provides evidence to the contrary: Language models and computer vision models (VMs) are trained on independent data sources (at least for unsupervised computer vision models). The only common source of bias is the world. If LMs and VMs exhibit similarities, it must be because they both model the world. We examine the representations learned by different LMs and VMs by measuring how similar their geometries are. We consistently find that the better the LMs are, the more they induce representations similar to those induced by computer vision models. The similarity between the two spaces is such that from a very small set of parallel examples we are able to linearly project VMs representations to the language space and retrieve highly accurate captions, as shown by the examples in Figure 1.

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Contributions. We present a series of evaluations of the vector spaces induced by three families of VMs and four families of LMs, i.e., a total of fourteen VMs and fourteen LMs. We show that within each family, the larger the LMs, the more their vector spaces become structurally similar to

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receives text messages in this language and follows a rule book to reply to the messages. The interlocutor is Searle's caricature of artificial intelligence, and is obviously, Searle claims, not endowed with meaning or understanding, but merely symbol manipulation.

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$^{3}$See Marconi (1997) for this distinction.

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those of computer vision models. This enables retrieval of language representations of images (referential semantics) with minimal supervision. Retrieval precision depends on dispersion of image and language, polysemy, and frequency, but consistently improves with language model size. We discuss the implications of the finding that language and computer vision models learn representations with similar geometries.

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2 Related Work

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Inspiration from cognitive science. Computational modeling is a cornerstone of cognitive science in the pursuit for a better understanding of how representations in the brain come about. As such, the field has shown a growing interest in computational representations induced with self-supervised learning (Orhan et al., 2020; Halvagal and Zenke, 2022). Cognitive scientists have also noted how the objectives of supervised language and vision models bear resemblances to predictive processing (Schrimpf et al., 2018; Goldstein et al., 2021; Caucheteux et al., 2022; Li et al., 2023) (but see Antonello and Huth (2022) for a critical discussion of such work).

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Studies have looked at the alignability of neural language representations and human brain activations, with more promising results as language models grow better at modeling language (Sassenhagen and Fiebach, 2020; Schrimpf et al., 2021). In these studies, the partial alignability of brain and model representations is interpreted as evidence that brain and models might process language in the same way (Caucheteux and King, 2022).

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{"self_ref": "#/texts/22", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 2, "bbox": {"l": 71.25102233886719, "t": 433.5199279785156, "r": 292.1755065917969, "b": 313.6751708984375, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 434]}], "orig": "Studies have looked at the alignability of neural language representations and human brain activations, with more promising results as language models grow better at modeling language (Sassenhagen and Fiebach, 2020; Schrimpf et al., 2021). In these studies, the partial alignability of brain and model representations is interpreted as evidence that brain and models might process language in the same way (Caucheteux and King, 2022).", "text": "Studies have looked at the alignability of neural language representations and human brain activations, with more promising results as language models grow better at modeling language (Sassenhagen and Fiebach, 2020; Schrimpf et al., 2021). In these studies, the partial alignability of brain and model representations is interpreted as evidence that brain and models might process language in the same way (Caucheteux and King, 2022)."}

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Cross-modal alignment. The idea of crossmodal retrieval is not new (Lazaridou et al., 2014), but previously it has mostly been studied with practical considerations in mind. Recently, Merullo et al. (2023) showed that language representations in LMs are functionally similar to image representations in VMs, in that a linear transformation applied to an image representation can be used to prompt a language model into producing a relevant caption. We dial back from function and study whether the concept representations converge toward structural similarity (isomorphism). The key question we address is whether despite the lack of explicit grounding, the representations learned by large pretrained language models structurally resemble properties of the physical world as captured by vision models. More related to our work,

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{"self_ref": "#/texts/23", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 2, "bbox": {"l": 71.18010711669922, "t": 304.51641845703125, "r": 292.0832214355469, "b": 76.014892578125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 828]}], "orig": "Cross-modal alignment. The idea of crossmodal retrieval is not new (Lazaridou et al., 2014), but previously it has mostly been studied with practical considerations in mind. Recently, Merullo et al. (2023) showed that language representations in LMs are functionally similar to image representations in VMs, in that a linear transformation applied to an image representation can be used to prompt a language model into producing a relevant caption. We dial back from function and study whether the concept representations converge toward structural similarity (isomorphism). The key question we address is whether despite the lack of explicit grounding, the representations learned by large pretrained language models structurally resemble properties of the physical world as captured by vision models. More related to our work,", "text": "Cross-modal alignment. The idea of crossmodal retrieval is not new (Lazaridou et al., 2014), but previously it has mostly been studied with practical considerations in mind. Recently, Merullo et al. (2023) showed that language representations in LMs are functionally similar to image representations in VMs, in that a linear transformation applied to an image representation can be used to prompt a language model into producing a relevant caption. We dial back from function and study whether the concept representations converge toward structural similarity (isomorphism). The key question we address is whether despite the lack of explicit grounding, the representations learned by large pretrained language models structurally resemble properties of the physical world as captured by vision models. More related to our work,"}

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Figure 1: Mapping from MAE$_{Huge}$ (images) to OPT$_{30B}$ (text). Gold labels are in green.

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{"self_ref": "#/texts/24", "parent": {"cref": "#/body"}, "children": [], "label": "caption", "prov": [{"page_no": 2, "bbox": {"l": 306.5188903808594, "t": 511.5455017089844, "r": 525.5476684570312, "b": 487.3186340332031, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 93]}], "orig": "Figure 1: Mapping from MAE$_{Huge}$ (images) to OPT$_{30B}$ (text). Gold labels are in green.", "text": "Figure 1: Mapping from MAE$_{Huge}$ (images) to OPT$_{30B}$ (text). Gold labels are in green."}

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Figure 1: Mapping from MAE$_{Huge}$ (images) to OPT$_{30B}$ (text). Gold labels are in green.

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Huh et al. (2024) proposes a similar hypothesis, although studying it from a different perspective, and our findings corroborate theirs.

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{"self_ref": "#/texts/25", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 2, "bbox": {"l": 306.4500427246094, "t": 463.1133728027344, "r": 526.9063720703125, "b": 424.90692138671875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 136]}], "orig": "Huh et al. (2024) proposes a similar hypothesis, although studying it from a different perspective, and our findings corroborate theirs.", "text": "Huh et al. (2024) proposes a similar hypothesis, although studying it from a different perspective, and our findings corroborate theirs."}

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section_header

3 Methodology

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Our primary objective is to compare the representations derived from VMs and LMs and assess their alignability, i.e. the extent to which LMs converge toward VMs' geometries. In the following sections, we introduce the procedures for obtaining the representations and aligning them, with an illustration of our methodology provided in Figure 2.

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{"self_ref": "#/texts/27", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 2, "bbox": {"l": 306.3543395996094, "t": 390.9617919921875, "r": 527.3591918945312, "b": 297.9390869140625, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 343]}], "orig": "Our primary objective is to compare the representations derived from VMs and LMs and assess their alignability, i.e. the extent to which LMs converge toward VMs' geometries. In the following sections, we introduce the procedures for obtaining the representations and aligning them, with an illustration of our methodology provided in Figure 2.", "text": "Our primary objective is to compare the representations derived from VMs and LMs and assess their alignability, i.e. the extent to which LMs converge toward VMs' geometries. In the following sections, we introduce the procedures for obtaining the representations and aligning them, with an illustration of our methodology provided in Figure 2."}

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Vision models. We include fourteen VMs in our experiments, representing three model families: SegFormer (Xie et al., 2021), MAE (He et al., 2022), and ResNet (He et al., 2016). For all three types of VMs, we only employ the encoder component as a visual feature extractor. 4

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{"self_ref": "#/texts/28", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 2, "bbox": {"l": 306.2715148925781, "t": 288.335693359375, "r": 527.359375, "b": 210.1456298828125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 274]}], "orig": "Vision models. We include fourteen VMs in our experiments, representing three model families: SegFormer (Xie et al., 2021), MAE (He et al., 2022), and ResNet (He et al., 2016). For all three types of VMs, we only employ the encoder component as a visual feature extractor. 4", "text": "Vision models. We include fourteen VMs in our experiments, representing three model families: SegFormer (Xie et al., 2021), MAE (He et al., 2022), and ResNet (He et al., 2016). For all three types of VMs, we only employ the encoder component as a visual feature extractor. 4"}

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SegFormer models consist of a Transformerbased encoder and a light-weight feed-forward decoder. They are pretrained on object classification data and finetuned on scene parsing data for scene segmentation and object classification. We hypothesize that the reasoning necessary to

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$^{4}$We ran experiments with CLIP (Radford et al., 2021), but report on these separately, since CLIP does not meet the criteria of our study, being trained on a mixture of text and images. CLIP results are presented in Appendix C.

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Figure 2: Experiments stages: During our experiments, words, sentences, and images are selected from the aliases list (wordlist and ImageNet-21K aliases), Wikipedia and ImageNet-21K, respectively. The source and target spaces are constructed utilizing image and word embeddings which are extracted by specialized vision and language models.

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Figure 2: Experiments stages: During our experiments, words, sentences, and images are selected from the aliases list (wordlist and ImageNet-21K aliases), Wikipedia and ImageNet-21K, respectively. The source and target spaces are constructed utilizing image and word embeddings which are extracted by specialized vision and language models.

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perform segmentation in context promotes representations that are more similar to those of LMs, which also operate in a discrete space (a vocabulary). The SegFormer models we use are pretrained with ImageNet-1K (Russakovsky et al., 2015) and finetuned with ADE20K (Zhou et al., 2017).

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{"self_ref": "#/texts/32", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 3, "bbox": {"l": 71.2052993774414, "t": 519.85791015625, "r": 292.0829162597656, "b": 441.4917297363281, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 284]}], "orig": "perform segmentation in context promotes representations that are more similar to those of LMs, which also operate in a discrete space (a vocabulary). The SegFormer models we use are pretrained with ImageNet-1K (Russakovsky et al., 2015) and finetuned with ADE20K (Zhou et al., 2017).", "text": "perform segmentation in context promotes representations that are more similar to those of LMs, which also operate in a discrete space (a vocabulary). The SegFormer models we use are pretrained with ImageNet-1K (Russakovsky et al., 2015) and finetuned with ADE20K (Zhou et al., 2017)."}

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MAE models relies on a Transformer-based encoder-decoder architecture, with the VisionTransformer (ViT) (Dosovitskiy et al., 2021) as the encoder backbone. MAE models are trained to reconstruct masked patches in images, i.e., a fully unsupervised training objective, similar to masked language modeling. The encoder takes as input the unmasked image patches, while a lightweight decoder reconstructs the original image from the latent representation of unmasked patches interleaved with mask tokens. The MAE models we use are pretrained on ImageNet-1K.

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{"self_ref": "#/texts/33", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 3, "bbox": {"l": 71.08782196044922, "t": 437.7105407714844, "r": 292.07537841796875, "b": 277.903564453125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 552]}], "orig": "MAE models relies on a Transformer-based encoder-decoder architecture, with the VisionTransformer (ViT) (Dosovitskiy et al., 2021) as the encoder backbone. MAE models are trained to reconstruct masked patches in images, i.e., a fully unsupervised training objective, similar to masked language modeling. The encoder takes as input the unmasked image patches, while a lightweight decoder reconstructs the original image from the latent representation of unmasked patches interleaved with mask tokens. The MAE models we use are pretrained on ImageNet-1K.", "text": "MAE models relies on a Transformer-based encoder-decoder architecture, with the VisionTransformer (ViT) (Dosovitskiy et al., 2021) as the encoder backbone. MAE models are trained to reconstruct masked patches in images, i.e., a fully unsupervised training objective, similar to masked language modeling. The encoder takes as input the unmasked image patches, while a lightweight decoder reconstructs the original image from the latent representation of unmasked patches interleaved with mask tokens. The MAE models we use are pretrained on ImageNet-1K."}

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ResNet models for object classification consist of a bottleneck convolutional neural network with residual blocks as an encoder, with a classification head. They are pretrained on the ImageNet-1K.

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Language models. We include fourteen Transformer-based LMs in our experiments, representing four model families: BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019), OPT (Zhang et al., 2022) and LLaMA-2 (Touvron et al., 2023). We use six different sizes of BERT (all uncased): BERT$_{Base}$ and BERT$_{Large}$, which are pretrained on the BooksCorpus (Zhu et al., 2015) and English Wikipedia (Foundation), and four smaller BERT sizes, distilled from BERT$_{Large}$ (Turc et al., 2019).

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{"self_ref": "#/texts/35", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 3, "bbox": {"l": 70.57910919189453, "t": 208.846435546875, "r": 292.1816101074219, "b": 76.1505126953125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 490]}], "orig": "Language models. We include fourteen Transformer-based LMs in our experiments, representing four model families: BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019), OPT (Zhang et al., 2022) and LLaMA-2 (Touvron et al., 2023). We use six different sizes of BERT (all uncased): BERT$_{Base}$ and BERT$_{Large}$, which are pretrained on the BooksCorpus (Zhu et al., 2015) and English Wikipedia (Foundation), and four smaller BERT sizes, distilled from BERT$_{Large}$ (Turc et al., 2019).", "text": "Language models. We include fourteen Transformer-based LMs in our experiments, representing four model families: BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019), OPT (Zhang et al., 2022) and LLaMA-2 (Touvron et al., 2023). We use six different sizes of BERT (all uncased): BERT$_{Base}$ and BERT$_{Large}$, which are pretrained on the BooksCorpus (Zhu et al., 2015) and English Wikipedia (Foundation), and four smaller BERT sizes, distilled from BERT$_{Large}$ (Turc et al., 2019)."}

35c1f1fe-1b43-4ff4-8be7-b962ec994878

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GPT-2, an auto-regressive decoder-only LM, comes in three sizes, pretrained on the WebText dataset (Radford et al., 2019). OPT also comes in three sizes, pretrained on the union of five datasets (Zhang et al., 2022). LLaMA-2 was pretrained on two trillion tokens.

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Vision representations. The visual representation of a concept is obtained by embedding the images available for the concept with a given VM encoder and then averaging these representations. When applying SegFormer, we average the patches' representations from the last hidden state as the basis for every image, whereas we use the penultimate hidden state for MAE models. 5 ResNet models generate a single vector per input image from the average pooling layer.

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{"self_ref": "#/texts/37", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 3, "bbox": {"l": 306.2260437011719, "t": 429.16314697265625, "r": 527.4528198242188, "b": 296.0677490234375, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 461]}], "orig": "Vision representations. The visual representation of a concept is obtained by embedding the images available for the concept with a given VM encoder and then averaging these representations. When applying SegFormer, we average the patches' representations from the last hidden state as the basis for every image, whereas we use the penultimate hidden state for MAE models. 5 ResNet models generate a single vector per input image from the average pooling layer.", "text": "Vision representations. The visual representation of a concept is obtained by embedding the images available for the concept with a given VM encoder and then averaging these representations. When applying SegFormer, we average the patches' representations from the last hidden state as the basis for every image, whereas we use the penultimate hidden state for MAE models. 5 ResNet models generate a single vector per input image from the average pooling layer."}

a561ca2b-6f29-40bb-88cd-8a7475f2c7d2

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Language representations. The LMs included here were trained on text segments, so applying them to words in isolation could result in unpredictable behavior. We therefore represent words by embedding English Wikipedia sentences, using the token representations that form the concept, decontextualizing these representations by averaging across different sentences (Abdou et al., 2021). In the case of masked language models, we employ

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{"self_ref": "#/texts/38", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 3, "bbox": {"l": 306.23394775390625, "t": 283.43695068359375, "r": 527.3591918945312, "b": 164.11749267578125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 434]}], "orig": "Language representations. The LMs included here were trained on text segments, so applying them to words in isolation could result in unpredictable behavior. We therefore represent words by embedding English Wikipedia sentences, using the token representations that form the concept, decontextualizing these representations by averaging across different sentences (Abdou et al., 2021). In the case of masked language models, we employ", "text": "Language representations. The LMs included here were trained on text segments, so applying them to words in isolation could result in unpredictable behavior. We therefore represent words by embedding English Wikipedia sentences, using the token representations that form the concept, decontextualizing these representations by averaging across different sentences (Abdou et al., 2021). In the case of masked language models, we employ"}

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footnote

$^{5}$We also experimented with utilizing the representations from the last hidden state; however, the results were not as promising as those obtained from the penultimate hidden state. Caron et al. (2021) demonstrate the penultimate-layer features in ViTs trained with DINO exhibit strong correlations with saliency information in the visual input, such as object boundaries and so on.

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{"self_ref": "#/texts/39", "parent": {"cref": "#/body"}, "children": [], "label": "footnote", "prov": [{"page_no": 3, "bbox": {"l": 306.2687072753906, "t": 152.629638671875, "r": 527.111083984375, "b": 76.98725891113281, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 386]}], "orig": "$^{5}$We also experimented with utilizing the representations from the last hidden state; however, the results were not as promising as those obtained from the penultimate hidden state. Caron et al. (2021) demonstrate the penultimate-layer features in ViTs trained with DINO exhibit strong correlations with saliency information in the visual input, such as object boundaries and so on.", "text": "$^{5}$We also experimented with utilizing the representations from the last hidden state; however, the results were not as promising as those obtained from the penultimate hidden state. Caron et al. (2021) demonstrate the penultimate-layer features in ViTs trained with DINO exhibit strong correlations with saliency information in the visual input, such as object boundaries and so on."}

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an averaging approach on the token representations forming the concept; otherwise, we choose for the last token within the concept (Zou et al., 2023).

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Linear projection. Since we are interested in the extent to which vision and language representations are isomorphic, we focus on linear projections. 6 Following Conneau et al. (2018), we use Procrustes analysis (Schönemann, 1966) to align the representations of VMs to those of LMs, given a bimodal dictionary (§ 4.1). Given the VM matrix A (i.e., the visual representations of concepts) and the LM matrix B (i.e. the language representation of the concepts) we use Procrustes analysis to find the orthogonal matrix Ω that most closely maps source space A onto the target space B . Given the constrain of orthogonality the optimization Ω = min$_{R}$ ∥ RA - B ∥$_{F}$ , s.t. R $^{T}$R = I has the closed form solution Ω = UV $^{T}$,U Σ V = SVD ( BA $^{T}$) , where SVD stands for singular value decomposition. We induce the alignment from a small set of dictionary pairs, evaluating it on held-out data (§ 4.2). Given the necessity for both the source and target space to have the same dimensionality, we employ principal component analysis (PCA) to reduce the dimensionality of the larger space in cases of a mismatch. 7

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{"self_ref": "#/texts/41", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 4, "bbox": {"l": 70.89579772949219, "t": 726.5772705078125, "r": 292.08294677734375, "b": 417.6516418457031, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 1121]}], "orig": "Linear projection. Since we are interested in the extent to which vision and language representations are isomorphic, we focus on linear projections. 6 Following Conneau et al. (2018), we use Procrustes analysis (Sch\u00f6nemann, 1966) to align the representations of VMs to those of LMs, given a bimodal dictionary (\u00a7 4.1). Given the VM matrix A (i.e., the visual representations of concepts) and the LM matrix B (i.e. the language representation of the concepts) we use Procrustes analysis to find the orthogonal matrix \u2126 that most closely maps source space A onto the target space B . Given the constrain of orthogonality the optimization \u2126 = min$_{R}$ \u2225 RA - B \u2225$_{F}$ , s.t. R $^{T}$R = I has the closed form solution \u2126 = UV $^{T}$,U \u03a3 V = SVD ( BA $^{T}$) , where SVD stands for singular value decomposition. We induce the alignment from a small set of dictionary pairs, evaluating it on held-out data (\u00a7 4.2). Given the necessity for both the source and target space to have the same dimensionality, we employ principal component analysis (PCA) to reduce the dimensionality of the larger space in cases of a mismatch. 7", "text": "Linear projection. Since we are interested in the extent to which vision and language representations are isomorphic, we focus on linear projections. 6 Following Conneau et al. (2018), we use Procrustes analysis (Sch\u00f6nemann, 1966) to align the representations of VMs to those of LMs, given a bimodal dictionary (\u00a7 4.1). Given the VM matrix A (i.e., the visual representations of concepts) and the LM matrix B (i.e. the language representation of the concepts) we use Procrustes analysis to find the orthogonal matrix \u2126 that most closely maps source space A onto the target space B . Given the constrain of orthogonality the optimization \u2126 = min$_{R}$ \u2225 RA - B \u2225$_{F}$ , s.t. R $^{T}$R = I has the closed form solution \u2126 = UV $^{T}$,U \u03a3 V = SVD ( BA $^{T}$) , where SVD stands for singular value decomposition. We induce the alignment from a small set of dictionary pairs, evaluating it on held-out data (\u00a7 4.2). Given the necessity for both the source and target space to have the same dimensionality, we employ principal component analysis (PCA) to reduce the dimensionality of the larger space in cases of a mismatch. 7"}

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4 Experimental Setup

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In this section, we discuss details around bimodal dictionary compilation (§ 4.1), evaluation metrics, as well as our baselines (§ 4.2).

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4.1 Bimodal Dictionary Compilation

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We build bimodal dictionaries of image-text pairs based on the ImageNet21K dataset (Russakovsky et al., 2015) and the CLDI (cross-lingual dictionary induction) dataset (Hartmann and Søgaard, 2018). In ImageNet, a concept class has a unique ID and is represented by multiple images and one or more names (which we refer to as aliases ), many of which are multi-word expressions. We filter the data from ImageNet-21K: keeping classes with over 100 images available, aliases that appear at least five times in Wikipedia, and classes with at

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{"self_ref": "#/texts/45", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 4, "bbox": {"l": 70.98979187011719, "t": 310.3228759765625, "r": 292.07537841796875, "b": 163.00567626953125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 537]}], "orig": "We build bimodal dictionaries of image-text pairs based on the ImageNet21K dataset (Russakovsky et al., 2015) and the CLDI (cross-lingual dictionary induction) dataset (Hartmann and S\u00f8gaard, 2018). In ImageNet, a concept class has a unique ID and is represented by multiple images and one or more names (which we refer to as aliases ), many of which are multi-word expressions. We filter the data from ImageNet-21K: keeping classes with over 100 images available, aliases that appear at least five times in Wikipedia, and classes with at", "text": "We build bimodal dictionaries of image-text pairs based on the ImageNet21K dataset (Russakovsky et al., 2015) and the CLDI (cross-lingual dictionary induction) dataset (Hartmann and S\u00f8gaard, 2018). In ImageNet, a concept class has a unique ID and is represented by multiple images and one or more names (which we refer to as aliases ), many of which are multi-word expressions. We filter the data from ImageNet-21K: keeping classes with over 100 images available, aliases that appear at least five times in Wikipedia, and classes with at"}

c20d0945-d3c3-440c-9645-e23e6f264b44

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$^{6}$For work on non-linear projection between representation spaces, see Nakashole (2018); Zhao and Gilman (2020); Glavaš and Vuli´c (2020).

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{"self_ref": "#/texts/46", "parent": {"cref": "#/body"}, "children": [], "label": "footnote", "prov": [{"page_no": 4, "bbox": {"l": 71.50354766845703, "t": 152.3046875, "r": 291.7594909667969, "b": 120.85226440429688, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 142]}], "orig": "$^{6}$For work on non-linear projection between representation spaces, see Nakashole (2018); Zhao and Gilman (2020); Glava\u0161 and Vuli\u00b4c (2020).", "text": "$^{6}$For work on non-linear projection between representation spaces, see Nakashole (2018); Zhao and Gilman (2020); Glava\u0161 and Vuli\u00b4c (2020)."}

8242f6ac-1f27-4b3f-9a93-f2fdc5fe0d78

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$^{7}$The variance is retained for most models after dimensionality reduction, except for a few cases where there is some loss of information. The cumulative of explained variance ratios for different models are presented in Table 8.

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{"self_ref": "#/texts/47", "parent": {"cref": "#/body"}, "children": [], "label": "footnote", "prov": [{"page_no": 4, "bbox": {"l": 71.3525619506836, "t": 118.89080810546875, "r": 291.7541809082031, "b": 76.62451171875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 233]}], "orig": "$^{7}$The variance is retained for most models after dimensionality reduction, except for a few cases where there is some loss of information. The cumulative of explained variance ratios for different models are presented in Table 8.", "text": "$^{7}$The variance is retained for most models after dimensionality reduction, except for a few cases where there is some loss of information. The cumulative of explained variance ratios for different models are presented in Table 8."}

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Table 1: Statistics of the bimodal dictionaries.

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table

Set	Num. of classes	Num. of aliases	Num. of pairs
Only-1K	491	655	655
Exclude-1K	5,942	7,194	7,194
EN-CLDI	1,690	1,690	1,690

Table 1: Statistics of the bimodal dictionaries.

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754.02197265625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 1, "end_row_offset_idx": 2, "start_col_offset_idx": 0, "end_col_offset_idx": 1, "text": "Only-1K", "column_header": false, "row_header": true, "row_section": false}, {"bbox": {"l": 400.0690002441406, "t": 760.9743041992188, "r": 411.7339782714844, "b": 754.02197265625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 1, "end_row_offset_idx": 2, "start_col_offset_idx": 1, "end_col_offset_idx": 2, "text": "491", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 457.6551818847656, "t": 760.9743041992188, "r": 469.3201599121094, "b": 754.02197265625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 1, "end_row_offset_idx": 2, "start_col_offset_idx": 2, "end_col_offset_idx": 3, "text": "655", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 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false, "row_header": false, "row_section": false}, {"bbox": {"l": 451.8225402832031, "t": 751.3157958984375, "r": 469.3200378417969, "b": 744.3634643554688, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 2, "end_row_offset_idx": 3, "start_col_offset_idx": 2, "end_col_offset_idx": 3, "text": "7,194", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 503.7939758300781, "t": 751.3157958984375, "r": 521.2914428710938, "b": 744.3634643554688, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 2, "end_row_offset_idx": 3, "start_col_offset_idx": 3, "end_col_offset_idx": 4, "text": "7,194", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 313.4814453125, "t": 737.5939331054688, "r": 344.5802917480469, "b": 730.6416015625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 3, "end_row_offset_idx": 4, "start_col_offset_idx": 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"start_row_offset_idx": 3, "end_row_offset_idx": 4, "start_col_offset_idx": 3, "end_col_offset_idx": 4, "text": "1,690", "column_header": false, "row_header": false, "row_section": false}], "num_rows": 4, "num_cols": 4, "grid": [[{"bbox": {"l": 313.4814453125, "t": 774.6961669921875, "r": 323.4200134277344, "b": 767.7437744140625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 0, "end_row_offset_idx": 1, "start_col_offset_idx": 0, "end_col_offset_idx": 1, "text": "Set", "column_header": true, "row_header": false, "row_section": false}, {"bbox": {"l": 361.808349609375, "t": 774.6961669921875, "r": 411.7344970703125, "b": 767.7437744140625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 0, "end_row_offset_idx": 1, "start_col_offset_idx": 1, "end_col_offset_idx": 2, "text": "Num. of classes", "column_header": true, "row_header": false, "row_section": false}, {"bbox": {"l": 420.2577209472656, "t": 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27d964d3-7aea-42d2-aa69-cddcfe5b13ef

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text

least one alias. As a result, 11,338 classes and 13,460 aliases meet the criteria. We further filter aliases that are shared by two different class IDs, and aliases for which their hyponyms are already in the aliases set. 8 To avoid any form of bias, given that the VMs we experiment with have been pretrained on ImageNet-1K, we report results on ImageNet-21K excluding the concepts in ImageNet-1K (Exclude-1K).

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6a58186a-e7f7-4af5-bed5-9cd344e844e7

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text

One important limitation of the Exclude-1K bimodal dictionary is that all concepts are nouns. Therefore, to investigate how our results generalize to other parts of speech (POS), we also use the English subset of CLDI dataset (EN-CLDI), which contains images paired with verbs and adjectives. Each word within this set is unique and paired with at least 22 images. Final statistics of the processed datasets are reported in Table 1.

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4486b15d-794a-4f20-87c0-89454067deb3

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The pairs in these bimodal dictionaries are split 70-30 for training and testing based on the class IDs to avoid train-test leakage. 9 We compute five such splits at random and report averaged results. See § 6 for the impact of training set size variations.

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section_header

4.2 Evaluation

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fb9d2a8c-5170-4f2d-99f2-e9ede95d7298

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We induce a linear mapping Ω based on training image-text pairs sampled from A and B , respectively. We then evaluate how close A Ω is to B by computing retrieval precision on held-out imagetext pairs. To make the retrieval task as challenging as possible, the target space B is expanded with 65,599 words from an English wordlist in addition to 13,460 aliases, resulting in a total of 79,059 aliases in the final target space.

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{"self_ref": "#/texts/53", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 4, "bbox": {"l": 306.2489013671875, "t": 345.0776672363281, "r": 527.352783203125, "b": 225.149169921875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 427]}], "orig": "We induce a linear mapping \u2126 based on training image-text pairs sampled from A and B , respectively. We then evaluate how close A \u2126 is to B by computing retrieval precision on held-out imagetext pairs. To make the retrieval task as challenging as possible, the target space B is expanded with 65,599 words from an English wordlist in addition to 13,460 aliases, resulting in a total of 79,059 aliases in the final target space.", "text": "We induce a linear mapping \u2126 based on training image-text pairs sampled from A and B , respectively. We then evaluate how close A \u2126 is to B by computing retrieval precision on held-out imagetext pairs. To make the retrieval task as challenging as possible, the target space B is expanded with 65,599 words from an English wordlist in addition to 13,460 aliases, resulting in a total of 79,059 aliases in the final target space."}

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Metrics. We evaluate alignment in terms of precision-atk (P@ k ), a well-established metric employed in the evaluation of multilingual word embeddings (Conneau et al., 2018), with k ∈ { 1 , 10 , 100 } . 10 Note that this performance metric

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{"self_ref": "#/texts/54", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 4, "bbox": {"l": 306.3006286621094, "t": 215.8372802734375, "r": 525.5789184570312, "b": 148.8270263671875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 239]}], "orig": "Metrics. We evaluate alignment in terms of precision-atk (P@ k ), a well-established metric employed in the evaluation of multilingual word embeddings (Conneau et al., 2018), with k \u2208 { 1 , 10 , 100 } . 10 Note that this performance metric", "text": "Metrics. We evaluate alignment in terms of precision-atk (P@ k ), a well-established metric employed in the evaluation of multilingual word embeddings (Conneau et al., 2018), with k \u2208 { 1 , 10 , 100 } . 10 Note that this performance metric"}

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footnote

$^{8}$We obtain the aliases hypernyms and hyponyms from the Princeton WordNet (Fellbaum, 2010).

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footnote

$^{9}$In the EN-CLDI set, we simply use words to mitigate the risk of train-test leakage.

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817261b3-6267-4805-89fa-7af4c9287a4f

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$^{10}$For example, we could use the mapping of the image of an apple into the word ‘apple’, and the mapping of the image

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{"self_ref": "#/texts/57", "parent": {"cref": "#/body"}, "children": [], "label": "footnote", "prov": [{"page_no": 4, "bbox": {"l": 306.67706298828125, "t": 96.8956298828125, "r": 525.7845458984375, "b": 75.97491455078125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 121]}], "orig": "$^{10}$For example, we could use the mapping of the image of an apple into the word \u2018apple\u2019, and the mapping of the image", "text": "$^{10}$For example, we could use the mapping of the image of an apple into the word \u2018apple\u2019, and the mapping of the image"}

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Table 2: Alignment results for our baselines. All the Precision@ k scores are reported in percentage.

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table

Baseline	P@1	P@10	P@100
Random retrieval	0.0015	0.0153	0.1531
Length-frequency alignment	0.0032	0.0127	0.6053
Non-isomorphic alignment	0.0000	0.0121	0.1105

Table 2: Alignment results for our baselines. All the Precision@ k scores are reported in percentage.

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"0.0032", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 224.7335968017578, "t": 747.3314819335938, "r": 249.18841552734375, "b": 739.3814697265625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 2, "end_row_offset_idx": 3, "start_col_offset_idx": 2, "end_col_offset_idx": 3, "text": "0.0127", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 260.9533996582031, "t": 747.3314819335938, "r": 285.408203125, "b": 739.3814697265625, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 2, "end_row_offset_idx": 3, "start_col_offset_idx": 3, "end_col_offset_idx": 4, "text": "0.6053", "column_header": false, "row_header": false, "row_section": false}, {"bbox": {"l": 79.09597778320312, "t": 736.286865234375, "r": 175.18118286132812, "b": 728.3368530273438, "coord_origin": "BOTTOMLEFT"}, "row_span": 1, "col_span": 1, "start_row_offset_idx": 3, 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9cffc2a5-950c-425e-848f-99d35b459371

2302.06555v2.pdf

text

is much more conservative than other metrics used for similar problems, including pairwise matching accuracy, percentile rank, and Pearson correlation (Minnema and Herbelot, 2019). Pairwise matching accuracy and percentile rank have random baseline scores of 0.5, and they converge in the limit. If a has a percentile rank of p in a list A , it will be higher than a random member of A p percent of the time. Pearson correlation is monotonically increasing with pairwise matching accuracy, but P@ k scores are more conservative than any of them for reasonably small values of k . In our case, our target space is 79,059 words, so it is possible to have P@100 values of 0.0 and yet still have near-perfect pairwise matching accuracy, percentile rank, and Pearson correlation scores. P@ k scores also have the advantage that they are intuitive and practically relevant, e.g., for decoding.

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{"self_ref": "#/texts/59", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 71.28717041015625, "t": 664.7708740234375, "r": 292.0834045410156, "b": 422.3381652832031, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 887]}], "orig": "is much more conservative than other metrics used for similar problems, including pairwise matching accuracy, percentile rank, and Pearson correlation (Minnema and Herbelot, 2019). Pairwise matching accuracy and percentile rank have random baseline scores of 0.5, and they converge in the limit. If a has a percentile rank of p in a list A , it will be higher than a random member of A p percent of the time. Pearson correlation is monotonically increasing with pairwise matching accuracy, but P@ k scores are more conservative than any of them for reasonably small values of k . In our case, our target space is 79,059 words, so it is possible to have P@100 values of 0.0 and yet still have near-perfect pairwise matching accuracy, percentile rank, and Pearson correlation scores. P@ k scores also have the advantage that they are intuitive and practically relevant, e.g., for decoding.", "text": "is much more conservative than other metrics used for similar problems, including pairwise matching accuracy, percentile rank, and Pearson correlation (Minnema and Herbelot, 2019). Pairwise matching accuracy and percentile rank have random baseline scores of 0.5, and they converge in the limit. If a has a percentile rank of p in a list A , it will be higher than a random member of A p percent of the time. Pearson correlation is monotonically increasing with pairwise matching accuracy, but P@ k scores are more conservative than any of them for reasonably small values of k . In our case, our target space is 79,059 words, so it is possible to have P@100 values of 0.0 and yet still have near-perfect pairwise matching accuracy, percentile rank, and Pearson correlation scores. P@ k scores also have the advantage that they are intuitive and practically relevant, e.g., for decoding."}

5c634071-8d05-4683-9f05-c402eec59de6

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text

Random retrieval baseline. Our target space of 79,059 words makes the random retrieval baseline:

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{"self_ref": "#/texts/60", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 71.1332015991211, "t": 412.76654052734375, "r": 291.7831726074219, "b": 388.6746520996094, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 96]}], "orig": "Random retrieval baseline. Our target space of 79,059 words makes the random retrieval baseline:", "text": "Random retrieval baseline. Our target space of 79,059 words makes the random retrieval baseline:"}

1278ce02-1320-42a5-9cfb-d30565291a10

2302.06555v2.pdf

formula

P@ 1 = 1 N N ∑ i =1 n$_{i}$ U (1)

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{"self_ref": "#/texts/61", "parent": {"cref": "#/body"}, "children": [], "label": "formula", "prov": [{"page_no": 5, "bbox": {"l": 140.55914306640625, "t": 377.66351318359375, "r": 290.9989929199219, "b": 342.2218017578125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 33]}], "orig": "P@ 1 = 1 N N \u2211 i =1 n$_{i}$ U (1)", "text": "P@ 1 = 1 N N \u2211 i =1 n$_{i}$ U (1)"}

89af5241-b077-4675-971d-19f36ea358fa

2302.06555v2.pdf

text

where N represents the total number of image classes; i iterates over each image class; n$_{i}$ denotes the number of labels for image class i ; U refers to the total number of unique aliases. From Equation 1, we get P@1 ≈ 0 . 0015% .

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{"self_ref": "#/texts/62", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 71.25822448730469, "t": 331.0116271972656, "r": 292.0785217285156, "b": 265.8031005859375, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 234]}], "orig": "where N represents the total number of image classes; i iterates over each image class; n$_{i}$ denotes the number of labels for image class i ; U refers to the total number of unique aliases. From Equation 1, we get P@1 \u2248 0 . 0015% .", "text": "where N represents the total number of image classes; i iterates over each image class; n$_{i}$ denotes the number of labels for image class i ; U refers to the total number of unique aliases. From Equation 1, we get P@1 \u2248 0 . 0015% ."}

55e1d195-297b-4a19-9e09-b0abb40ec9f9

2302.06555v2.pdf

text

Length-frequency alignment baseline. The random retrieval baseline tells us how well we can align representations across the two modalities in the absence of any signal (by chance). However, the fact that we can do better than a random baseline, does not, strictly speaking, prove that our models partially converge toward any sophisticated form of modeling the world. Maybe they simply

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{"self_ref": "#/texts/63", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 71.22360229492188, "t": 255.29852294921875, "r": 292.08270263671875, "b": 149.0504150390625, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 386]}], "orig": "Length-frequency alignment baseline. The random retrieval baseline tells us how well we can align representations across the two modalities in the absence of any signal (by chance). However, the fact that we can do better than a random baseline, does not, strictly speaking, prove that our models partially converge toward any sophisticated form of modeling the world. Maybe they simply", "text": "Length-frequency alignment baseline. The random retrieval baseline tells us how well we can align representations across the two modalities in the absence of any signal (by chance). However, the fact that we can do better than a random baseline, does not, strictly speaking, prove that our models partially converge toward any sophisticated form of modeling the world. Maybe they simply"}

315395b8-2614-46b1-9ef5-e562835a112b

2302.06555v2.pdf

footnote

of a banana into the word ‘banana’, as training pairs to induce a mapping Ω . If Ω then maps the image of a lemon onto the word ‘lemon’ as its nearest neighbor, we say that the precisionat-one for this mapping is 100%. If two target aliases were listed in the bimodal dictionary for the source image, mapping the image onto either of them would result in P@ 1 = 100% .

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{"self_ref": "#/texts/64", "parent": {"cref": "#/body"}, "children": [], "label": "footnote", "prov": [{"page_no": 5, "bbox": {"l": 70.99034881591797, "t": 141.355224609375, "r": 291.7580261230469, "b": 76.57489013671875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 368]}], "orig": "of a banana into the word \u2018banana\u2019, as training pairs to induce a mapping \u2126 . If \u2126 then maps the image of a lemon onto the word \u2018lemon\u2019 as its nearest neighbor, we say that the precisionat-one for this mapping is 100%. If two target aliases were listed in the bimodal dictionary for the source image, mapping the image onto either of them would result in P@ 1 = 100% .", "text": "of a banana into the word \u2018banana\u2019, as training pairs to induce a mapping \u2126 . If \u2126 then maps the image of a lemon onto the word \u2018lemon\u2019 as its nearest neighbor, we say that the precisionat-one for this mapping is 100%. If two target aliases were listed in the bimodal dictionary for the source image, mapping the image onto either of them would result in P@ 1 = 100% ."}

801cd3c0-c84e-4cd1-9371-710f36591cc2

2302.06555v2.pdf

caption

Figure 3: t-SNE plot of 5 words mapped from MAE$_{Huge}$ (blue) to OPT$_{30B}$ (orange) using Procrustes analysis. The green represent the mapped MAE$_{Huge}$ embeddings.

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{"self_ref": "#/texts/65", "parent": {"cref": "#/body"}, "children": [], "label": "caption", "prov": [{"page_no": 5, "bbox": {"l": 306.365478515625, "t": 638.8778076171875, "r": 527.3575439453125, "b": 586.4058837890625, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 170]}], "orig": "Figure 3: t-SNE plot of 5 words mapped from MAE$_{Huge}$ (blue) to OPT$_{30B}$ (orange) using Procrustes analysis. The green represent the mapped MAE$_{Huge}$ embeddings.", "text": "Figure 3: t-SNE plot of 5 words mapped from MAE$_{Huge}$ (blue) to OPT$_{30B}$ (orange) using Procrustes analysis. The green represent the mapped MAE$_{Huge}$ embeddings."}

00842dd0-5503-45db-93eb-e97de5e70515

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Figure 3: t-SNE plot of 5 words mapped from MAE$_{Huge}$ (blue) to OPT$_{30B}$ (orange) using Procrustes analysis. The green represent the mapped MAE$_{Huge}$ embeddings.

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a114e3d5-0d2c-4bc9-96a2-f3c4388fe4b6

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text

pick up on shallow characteristics shared across the two spaces. One example is frequency: frequent words may refer to frequently depicted objects. Learning what is rare is learning about the world, but more is at stake in the debate around whether LMs understand. Or consider length: word length may correlate with the structural complexity of objects (in some way), and maybe this is what drives our alignment precision? To control for such effects, we run a second baseline aligning representations from computer vision models to two-dimensional word representations, representing words by their length and frequency. We collected frequency data based on English Wikipedia using NLTK (Bird et al., 2009) for all aliases within our target space. We use PCA and Procrustes Analysis or ridge regression (Toneva and Wehbe, 2019) to map into the length-frequency space and report the best of those as a second, stronger baseline.

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{"self_ref": "#/texts/66", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 306.16961669921875, "t": 560.0623779296875, "r": 527.3591918945312, "b": 305.34613037109375, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 927]}], "orig": "pick up on shallow characteristics shared across the two spaces. One example is frequency: frequent words may refer to frequently depicted objects. Learning what is rare is learning about the world, but more is at stake in the debate around whether LMs understand. Or consider length: word length may correlate with the structural complexity of objects (in some way), and maybe this is what drives our alignment precision? To control for such effects, we run a second baseline aligning representations from computer vision models to two-dimensional word representations, representing words by their length and frequency. We collected frequency data based on English Wikipedia using NLTK (Bird et al., 2009) for all aliases within our target space. We use PCA and Procrustes Analysis or ridge regression (Toneva and Wehbe, 2019) to map into the length-frequency space and report the best of those as a second, stronger baseline.", "text": "pick up on shallow characteristics shared across the two spaces. One example is frequency: frequent words may refer to frequently depicted objects. Learning what is rare is learning about the world, but more is at stake in the debate around whether LMs understand. Or consider length: word length may correlate with the structural complexity of objects (in some way), and maybe this is what drives our alignment precision? To control for such effects, we run a second baseline aligning representations from computer vision models to two-dimensional word representations, representing words by their length and frequency. We collected frequency data based on English Wikipedia using NLTK (Bird et al., 2009) for all aliases within our target space. We use PCA and Procrustes Analysis or ridge regression (Toneva and Wehbe, 2019) to map into the length-frequency space and report the best of those as a second, stronger baseline."}

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2302.06555v2.pdf

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Non-isomorphic alignment baseline. The former two baselines examine the possibility of aligning representations across two modalities based on chance or shallow signals. While informative, neither strictly demonstrates that a linear projection cannot effectively establish a connection between two non-isomorphic representation spaces, potentially outperforming the random or lengthfrequency baselines. To rigorously explore this, we disrupt the relationship between words and their corresponding representations by shuffling them. This permutation ensures that the source and target spaces become non-isomorphic. Specifically, we shuffled OPT$_{30B}$ three times at random and report the alignment results between those and original OPT$_{30B}$, we use the same Procrustes analysis for

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{"self_ref": "#/texts/67", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 5, "bbox": {"l": 306.20733642578125, "t": 289.99688720703125, "r": 527.4515380859375, "b": 76.0753173828125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 786]}], "orig": "Non-isomorphic alignment baseline. The former two baselines examine the possibility of aligning representations across two modalities based on chance or shallow signals. While informative, neither strictly demonstrates that a linear projection cannot effectively establish a connection between two non-isomorphic representation spaces, potentially outperforming the random or lengthfrequency baselines. To rigorously explore this, we disrupt the relationship between words and their corresponding representations by shuffling them. This permutation ensures that the source and target spaces become non-isomorphic. Specifically, we shuffled OPT$_{30B}$ three times at random and report the alignment results between those and original OPT$_{30B}$, we use the same Procrustes analysis for", "text": "Non-isomorphic alignment baseline. The former two baselines examine the possibility of aligning representations across two modalities based on chance or shallow signals. While informative, neither strictly demonstrates that a linear projection cannot effectively establish a connection between two non-isomorphic representation spaces, potentially outperforming the random or lengthfrequency baselines. To rigorously explore this, we disrupt the relationship between words and their corresponding representations by shuffling them. This permutation ensures that the source and target spaces become non-isomorphic. Specifically, we shuffled OPT$_{30B}$ three times at random and report the alignment results between those and original OPT$_{30B}$, we use the same Procrustes analysis for"}

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2302.06555v2.pdf

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Figure 4: LMs converge toward the geometry of visual models as they grow larger on Exclude-1K set.

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Figure 4: LMs converge toward the geometry of visual models as they grow larger on Exclude-1K set.

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2302.06555v2.pdf

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computing the alignment. Table 2 presents a comparison of the three different baselines. All baselines have P@100 well below 1%. Our mappings between VMs and LMs score much higher (up to 64%), showing the strength of the correlation between the geometries induced by these models with respect to a conservative performance metric.

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{"self_ref": "#/texts/69", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 6, "bbox": {"l": 71.34822082519531, "t": 354.8316955566406, "r": 292.0813903808594, "b": 262.27301025390625, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 330]}], "orig": "computing the alignment. Table 2 presents a comparison of the three different baselines. All baselines have P@100 well below 1%. Our mappings between VMs and LMs score much higher (up to 64%), showing the strength of the correlation between the geometries induced by these models with respect to a conservative performance metric.", "text": "computing the alignment. Table 2 presents a comparison of the three different baselines. All baselines have P@100 well below 1%. Our mappings between VMs and LMs score much higher (up to 64%), showing the strength of the correlation between the geometries induced by these models with respect to a conservative performance metric."}

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2302.06555v2.pdf

section_header

5 Results

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2302.06555v2.pdf

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Similarities between visual and textual representations and how they are recovered through Procrustes Analysis are visualized through t-SNE in Figure 3. Our main results for nine VMs and all LMs are presented in Figure 4. The best P@100 scores are around 64%, with baseline scores lower than 1% (Table 2). In general, even the smallest language models outperform the baselines by orders of magnitude. We focus mainly on P@10 and P@100 scores because P@1 only allows one surface form to express a visual concept, but in reality,

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{"self_ref": "#/texts/71", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 6, "bbox": {"l": 71.2156753540039, "t": 222.7291259765625, "r": 292.0754089355469, "b": 75.686279296875, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 527]}], "orig": "Similarities between visual and textual representations and how they are recovered through Procrustes Analysis are visualized through t-SNE in Figure 3. Our main results for nine VMs and all LMs are presented in Figure 4. The best P@100 scores are around 64%, with baseline scores lower than 1% (Table 2). In general, even the smallest language models outperform the baselines by orders of magnitude. We focus mainly on P@10 and P@100 scores because P@1 only allows one surface form to express a visual concept, but in reality,", "text": "Similarities between visual and textual representations and how they are recovered through Procrustes Analysis are visualized through t-SNE in Figure 3. Our main results for nine VMs and all LMs are presented in Figure 4. The best P@100 scores are around 64%, with baseline scores lower than 1% (Table 2). In general, even the smallest language models outperform the baselines by orders of magnitude. We focus mainly on P@10 and P@100 scores because P@1 only allows one surface form to express a visual concept, but in reality,"}

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2302.06555v2.pdf

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an artifact such as a vehicle may be denoted by many lexemes (car, automobile, SUV, etc.), each of which may have multiple inflections and derivations (car, cars, car's, etc.). Figure 5 shows examples where the top predictions seem 'as good' as the gold standard. We find that a region of 10 neighbours corresponds roughly to grammatical forms or synonyms, and a neighbourhood of 100 word forms corresponds roughly to coarse-grained semantic classes. Results of P@10 in Figure 4, show that up to one in five of all visual concepts were mapped to the correct region of the language space, with only a slight deviation from the specific surface form. Considering P@100, we see that more than two thirds of the visual concepts find a semantic match in the language space when using ResNet152 and OPT or LLaMA-2, for example. We see that ResNet models score highest overall, followed by SegFormers, while MAE models rank third. We presume that this ranking is the result, in

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{"self_ref": "#/texts/72", "parent": {"cref": "#/body"}, "children": [], "label": "text", "prov": [{"page_no": 6, "bbox": {"l": 306.32073974609375, "t": 354.6774597167969, "r": 527.4515380859375, "b": 86.65802001953125, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 970]}], "orig": "an artifact such as a vehicle may be denoted by many lexemes (car, automobile, SUV, etc.), each of which may have multiple inflections and derivations (car, cars, car's, etc.). Figure 5 shows examples where the top predictions seem 'as good' as the gold standard. We find that a region of 10 neighbours corresponds roughly to grammatical forms or synonyms, and a neighbourhood of 100 word forms corresponds roughly to coarse-grained semantic classes. Results of P@10 in Figure 4, show that up to one in five of all visual concepts were mapped to the correct region of the language space, with only a slight deviation from the specific surface form. Considering P@100, we see that more than two thirds of the visual concepts find a semantic match in the language space when using ResNet152 and OPT or LLaMA-2, for example. We see that ResNet models score highest overall, followed by SegFormers, while MAE models rank third. We presume that this ranking is the result, in", "text": "an artifact such as a vehicle may be denoted by many lexemes (car, automobile, SUV, etc.), each of which may have multiple inflections and derivations (car, cars, car's, etc.). Figure 5 shows examples where the top predictions seem 'as good' as the gold standard. We find that a region of 10 neighbours corresponds roughly to grammatical forms or synonyms, and a neighbourhood of 100 word forms corresponds roughly to coarse-grained semantic classes. Results of P@10 in Figure 4, show that up to one in five of all visual concepts were mapped to the correct region of the language space, with only a slight deviation from the specific surface form. Considering P@100, we see that more than two thirds of the visual concepts find a semantic match in the language space when using ResNet152 and OPT or LLaMA-2, for example. We see that ResNet models score highest overall, followed by SegFormers, while MAE models rank third. We presume that this ranking is the result, in"}

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Image Classes

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section_header

Nearest Neighbors (Top 100)

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palmyra, palmyra palm, palm, palais, palatines, royal palm , palazzi, palazzo, palisades, palatinate, regency, palatial, palas, palatinates, palms, palimony, caribe, palmier, paladins, banyan tree, bermudas, bruneian, palazzos, bahamian, palmers, malacca, madeira, ceiba tree, palmettos, palmtop, oil palm, pal, royal, regal, roystonea regia , lindens, palaces, athenaeum, arboricultural, gabonese, palming, sugar palm, elm tree, palings, palm tree, palaeography, coconut palm, palisaded, bahraini, nicaraguan, … … , regent, myrtle, estancia, pavonia, imperial, royalist, regnal, historic, annals, maduro, rozelle, dominical, hydropathic, andorran

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drinking fountain , water fountain , cesspools, water cooler, manhole cover, bird feeder, birdbath, water jug, drainage system, fountain, water tap, watering can, garbage disposal, cesspit, recycling bin, water tank, garbage can, water pipe, manhole, toilet bowl, water closet, cement mixer, trash bin, soda fountain, bubblers, ice chest, footstone, ice machine, churns, milk float, overflowing, privies, grate, disposal, bathing, water bed, trickles, waterworks, drinking vessel, wading pool, carafe, vending machine, toilet water, sandboxes, toilet seat, drainpipe, draining, … … , spring water, ice maker, retaining wall, charcoal burner, litter, sentry box, cistern, waterhole, manholes, baptismal font, waterless

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clamp, wrench, screwdriver, socket wrench, carabiner , torque wrench, screwdrivers, fastener, elastic bandage, pliers, retractor, screw thread, carabiners, plunger, spanner, corer, screw, aspirator, clamps, adjustable spanner, applicator, center punch, latch, extractor, lever, adaptor, hose, gripper, compensator, pipe wrench, power drill, retractors, bicycle pump, holding device, grappling hook, fasteners, extension cord, locknuts, bungee cord, drill press, ratcheting, elastic band, reamer, soldering iron, handlebar, plug, stopper knot, tongs, twist drill, crimpers, … … , shock absorber, caliper, shackle, wristband, reducer, wrenches, loop knot, safety belt

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community center, training school, school, youth hostel, service department, conference center, music school, day school, student union , academy, life office, hall, orphanage, school system, meeting, college, ministry, school principal, government building, house, council, clinic, business office, schoolmaster, workshop, council board, boardinghouse, club, service club, schools, detention centre, gymnasium, gym, schoolmasters, … … , nursing home, meeting house, church, education, reform school, semester, schoolmate, study hall, member, schoolrooms, assembly hall, meetings, hotel, district manager, arena, staff member, firm

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Figure 5: Examples featuring the 100 nearest neighbors in the mapping of image classes into the language representation space (from MAE$_{Huge}$ to OPT$_{30B}$). The golden labels are highlighted in green.

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{"self_ref": "#/texts/79", "parent": {"cref": "#/body"}, "children": [], "label": "caption", "prov": [{"page_no": 7, "bbox": {"l": 71.26412200927734, "t": 521.2467041015625, "r": 525.5408325195312, "b": 497.1179504394531, "coord_origin": "BOTTOMLEFT"}, "charspan": [0, 205]}], "orig": "Figure 5: Examples featuring the 100 nearest neighbors in the mapping of image classes into the language representation space (from MAE$_{Huge}$ to OPT$_{30B}$). The golden labels are highlighted in green.", "text": "Figure 5: Examples featuring the 100 nearest neighbors in the mapping of image classes into the language representation space (from MAE$_{Huge}$ to OPT$_{30B}$). The golden labels are highlighted in green."}