Original: R EVEALING INTERPRETABLE OBJECT REPRESENTATIONS FROM HUMAN BEHAVIOR
Revised: R EVEALING INTERPRETABLE OBJECT REPRESENTATIONS FROM HUMAN BEHAVIOR

Original: Institute
Revised: Institute

Original: Mental charles.zheng@nih.gov francisco.pereira@nih
Revised: Mental charles.zheng@nih.gov francisco.pereira@nih

Original: gov
Revised: gov

Original: A BSTRACT
Revised: A BSTRACT

Original: To study how mental object representations are related to behavior we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories.
Revised: To study how mental object representations are related to behavior we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories.

Original: These representations predicted a latent similarity structure between objects, which captured most of the explainable variance in human behavioral judgments.
Revised: These representations predicted a latent similarity structure between objects, which captured most of the explainable variance in human behavioral judgments.

Original: Individual dimensions in the low-dimensional embedding were found to be highly reproducible and interpretable as conveying degrees of taxonomic membership, functionality and perceptual attributes.
Revised: Individual dimensions in the low-dimensional embedding were found to be highly reproducible and interpretable as conveying degrees of taxonomic membership, functionality and perceptual attributes.

Original: We further demonstrated the predictive power of the embeddings for explaining other forms of human behavior, including categorization, typicality judgments and feature ratings, suggesting that the dimensions reﬂect human conceptual representations of objects beyond the speciﬁc task
Revised: We further demonstrated the predictive power of the embeddings for explaining other forms of human behavior, including categorization, typicality judgments and feature ratings, suggesting that the dimensions reﬂect human conceptual representations of objects beyond the speciﬁc task

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: A central goal in understanding the human mind is to determine how object concepts are represented and how they relate to human behavior.
Revised: A central goal in understanding the human mind is to determine how object concepts are represented and how they relate to human behavior.

Original: Given the near-inﬁnite number of tasks or contexts of usage, this might appear to be an impossible prospect.
Revised: Given the near-inﬁnite number of tasks or contexts of usage, this might appear to be an impossible prospect.

Original: Take the example of picking a tomato in a grocery store.
Revised: Take the example of picking a tomato in a grocery store.

Original: A person may recognize it by its color, shape, size, or texture; they may also know many of the more conceptual dimensions of a tomato, such as it being a fruit, or functional ones such as being a salad item.
Revised: A person may recognize it by its color, shape, size, or texture; they may also know many of the more conceptual dimensions of a tomato, such as it being a fruit, or functional ones such as being a salad item.

Original: In most cases, however, only a few of these aspects might matter, depending on task context (e.g. as a grocery item or as a projectile in an audience that is not pleased with a presentation).
Revised: In most cases, however, only a few of these aspects might matter, depending on task context (e.g. as a grocery item or as a projectile in an audience that is not pleased with a presentation).

Original: Thus, to understand how we interact meaningfully with the objects around us, we need to tackle three problems simultaneously: (1) determine the object concept, the cognitive representation of behaviorally-relevant dimensions that distinguish an object from other objects.
Revised: Thus, to understand how we interact meaningfully with the objects around us, we need to tackle three problems simultaneously: (1) determine the object concept, the cognitive representation of behaviorally-relevant dimensions that distinguish an object from other objects.

Original: (2) determine which object concept representations are integrated into our perceptual decisions.
Revised: (2) determine which object concept representations are integrated into our perceptual decisions.

Original: (3) characterize the inﬂuence of the context – determined by the surrounding objects – on those decisions.
Revised: (3) characterize the inﬂuence of the context – determined by the surrounding objects – on those decisions.

Original: There have been many attempts to represent object concepts in terms of semantic features , a vector of variables indicating the presence of different aspects of their meaning.
Revised: There have been many attempts to represent object concepts in terms of semantic features , a vector of variables indicating the presence of different aspects of their meaning.

Original: These representations have been used to model phenomena such as judgments of typicality or similarity between concepts, or reaction times in various semantic tasks, with the goal of drawing conclusions about mental representations of those concepts (see Murphy (2004) for an extensive review of this literature).
Revised: These representations have been used to model phenomena such as judgments of typicality or similarity between concepts, or reaction times in various semantic tasks, with the goal of drawing conclusions about mental representations of those concepts (see Murphy (2004) for an extensive review of this literature).

Original: These features have usually been binary properties, postulated by researchers.
Revised: These features have usually been binary properties, postulated by researchers.

Original: A landmark study
Revised: A landmark study

Original: McRae et al.
Revised: McRae et al.

Original: (2005) departed from this approach by instead asking hundreds of subjects to name binary properties of 541 objects, yielding 2,526 such semantic features.
Revised: (2005) departed from this approach by instead asking hundreds of subjects to name binary properties of 541 objects, yielding 2,526 such semantic features.

Original: These corresponded to different types of information, e.g. for the concept "hammer" subjects might list taxonomic ("is a tool"), functional ("is used to hammer nails"), perceptual ("heavy"), among others.
Revised: These corresponded to different types of information, e.g. for the concept "hammer" subjects might list taxonomic ("is a tool"), functional ("is used to hammer nails"), perceptual ("heavy"), among others.

Original: The results revealed that concepts for objects in the same basic level category shared many features; at the same time, there were also features that distinguished even very similar concepts.
Revised: The results revealed that concepts for objects in the same basic level category shared many features; at the same time, there were also features that distinguished even very similar concepts.

Original: This effort was later replicated and extended by Devereux et al.
Revised: This effort was later replicated and extended by Devereux et al.

Original: (2014), generating 5,929 semantic features for 638 objects.
Revised: (2014), generating 5,929 semantic features for 638 objects.

Original: The main issues with features produced in either study are the lack of degree (they can only be present or absent, albeit with varying naming frequencies), the extreme speciﬁcity of some features, and the omission of many features shared by the majority of concepts.
Revised: The main issues with features produced in either study are the lack of degree (they can only be present or absent, albeit with varying naming frequencies), the extreme speciﬁcity of some features, and the omission of many features shared by the majority of concepts.

Original: A separate concern is the fact that, absent a speciﬁc context of use for each object, subjects will not likely think of many valid properties (e.g. that a tomato can be thrown).
Revised: A separate concern is the fact that, absent a speciﬁc context of use for each object, subjects will not likely think of many valid properties (e.g. that a tomato can be thrown).

Original: A different approach is to postulate the existence of certain semantic features and ask subjects to judge the degree to which features are salient for each concept, instead of assuming binary features.
Revised: A different approach is to postulate the existence of certain semantic features and ask subjects to judge the degree to which features are salient for each concept, instead of assuming binary features.

Original: Binder et al.
Revised: Binder et al.

Original: (2016) did this for 65 features corresponding to types of information for which there is evidence of brain representation (in their terminology: sensory, motor, spatial, temporal, affective, social, cognitive, etc).
Revised: (2016) did this for 65 features corresponding to types of information for which there is evidence of brain representation (in their terminology: sensory, motor, spatial, temporal, affective, social, cognitive, etc).

Original: This requires experts to specify the features in advance, and not all features can be judged easily by salience.
Revised: This requires experts to specify the features in advance, and not all features can be judged easily by salience.

Original: In all three approaches outlined above, there is also no clear way of determining which features are critical to semantic behavior.
Revised: In all three approaches outlined above, there is also no clear way of determining which features are critical to semantic behavior.

Original: Here we introduce an approach that uses only information from behavioral judgments about the grouping of object images in the context of other objects to estimate representations of object concepts.
Revised: Here we introduce an approach that uses only information from behavioral judgments about the grouping of object images in the context of other objects to estimate representations of object concepts.

Original: We demonstrate that this approach can predict human behavior in face of new combinations of objects and that it also allows prediction of results in other behavioral tasks.
Revised: We demonstrate that this approach can predict human behavior in face of new combinations of objects and that it also allows prediction of results in other behavioral tasks.

Original: We show that individual dimensions in the low-dimensional embedding represent complex combinations of the information in the binary features in Devereux et al.
Revised: We show that individual dimensions in the low-dimensional embedding represent complex combinations of the information in the binary features in Devereux et al.

Original: and, furthermore, are interpretable as conveying taxonomic, functional, or perceptual information.
Revised: and, furthermore, are interpretable as conveying taxonomic, functional, or perceptual information.

Original: Finally, we will discuss the way in which this representation suggests a simple, effective model of judgments of semantic similarity in context.
Revised: Finally, we will discuss the way in which this representation suggests a simple, effective model of judgments of semantic similarity in context.

Original:  D ATA AND M ETHODS 2. T HE O DD - ONE - OUT DATASET
Revised:  D ATA AND M ETHODS 2. T HE O DD - ONE - OUT DATASET

Original: The collection of the Odd-one-out behavioral dataset is an ongoing project by the authors.
Revised: The collection of the Odd-one-out behavioral dataset is an ongoing project by the authors.

Original: The dataset contains information about 1,854 different object concepts, which we will denote by c 1 , . .
Revised: The dataset contains information about 1,854 different object concepts, which we will denote by c 1 , . .

Original: , c m (e.g. c 1 = ‘aardvark’,..., c 1854 = ‘zucchini’).
Revised: , c m (e.g. c 1 = ‘aardvark’,..., c 1854 = ‘zucchini’).

Original: A triplet consists of a set of three concepts { c i 1 , c i 2 , c i 3 } , for instance, { c 2 , c 117 , c 136 } = { ‘abacus’ , ‘beetle’ , ‘bison’ } , presented to Amazon Mechanical Turk (AMT) workers as three photographs of exemplars, one for each of the three concepts.
Revised: A triplet consists of a set of three concepts { c i 1 , c i 2 , c i 3 } , for instance, { c 2 , c 117 , c 136 } = { ‘abacus’ , ‘beetle’ , ‘bison’ } , presented to Amazon Mechanical Turk (AMT) workers as three photographs of exemplars, one for each of the three concepts.

Original: Importantly, these photographs were accompanied neither by labels or captions, meaning behavior was based only on those pictures.
Revised: Importantly, these photographs were accompanied neither by labels or captions, meaning behavior was based only on those pictures.

Original: Workers were asked to consider the three pairs within the triplet { ( c i 1 , c i 2 ) , ( c i 1 , c i 3 ) , ( c i 2 , c i 3 ) } , and to decide which item had the smallest similarity to the other two (the "odd-one-out").
Revised: Workers were asked to consider the three pairs within the triplet { ( c i 1 , c i 2 ) , ( c i 1 , c i 3 ) , ( c i 2 , c i 3 ) } , and to decide which item had the smallest similarity to the other two (the "odd-one-out").

Original: This is equivalent to choosing the pair with the greatest similarity.
Revised: This is equivalent to choosing the pair with the greatest similarity.

Original: Let ( y 1 , y 2 ) denote the indices in this pair, e.g. for ‘beetle’ and ‘bison’ they would be ( y 1 , y 2 ) =
Revised: Let ( y 1 , y 2 ) denote the indices in this pair, e.g. for ‘beetle’ and ‘bison’ they would be ( y 1 , y 2 ) =

Original: The large number of objects in this dataset has two different motivations.
Revised: The large number of objects in this dataset has two different motivations.

Original: The ﬁrst is obtaining behavioral data about objects from a wide range of semantic categories (tools, animals, insects, weapons, food, body parts, etc), rather than the much smaller numbers in prior studies.
Revised: The ﬁrst is obtaining behavioral data about objects from a wide range of semantic categories (tools, animals, insects, weapons, food, body parts, etc), rather than the much smaller numbers in prior studies.

Original: We will use the term "category" loosely, to refer to a taxonomic level above that of the individual object; this is often, but not always, a basic level category (Murphy, 2004).
Revised: We will use the term "category" loosely, to refer to a taxonomic level above that of the individual object; this is often, but not always, a basic level category (Murphy, 2004).

Original: The second is to have subjects consider each object in as many different contexts as possible.
Revised: The second is to have subjects consider each object in as many different contexts as possible.

Original: We take the contexts instantiated by comparing each object to the others in the triplet as a proxy of the many situations each object might appear or be used in.
Revised: We take the contexts instantiated by comparing each object to the others in the triplet as a proxy of the many situations each object might appear or be used in.

Original: For instance, "tomato" might be paired with "milk" if the third object in the triplet were "table" ("tomato" and "milk" are food), but perhaps not if the third object was "wine" ("milk" and "wine" are a more speciﬁc kind of food).
Revised: For instance, "tomato" might be paired with "milk" if the third object in the triplet were "table" ("tomato" and "milk" are food), but perhaps not if the third object was "wine" ("milk" and "wine" are a more speciﬁc kind of food).

Original: If "tomato" were presented with "lipstick" and "rock", it could be paired with the former (because they are red) or the latter (because they can both be projectiles).
Revised: If "tomato" were presented with "lipstick" and "rock", it could be paired with the former (because they are red) or the latter (because they can both be projectiles).

Original: Finally, the presence of several objects sharing a given semantic category means that there is redundancy.
Revised: Finally, the presence of several objects sharing a given semantic category means that there is redundancy.

Original: Hence, one should be able to predict behavior in face of an object in novel contexts, if similar objects have already been observed in those contexts.
Revised: Hence, one should be able to predict behavior in face of an object in novel contexts, if similar objects have already been observed in those contexts.

Original: The dataset in this paper contains judgments on 1,450,119 randomly selected triplets, roughly 0 .
Revised: The dataset in this paper contains judgments on 1,450,119 randomly selected triplets, roughly 0 .

Original: 13% out of all possible triplets using the 1,854 concepts.
Revised: 13% out of all possible triplets using the 1,854 concepts.

Original: These were the triplets remaining after excluding
Revised: These were the triplets remaining after excluding

Original: AMT participants that showed evidence of inappropriate subject behavior, namely if responses were unusually fast, exhibited systematic response bias, or were empty (137,281 triplets or 8 .
Revised: AMT participants that showed evidence of inappropriate subject behavior, namely if responses were unusually fast, exhibited systematic response bias, or were empty (137,281 triplets or 8 .

Original: We plan to collect additional triplets and release all data by the end of the study.
Revised: We plan to collect additional triplets and release all data by the end of the study.

Original: 2. S PARSE PO SITIVE S IMILARITY E MBEDDING (SP O SE)
Revised: 2. S PARSE PO SITIVE S IMILARITY E MBEDDING (SP O SE)

Original: Semantic representation of concepts Our method, Sparse Positive Similarity Embedding (SPoSE) is based on three assumptions.
Revised: Semantic representation of concepts Our method, Sparse Positive Similarity Embedding (SPoSE) is based on three assumptions.

Original: The ﬁrst is that each object concept c i can be represented by semantic features, quantiﬁed in a vector x i =
Revised: The ﬁrst is that each object concept c i can be represented by semantic features, quantiﬁed in a vector x i =

Original: ( x i 1 , . . . , x ip ) .
Revised: ( x i 1 , . . . , x ip ) .

Original: These features represent aspects of meaning of the concept known by subjects, and correspond to dimensions of a space where the geometrical relationships between vectors encode the (dis)similarity of the corresponding concepts.
Revised: These features represent aspects of meaning of the concept known by subjects, and correspond to dimensions of a space where the geometrical relationships between vectors encode the (dis)similarity of the corresponding concepts.

Original: We estimate semantic features from behavioral data alone , using the probabilistic model described in the next section.
Revised: We estimate semantic features from behavioral data alone , using the probabilistic model described in the next section.

Original: In our model, each feature/dimension x if in the vector x i is real and non-negative, so as to make it interpretable as the degree to which the aspect of meaning it represents is present and inﬂuences subject behavior (Murphy et al., 2012).
Revised: In our model, each feature/dimension x if in the vector x i is real and non-negative, so as to make it interpretable as the degree to which the aspect of meaning it represents is present and inﬂuences subject behavior (Murphy et al., 2012).

Original: Further, we expect features/dimensions to be sparse McRae et al.
Revised: Further, we expect features/dimensions to be sparse McRae et al.

Original: (2005), which led us to add a sparsity parameter to our model.
Revised: (2005), which led us to add a sparsity parameter to our model.

Original: Based on related work in sparse positive word embeddings of words from text corpora (Murphy et al., 2012), we expect some of the dimensions to indicate membership of the semantic category the object belongs to (e.g. tool, vegetable, vehicle, etc).
Revised: Based on related work in sparse positive word embeddings of words from text corpora (Murphy et al., 2012), we expect some of the dimensions to indicate membership of the semantic category the object belongs to (e.g. tool, vegetable, vehicle, etc).

Original: If two objects in a triplet share a category and the third does not, subjects will tend to group objects with a common category with very high probability.
Revised: If two objects in a triplet share a category and the third does not, subjects will tend to group objects with a common category with very high probability.

Original: However, categories alone cannot fully explain subject performance in this task, as there may be triplets where either (a) all three objects belong to the same category or (b) no two objects share a category.
Revised: However, categories alone cannot fully explain subject performance in this task, as there may be triplets where either (a) all three objects belong to the same category or (b) no two objects share a category.

Original: We expect our method to ﬁnd non-taxonomic information similar to that in McRae et al.
Revised: We expect our method to ﬁnd non-taxonomic information similar to that in McRae et al.

Original: (2005) and Devereux et al.
Revised: (2005) and Devereux et al.

Original: (2014), if it allow us to explain semantic decision making behavior.
Revised: (2014), if it allow us to explain semantic decision making behavior.

Original: Probabilistic model Our second assumption is that the decision in a given trial is explained as a function of the similarity between the embedding vectors of the three concepts presented.
Revised: Probabilistic model Our second assumption is that the decision in a given trial is explained as a function of the similarity between the embedding vectors of the three concepts presented.

Original: Given two concepts c i and c j , the similarity S ij is the dot product of the corresponding vectors x i and x j :
Revised: Given two concepts c i and c j , the similarity S ij is the dot product of the corresponding vectors x i and x j :

Original: [Equation]
Revised: [Equation]

Original: Our third assumption is that the outcome of the triplet task is stochastic.
Revised: Our third assumption is that the outcome of the triplet task is stochastic.

Original: This assumption reﬂects both trial-to-trial inconsistencies in how an individual subject makes the decision, as well as subject differences in the decision-making process.
Revised: This assumption reﬂects both trial-to-trial inconsistencies in how an individual subject makes the decision, as well as subject differences in the decision-making process.

Original: Given that we pool data across many subjects, we do not distinguish between these two sources of randomness.
Revised: Given that we pool data across many subjects, we do not distinguish between these two sources of randomness.

Original: We model the probability that a subject will choose a given pair out of the three possible pairs as proportional to the exponential of the similarity,
Revised: We model the probability that a subject will choose a given pair out of the three possible pairs as proportional to the exponential of the similarity,

Original: [Equation]
Revised: [Equation]

Original: Since probabilities of the three possible outcomes add to one, this gives
Revised: Since probabilities of the three possible outcomes add to one, this gives

Original: [Equation]
Revised: [Equation]

Original: The vectors x i in this model are not normalized, in that each dimension – and, therefore, vector similarity – can be arbitrarily large.
Revised: The vectors x i in this model are not normalized, in that each dimension – and, therefore, vector similarity – can be arbitrarily large.

Original: In addition to the reasons described in the previous section, this allows us to model situations where the decision is close to being deterministic (e.g. two concepts are so similar that they will always be grouped together, regardless of third concept).
Revised: In addition to the reasons described in the previous section, this allows us to model situations where the decision is close to being deterministic (e.g. two concepts are so similar that they will always be grouped together, regardless of third concept).

Original: We also tried modeling choice probabilities using Euclidean distances (rather than dot product) between embedding vectors, but this resulted in similar (but overall slightly worse) results on our evaluations.
Revised: We also tried modeling choice probabilities using Euclidean distances (rather than dot product) between embedding vectors, but this resulted in similar (but overall slightly worse) results on our evaluations.

Original: Parameter ﬁtting We infer embedding vectors ( x 1 , . .
Revised: Parameter ﬁtting We infer embedding vectors ( x 1 , . .

Original: x m ) from data by ﬁtting a regularized maximum likelihood objective function.
Revised: x m ) from data by ﬁtting a regularized maximum likelihood objective function.

Original: Let n be the total number of triplets available for building the model.
Revised: Let n be the total number of triplets available for building the model.

Original: For the j th triplet in the dataset, let ( i 1 ,j , i 2 ,j , i 3 ,j ) denote the indices of the concepts in the triplet, and let ( y 1 ,j , y 2 ,j ) indicate the pair of concepts chosen, for triplet j = 1 , . . . , n .
Revised: For the j th triplet in the dataset, let ( i 1 ,j , i 2 ,j , i 3 ,j ) denote the indices of the concepts in the triplet, and let ( y 1 ,j , y 2 ,j ) indicate the pair of concepts chosen, for triplet j = 1 , . . . , n .

Original: We randomly split the dataset into n train triplets for training and n val for choosing the sparsity regularization parameter λ .
Revised: We randomly split the dataset into n train triplets for training and n val for choosing the sparsity regularization parameter λ .

Original: We index the training set by j = 1 , . . .
Revised: We index the training set by j = 1 , . . .

Original: , n train and the validation set by j = n train + 1 , . .
Revised: , n train and the validation set by j = n train + 1 , . .

Original: . , n .
Revised: . , n .

Original: The objective function for SPoSE, given a speciﬁed number of dimensions p , is
Revised: The objective function for SPoSE, given a speciﬁed number of dimensions p , is

Original: [Equation]
Revised: [Equation]

Original: Here || · || 1 is the L1 norm, so
Revised: Here || · || 1 is the L1 norm, so

Original: || x
Revised: || x

Original: || 1 =
Revised: || 1 =

Original: (cid:80) pf =1 | x f | , and x f ≥ 0 for f = 1 , . .
Revised: (cid:80) pf =1 | x f | , and x f ≥ 0 for f = 1 , . .

Original: . , p .
Revised: . , p .

Original: We use the Adam algorithm (Kingma & Ba, 2015) with an initial learning rate of 0.001 to minimize the objective function, using a ﬁxed number of 1,000 epochs over the training set, which was sufﬁcient to ensure convergence.
Revised: We use the Adam algorithm (Kingma & Ba, 2015) with an initial learning rate of 0.001 to minimize the objective function, using a ﬁxed number of 1,000 epochs over the training set, which was sufﬁcient to ensure convergence.

Original: Since this objective function is non-convex, Adam is likely to ﬁnd only a local minimum.
Revised: Since this objective function is non-convex, Adam is likely to ﬁnd only a local minimum.

Original: However, the combination of non-negativity and L1 penalty leads to very similar solutions across random initializations; we discuss this further in Section 3.1.
Revised: However, the combination of non-negativity and L1 penalty leads to very similar solutions across random initializations; we discuss this further in Section 3.1.

Original: We select the regularization parameter λ out of a grid of candidate values by choosing the one that achieves the lowest cross-entropy CE v on the validation set, deﬁned by
Revised: We select the regularization parameter λ out of a grid of candidate values by choosing the one that achieves the lowest cross-entropy CE v on the validation set, deﬁned by

Original: [Equation]
Revised: [Equation]

Original: The dimensionality of the embedding, p , can be determined heuristically from the data.
Revised: The dimensionality of the embedding, p , can be determined heuristically from the data.

Original: If p is set to be larger than the number of dimensions supported by the data, the SPoSE algorithm will shrink entire dimensions towards zero, where they can be easily thresholded.
Revised: If p is set to be larger than the number of dimensions supported by the data, the SPoSE algorithm will shrink entire dimensions towards zero, where they can be easily thresholded.

Original: We believe this happens because the L1 penalty objective encourages redundant similar dimensions to be merged, which would not happen with an L2 penalty; we provide a more formal justiﬁcation in the Supplementary Material.
Revised: We believe this happens because the L1 penalty objective encourages redundant similar dimensions to be merged, which would not happen with an L2 penalty; we provide a more formal justiﬁcation in the Supplementary Material.

Original: 2. R ELATED W ORK
Revised: 2. R ELATED W ORK

Original: There are several existing methods for estimating embeddings of items from behavioral judgments.
Revised: There are several existing methods for estimating embeddings of items from behavioral judgments.

Original: Agarwal et al.
Revised: Agarwal et al.

Original: (2007) introduced the generalized non-metric multidimensional scaling (GNMMDS) framework as a generalization of non-metric MDS.
Revised: (2007) introduced the generalized non-metric multidimensional scaling (GNMMDS) framework as a generalization of non-metric MDS.

Original: The behavioral task they study is a ‘quadruplet’ task, where a subject is shown two pairs of items, c i , c j and c k , c (cid:96) .
Revised: The behavioral task they study is a ‘quadruplet’ task, where a subject is shown two pairs of items, c i , c j and c k , c (cid:96) .

Original: Then the subject is asked to decide if the similarity between c i and c
Revised: Then the subject is asked to decide if the similarity between c i and c

Original: j is greater or less than the similarity between c k and c (cid:96) .
Revised: j is greater or less than the similarity between c k and c (cid:96) .

Original: GNMMDS learns embedding vectors for the concepts, so that the Euclidean distance between embedding vectors approximates the dissimilarity between the respective items.
Revised: GNMMDS learns embedding vectors for the concepts, so that the Euclidean distance between embedding vectors approximates the dissimilarity between the respective items.

Original: In the two-alternative forced-choice (2AFC) task of Xu et al.
Revised: In the two-alternative forced-choice (2AFC) task of Xu et al.

Original: (2011), the subject is shown an anchor c i and two alternatives c i , c j .
Revised: (2011), the subject is shown an anchor c i and two alternatives c i , c j .

Original: Xu et al.
Revised: Xu et al.

Original: (2011) study this task, under the assumption one already has parametric features
Revised: (2011) study this task, under the assumption one already has parametric features

Original: z i for the concepts c i .
Revised: z i for the concepts c i .

Original: In the triplet task of Tamuz et al.
Revised: In the triplet task of Tamuz et al.

Original: (2011), the subject is shown an anchor c i and asked which of c j or c k is more similar to c i .
Revised: (2011), the subject is shown an anchor c i and asked which of c j or c k is more similar to c i .

Original: This is also a special case of the quadruplet task, with pairs ( c i , c j ) and ( c i , c k ) .
Revised: This is also a special case of the quadruplet task, with pairs ( c i , c j ) and ( c i , c k ) .

Original: Tamuz et al.
Revised: Tamuz et al.

Original: (2011) use a model where Pr[( c i , c j ) more similar than ( c i , c k )] =
Revised: (2011) use a model where Pr[( c i , c j ) more similar than ( c i , c k )] =

Original: [Equation]
Revised: [Equation]

Original: where d i,j = || x
Revised: where d i,j = || x

Original: i − x j || 2 and where µ is some constant to be determined empirically.
Revised: i − x j || 2 and where µ is some constant to be determined empirically.

Original: Similarly, Wah et al.
Revised: Similarly, Wah et al.

Original: (2014) show a series of adaptive displays for an anchor c i , where the subject must partition the queries c j , c (cid:96) , . . .
Revised: (2014) show a series of adaptive displays for an anchor c i , where the subject must partition the queries c j , c (cid:96) , . . .

Original: into a set of similar and a set of dissimilar queries.
Revised: into a set of similar and a set of dissimilar queries.

Original: In contrast to our work, the aforementioned studies did not use sparsity or positivity constraints, nor did they intend to evaluate the interpretability of the embedding.
Revised: In contrast to our work, the aforementioned studies did not use sparsity or positivity constraints, nor did they intend to evaluate the interpretability of the embedding.

Original: Our requirements of having a sparse, positive vector representing each concept, and a three-choice probabilistic model, led us to develop a new method.
Revised: Our requirements of having a sparse, positive vector representing each concept, and a three-choice probabilistic model, led us to develop a new method.

Original: It is not straightforward to extend the probabilistic model of Xu et al.
Revised: It is not straightforward to extend the probabilistic model of Xu et al.

Original: (2011) to a task with more than 2 choices; it also requires an a priori feature matrix for the concepts, which is not available for our dataset.
Revised: (2011) to a task with more than 2 choices; it also requires an a priori feature matrix for the concepts, which is not available for our dataset.

Original: GNMMDS could potentially be applied to our data with added sparsity and positivity constraints, but does not produce probability estimates for the task.
Revised: GNMMDS could potentially be applied to our data with added sparsity and positivity constraints, but does not produce probability estimates for the task.

Original: Finally, the model in Tamuz et al.
Revised: Finally, the model in Tamuz et al.

Original: (2011) could be extended to the three-choice triplet task with sparsity and positivity constraints, but it would require an extra tuning parameter µ , in addition to the L1 sparsity penalty λ which is needed to obtain sparse embeddings.
Revised: (2011) could be extended to the three-choice triplet task with sparsity and positivity constraints, but it would require an extra tuning parameter µ , in addition to the L1 sparsity penalty λ which is needed to obtain sparse embeddings.

Original: An alternative approach for representing concepts is the use of word vector embeddings, derived from information about co-occurrence of words in very large text corpora, instead of behavior.
Revised: An alternative approach for representing concepts is the use of word vector embeddings, derived from information about co-occurrence of words in very large text corpora, instead of behavior.

Original: Pilehvar & Collier (2016) introduced a method for estimating vectors for each of the different concept senses (synsets) of a particular word, from its word2vec (Mikolov et al., 2013) embedding vector and the synset relationships in the WordNet ontology (Miller, 1995).
Revised: Pilehvar & Collier (2016) introduced a method for estimating vectors for each of the different concept senses (synsets) of a particular word, from its word2vec (Mikolov et al., 2013) embedding vector and the synset relationships in the WordNet ontology (Miller, 1995).

Original: Each of our concepts has a corresponding synset and, therefore, can be represented by a synset vector.
Revised: Each of our concepts has a corresponding synset and, therefore, can be represented by a synset vector.

Original: However, the latter are real-valued and dense, and hence do not satisfy any of our requirements.
Revised: However, the latter are real-valued and dense, and hence do not satisfy any of our requirements.

Original: There is an embedding method that enforces positive, sparse values for each dimension (NNSE, Murphy et al.
Revised: There is an embedding method that enforces positive, sparse values for each dimension (NNSE, Murphy et al.

Original: , but it produces one vector per word rather than synset.
Revised: , but it produces one vector per word rather than synset.

Original: Both methods have been used to generate behavioral predictions.
Revised: Both methods have been used to generate behavioral predictions.

Original: Hence, we will use them as an alternative concept representation in our experiments.
Revised: Hence, we will use them as an alternative concept representation in our experiments.

Original:  E XPERIMENTS 3. D ATA AND EXPERIMENTAL SETUP
Revised:  E XPERIMENTS 3. D ATA AND EXPERIMENTAL SETUP

Original: We used Tensorﬂow (Abadi et al., 2015) to ﬁt the model (3) to the 1,450,119 triplets collected, using a 90-10 train-validation split to pick the regularization parameter λ .
Revised: We used Tensorﬂow (Abadi et al., 2015) to ﬁt the model (3) to the 1,450,119 triplets collected, using a 90-10 train-validation split to pick the regularization parameter λ .

Original: Searching over parameters { 0 . 0070 , 0 . 0072 , . .
Revised: Searching over parameters { 0 . 0070 , 0 . 0072 , . .

Original: . , 0 . 0100 } we identiﬁed the parameter λ = 0 .
Revised: . , 0 . 0100 } we identiﬁed the parameter λ = 0 .

Original: 008 with the lowest loss on the validation set.
Revised: 008 with the lowest loss on the validation set.

Original: We initialized the model with 90 dimensions.
Revised: We initialized the model with 90 dimensions.

Original: After convergence, many of the dimensions were very small and very sparse, with an average value of less than 0.02 per item; the most dense dimension had maximum value of 2.3 and average value of 0.64.
Revised: After convergence, many of the dimensions were very small and very sparse, with an average value of less than 0.02 per item; the most dense dimension had maximum value of 2.3 and average value of 0.64.

Original: We discarded the small dimensions, yielding the 49-dimensional embedding used in all experiments.
Revised: We discarded the small dimensions, yielding the 49-dimensional embedding used in all experiments.

Original: The number of non-zero dimensions varied across object categories, with a median of 14 (minimum: 3, maximum: 29).
Revised: The number of non-zero dimensions varied across object categories, with a median of 14 (minimum: 3, maximum: 29).

Original: Due to random initialization and batch ordering, the solution will vary randomly corresponding to different local minima.
Revised: Due to random initialization and batch ordering, the solution will vary randomly corresponding to different local minima.

Original: To check the reproducibility of the embedding we found, we ran the model 11 additional times with the same parameters but different random seeds.
Revised: To check the reproducibility of the embedding we found, we ran the model 11 additional times with the same parameters but different random seeds.

Original: The number of resulting dimensions varied from 47 to 50, and between any two model ﬁts, an average of 38.75 dimensions could be matched between the two models with a correlation of 0.8 or higher.
Revised: The number of resulting dimensions varied from 47 to 50, and between any two model ﬁts, an average of 38.75 dimensions could be matched between the two models with a correlation of 0.8 or higher.

Original: For comparison with vectors derived from text information, we used synset Pilehvar & Collier (2016) and NNSE Murphy et al.
Revised: For comparison with vectors derived from text information, we used synset Pilehvar & Collier (2016) and NNSE Murphy et al.

Original: (2012)) vectors.
Revised: (2012)) vectors.

Original: We used 50-D vectors, corresponding to the dimensionality of our embedding, as well as 300-D (synset) and 2500-D (NNSE), corresponding to the best performing embeddings according to the original publications.
Revised: We used 50-D vectors, corresponding to the dimensionality of our embedding, as well as 300-D (synset) and 2500-D (NNSE), corresponding to the best performing embeddings according to the original publications.

Original: 3. G ENERALIZATION ON THE SAME TASK AND SIMILARITY PREDICTION
Revised: 3. G ENERALIZATION ON THE SAME TASK AND SIMILARITY PREDICTION

Original: Accuracy at predicting triplet decisions In order to test our model, we collected an independent test set of 25,000 triplets, with 25 repeats for each of 1,000 randomly selected triplets; none of these were present in the data used to build the model.
Revised: Accuracy at predicting triplet decisions In order to test our model, we collected an independent test set of 25,000 triplets, with 25 repeats for each of 1,000 randomly selected triplets; none of these were present in the data used to build the model.

Original: After applying the same quality control, there remained 614 unique triplets with at least 20 repeats.
Revised: After applying the same quality control, there remained 614 unique triplets with at least 20 repeats.

Original: Having this many repeats allows us to be conﬁdent of the probability of response for each triplet.
Revised: Having this many repeats allows us to be conﬁdent of the probability of response for each triplet.

Original: Furthermore, it allows us to establish a model-free estimate of the Bayes accuracy, the best possible accuracy achievable by any model.
Revised: Furthermore, it allows us to establish a model-free estimate of the Bayes accuracy, the best possible accuracy achievable by any model.

Original: Since the optimal classiﬁer predicts the population majority outcome for any triplet, this accuracy ceiling is therefore the average probability of the majority outcome over the set of all triplets (ties broken randomly).
Revised: Since the optimal classiﬁer predicts the population majority outcome for any triplet, this accuracy ceiling is therefore the average probability of the majority outcome over the set of all triplets (ties broken randomly).

Original: The ceiling estimated in this fashion was 0.673.
Revised: The ceiling estimated in this fashion was 0.673.

Original: The accuracy of our model was 0.637, above all baselines (see Table 1).
Revised: The accuracy of our model was 0.637, above all baselines (see Table 1).

Original: Note that, as only 1,097 of our 1,854 objects are in the NNSE lexicon, the evaluation set for NNSE results was reduced to 129 unique triplets
Revised: Note that, as only 1,097 of our 1,854 objects are in the NNSE lexicon, the evaluation set for NNSE results was reduced to 129 unique triplets

Original: [Table]
Revised: [Table]

Original: [Table]
Revised: [Table]

Original: Prediction of similarities In addition to prediction accuracy, we wanted to test ability of the model to capture ﬁne semantic distinctions, even though it was trained on extremely sparse, noisy data.
Revised: Prediction of similarities In addition to prediction accuracy, we wanted to test ability of the model to capture ﬁne semantic distinctions, even though it was trained on extremely sparse, noisy data.

Original: To this effect, we collected an independent test set containing every possible triplet for 48 objects chosen out of the 1,854, one representative of each of 48 common categories (see list in Supplementary
Revised: To this effect, we collected an independent test set containing every possible triplet for 48 objects chosen out of the 1,854, one representative of each of 48 common categories (see list in Supplementary

Original: Material).
Revised: Material).

Original: This dataset contained 43,200 triplets after quality control; there were 17 , 296 = (cid:0) 483 (cid:1) unique triplets, with two or three subject answers for each.
Revised: This dataset contained 43,200 triplets after quality control; there were 17 , 296 = (cid:0) 483 (cid:1) unique triplets, with two or three subject answers for each.

Original: For this particular evaluation we re-trained our model on a dataset excluding all the triplets containing any 2 of the 48 objects.
Revised: For this particular evaluation we re-trained our model on a dataset excluding all the triplets containing any 2 of the 48 objects.

Original: We then used the probability model (2) to predict the choice with the highest probability for each triplet in the 48-object dataset.
Revised: We then used the probability model (2) to predict the choice with the highest probability for each triplet in the 48-object dataset.

Original: This experimental setup ensured that any generalization had to rely on the observed relationships between objects outside the 48.
Revised: This experimental setup ensured that any generalization had to rely on the observed relationships between objects outside the 48.

Original: It was also signiﬁcantly harder than a random set of triplets, given that no two concepts in any triplet were in similar semantic categories.
Revised: It was also signiﬁcantly harder than a random set of triplets, given that no two concepts in any triplet were in similar semantic categories.

Original: We obtained an accuracy of 0 .
Revised: We obtained an accuracy of 0 .

Original: 592 , above all the baseline methods (see Table 1).
Revised: 592 , above all the baseline methods (see Table 1).

Original: A different way of examining prediction quality is to pool data across many triplets, by considering similarities between pairs of objects.
Revised: A different way of examining prediction quality is to pool data across many triplets, by considering similarities between pairs of objects.

Original: The pairwise similarity for objects A and B , S AB , is obtained by dividing the number of triplets where subjects group A and B by the total number of triplets where A and B both appear.
Revised: The pairwise similarity for objects A and B , S AB , is obtained by dividing the number of triplets where subjects group A and B by the total number of triplets where A and B both appear.

Original: We calculated this similarity matrix S for the 48-object dataset, as displayed in Figure 1 left.
Revised: We calculated this similarity matrix S for the 48-object dataset, as displayed in Figure 1 left.

Original: We then computed the expected similarity matrix according to our model.
Revised: We then computed the expected similarity matrix according to our model.

Original: The Pearson correlation coefﬁcient between off-diagonal entries of our prediction and the pairwise similarity derived from the 48-concept dataset was 0.899, above all the baseline methods (see Table 1).
Revised: The Pearson correlation coefﬁcient between off-diagonal entries of our prediction and the pairwise similarity derived from the 48-concept dataset was 0.899, above all the baseline methods (see Table 1).

Original: This is particularly important because it demonstrates that sparse sampling of triplet data still allows accurate prediction of similarity relations between objects.
Revised: This is particularly important because it demonstrates that sparse sampling of triplet data still allows accurate prediction of similarity relations between objects.

Original: 3. P REDICTION OF HUMAN - GENERATED SEMANTIC FEATURES
Revised: 3. P REDICTION OF HUMAN - GENERATED SEMANTIC FEATURES

Original: The second evaluation of our semantic vector representation was to test whether it could be used to predict the features in human-generated semantic feature sets: McRae (McRae et al., 2005) and
Revised: The second evaluation of our semantic vector representation was to test whether it could be used to predict the features in human-generated semantic feature sets: McRae (McRae et al., 2005) and

Original: CSLB (Devereux et al., 2014).
Revised: CSLB (Devereux et al., 2014).

Original: CSLB is more extensive than McRae, both in the number of features (5,929) and objects (638), and shares 413 objects in common with the intersection of the objects from our 1,854 object set and the NNSE lexicon; therefore, we limited our evaluation to CSLB.
Revised: CSLB is more extensive than McRae, both in the number of features (5,929) and objects (638), and shares 413 objects in common with the intersection of the objects from our 1,854 object set and the NNSE lexicon; therefore, we limited our evaluation to CSLB.

Original: Since many features are speciﬁc to only a few objects, they are sparse or blank when restricted to the 413 objects.
Revised: Since many features are speciﬁc to only a few objects, they are sparse or blank when restricted to the 413 objects.

Original: Hence, we selected the 100 features with the highest density as prediction targets; the lowest density feature appeared in 23 of the 413 objects.
Revised: Hence, we selected the 100 features with the highest density as prediction targets; the lowest density feature appeared in 23 of the 413 objects.

Original: We ﬁt a separate L2-regularized logistic regression to predict each of the 100 features from SPoSE or baseline vectors.
Revised: We ﬁt a separate L2-regularized logistic regression to predict each of the 100 features from SPoSE or baseline vectors.

Original: The prediction was done using 10-fold cross-validation, with a nested 10-fold cross-validation within each training set to pick the value of the regularization parameter.
Revised: The prediction was done using 10-fold cross-validation, with a nested 10-fold cross-validation within each training set to pick the value of the regularization parameter.

Original: We evaluated the prediction of each CSLB feature by computing the area under the curve (AUC) as the bias term was varied, reported on Table 1.
Revised: We evaluated the prediction of each CSLB feature by computing the area under the curve (AUC) as the bias term was varied, reported on Table 1.

Original: These results demonstrate that SPoSE dimensions contain the information present in the main CSLB features for the 413 objects considered.
Revised: These results demonstrate that SPoSE dimensions contain the information present in the main CSLB features for the 413 objects considered.

Original: This is also the case for 300-D synset vectors, but using almost 10 times as many dimensions as SPoSE.
Revised: This is also the case for 300-D synset vectors, but using almost 10 times as many dimensions as SPoSE.

Original: Although correlation between SPoSE and synset vector AUCs was 0.953, SPoSE AUC was signiﬁcantly higher in a few dimensions.
Revised: Although correlation between SPoSE and synset vector AUCs was 0.953, SPoSE AUC was signiﬁcantly higher in a few dimensions.

Original: These are related to shapes and other perceptual aspects (“is pink”, “is small”, “is ﬂat”,"is white"); we hypothesize that this is due to their having a strong effect on subject behavior, but being less salient in text corpora.
Revised: These are related to shapes and other perceptual aspects (“is pink”, “is small”, “is ﬂat”,"is white"); we hypothesize that this is due to their having a strong effect on subject behavior, but being less salient in text corpora.

Original: 3. I NTERPRETABILITY OF LEARNED SEMANTIC DIMENSIONS
Revised: 3. I NTERPRETABILITY OF LEARNED SEMANTIC DIMENSIONS

Original: The goal of this analysis was to show that SPoSE dimensions can be "explained" in terms of the elementary CSLB features, by testing how well the former predicted the latter.
Revised: The goal of this analysis was to show that SPoSE dimensions can be "explained" in terms of the elementary CSLB features, by testing how well the former predicted the latter.

Original: We ﬁt a L1-regularized non-negative regression model (NNLS) to predict each of the 49 SPoSE features from the 5,
Revised: We ﬁt a L1-regularized non-negative regression model (NNLS) to predict each of the 49 SPoSE features from the 5,

Original: CSLB features, for all 496 concepts present in both datasets.
Revised: CSLB features, for all 496 concepts present in both datasets.

Original: We used a 10-fold cross-validation, with a nested 10-fold cross-validation within each training set to pick the value of the regularization parameter.
Revised: We used a 10-fold cross-validation, with a nested 10-fold cross-validation within each training set to pick the value of the regularization parameter.

Original: The median correlation between each feature and its prediction was 0.58, indicating that most SPoSE features can be predicted well.
Revised: The median correlation between each feature and its prediction was 0.58, indicating that most SPoSE features can be predicted well.

Original: We then ﬁt a model to the entire dataset, in order to use the NNLS regression weights to determine which CSLB features most inﬂuenced the prediction of each SPoSE dimension.
Revised: We then ﬁt a model to the entire dataset, in order to use the NNLS regression weights to determine which CSLB features most inﬂuenced the prediction of each SPoSE dimension.

Original: Figure 2 displays the most inﬂuential CSLB features for four different
Revised: Figure 2 displays the most inﬂuential CSLB features for four different

Original: SPoSE features, selected to highlight the different types of information extracted.
Revised: SPoSE features, selected to highlight the different types of information extracted.

Original: Consider ﬁrst Dimension A.
Revised: Consider ﬁrst Dimension A.

Original: The corresponding panel shows pictures of the 4 objects with the highest weights for this SPoSE dimension.
Revised: The corresponding panel shows pictures of the 4 objects with the highest weights for this SPoSE dimension.

Original: To the right of the pictures, we list the 12 most important CSLB features for predicting the dimension.
Revised: To the right of the pictures, we list the 12 most important CSLB features for predicting the dimension.

Original: Their respective NNLS weights are shown by the size of the corresponding bars, and the CSLB feature type by the color (e.g. green is taxonomic).
Revised: Their respective NNLS weights are shown by the size of the corresponding bars, and the CSLB feature type by the color (e.g. green is taxonomic).

Original: Dimension
Revised: Dimension

Original: A appears to indicate the degree to which an object belongs to the “animal” semantic category.
Revised: A appears to indicate the degree to which an object belongs to the “animal” semantic category.

Original: There appear to be multiple such category indicator dimensions, e.g. “food”, “clothes”, “furniture” (shown in the Supplementary Material).
Revised: There appear to be multiple such category indicator dimensions, e.g. “food”, “clothes”, “furniture” (shown in the Supplementary Material).

Original: Consider now Dimensions B and C. These are examples of dimensions that correspond strongly to the type of material in objects, and that are well explained by CSLB features such as “made of metal” or “made of wood”.
Revised: Consider now Dimensions B and C. These are examples of dimensions that correspond strongly to the type of material in objects, and that are well explained by CSLB features such as “made of metal” or “made of wood”.

Original: These can also reﬂect category membership, if they are common characteristics of members of a given category.
Revised: These can also reﬂect category membership, if they are common characteristics of members of a given category.

Original: Finally, consider
Revised: Finally, consider

Original: Dimension D. This is an example of a dimension that captures purely visual aspects, e.g. it is very strongly explained by the “is red” CSLB feature, together with other visual/perceptual ones.
Revised: Dimension D. This is an example of a dimension that captures purely visual aspects, e.g. it is very strongly explained by the “is red” CSLB feature, together with other visual/perceptual ones.

Original: See
Revised: See

Original: Supplementary Material for a similar visualization for all 49 SPoSE dimensions.
Revised: Supplementary Material for a similar visualization for all 49 SPoSE dimensions.

Original: [Figure]
Revised: [Figure]

Original: 3. P REDICTION OF OTHER BEHAVIORAL OR HUMAN - ANNOTATED DATA Prediction of typicality ratings
Revised: 3. P REDICTION OF OTHER BEHAVIORAL OR HUMAN - ANNOTATED DATA Prediction of typicality ratings

Original: The typicality of an object with respect to its semantic category is a graded notion of category membership (e.g. "robin" is a more typical bird than "chicken").
Revised: The typicality of an object with respect to its semantic category is a graded notion of category membership (e.g. "robin" is a more typical bird than "chicken").

Original: As we saw earlier, concepts for objects in the same semantic category tend to share SPoSE dimensions.
Revised: As we saw earlier, concepts for objects in the same semantic category tend to share SPoSE dimensions.

Original: Hence, a natural test is to assess the degree to which distances between semantic vectors for objects within a category reﬂect their typicality.
Revised: Hence, a natural test is to assess the degree to which distances between semantic vectors for objects within a category reﬂect their typicality.

Original: To this effect, we collated a variety of pre-existing norms of typicality or naming frequency (Rosch (1975),McCloskey & Glucksberg (1978),Gruenenfelder (1984),Van Overschelde et al.
Revised: To this effect, we collated a variety of pre-existing norms of typicality or naming frequency (Rosch (1975),McCloskey & Glucksberg (1978),Gruenenfelder (1984),Van Overschelde et al.

Original: and used a collaborative ﬁltering method (Koren, 2008) to extract a single aggregate norm from these for as many objects as possible.
Revised: and used a collaborative ﬁltering method (Koren, 2008) to extract a single aggregate norm from these for as many objects as possible.

Original: After this, we matched objects from the aggregate typicality norms to our 1,854 items and NNSE lexicon.
Revised: After this, we matched objects from the aggregate typicality norms to our 1,854 items and NNSE lexicon.

Original: Given that correlation estimates can be noisy for small samples, we restricted the analysis to the 9 categories with 25 or more objects in our set.
Revised: Given that correlation estimates can be noisy for small samples, we restricted the analysis to the 9 categories with 25 or more objects in our set.

Original: For a given category, we computed a SPoSE vector for each category centroid, the mean of the vectors for all objects within that category.
Revised: For a given category, we computed a SPoSE vector for each category centroid, the mean of the vectors for all objects within that category.

Original: Next, we computed a proxy for the typicality of each object by calculating the dot product between its vector and the centroid vector.
Revised: Next, we computed a proxy for the typicality of each object by calculating the dot product between its vector and the centroid vector.

Original: Finally, we calculated the correlation between the proxy typicality scores and the typicality scores from the norms.
Revised: Finally, we calculated the correlation between the proxy typicality scores and the typicality scores from the norms.

Original: The median correlation with typicality across categories was 0.55.
Revised: The median correlation with typicality across categories was 0.55.

Original: After correcting for multiple comparisons, 5 of these results were statistically signiﬁcant (weapon, vehicle, clothing, vegetable, fruit, respectively, 0.69, 0.67, 0.66, 0.62, 0.55), whereas the other 4 were not (furniture, body part, tool, animal, respectively 0.43, 0.42, 0.34, -0.14).
Revised: After correcting for multiple comparisons, 5 of these results were statistically signiﬁcant (weapon, vehicle, clothing, vegetable, fruit, respectively, 0.69, 0.67, 0.66, 0.62, 0.55), whereas the other 4 were not (furniture, body part, tool, animal, respectively 0.43, 0.42, 0.34, -0.14).

Original: Results are comparable for 300-D synset vectors and 2500-D NNSE vectors, and above the other baselines (see Table 1).
Revised: Results are comparable for 300-D synset vectors and 2500-D NNSE vectors, and above the other baselines (see Table 1).

Original: These results suggest that SPoSE vectors for more typical objects are more similar to each other than for atypical ones.
Revised: These results suggest that SPoSE vectors for more typical objects are more similar to each other than for atypical ones.

Original: In combination with the fact that vectors are sparse, this suggests that more categorical SPoSE features also reﬂect its degree.
Revised: In combination with the fact that vectors are sparse, this suggests that more categorical SPoSE features also reﬂect its degree.

Original: Semantic category clustering Our ﬁnal evaluation focused on determining the degree to which objects in the same semantic category cluster compactly in the embedding space.
Revised: Semantic category clustering Our ﬁnal evaluation focused on determining the degree to which objects in the same semantic category cluster compactly in the embedding space.

Original: We ran a classiﬁcation task for assigning 318 objects to one of 23 categories with ≥ 5 items, as deﬁned in Battig &
Revised: We ran a classiﬁcation task for assigning 318 objects to one of 23 categories with ≥ 5 items, as deﬁned in Battig &

Original: Montague (1969).
Revised: Montague (1969).

Original: Leaving out each object in turn, we assign it the category of its nearest neighbor by cosine similarity; this is close to the task in Murphy et al.
Revised: Leaving out each object in turn, we assign it the category of its nearest neighbor by cosine similarity; this is close to the task in Murphy et al.

Original: but using 23-way accuracy rather than cluster purity.
Revised: but using 23-way accuracy rather than cluster purity.

Original: The resulting accuracies were 0.846 for both SPoSE and 300-dimensional synset, and above all other baselines (see Table 1).
Revised: The resulting accuracies were 0.846 for both SPoSE and 300-dimensional synset, and above all other baselines (see Table 1).

Original:  D ISCUSSION AND CONCLUSIONS
Revised:  D ISCUSSION AND CONCLUSIONS

Original: In this paper, we show that human behavioral judgments are well-explained by a strikingly lowdimensional semantic representation of concrete concepts.
Revised: In this paper, we show that human behavioral judgments are well-explained by a strikingly lowdimensional semantic representation of concrete concepts.

Original: This representation, which embeds each object in a 49-dimensional vector, allows prediction of subject behavior in face of new combinations of concepts not encountered before, as well as prediction of other behavioral or human-annotated data, such as typicality ratings or similarity judgments.
Revised: This representation, which embeds each object in a 49-dimensional vector, allows prediction of subject behavior in face of new combinations of concepts not encountered before, as well as prediction of other behavioral or human-annotated data, such as typicality ratings or similarity judgments.

Original: Moreover, the representation is readily interpretable, as positive, sparse dimensions make it easy to identify which concepts load on each dimension.
Revised: Moreover, the representation is readily interpretable, as positive, sparse dimensions make it easy to identify which concepts load on each dimension.

Original: Further, we demonstrate that the value of each dimension in this space can be explained in terms of elementary features elicited directly from human subjects in publicly available norms.
Revised: Further, we demonstrate that the value of each dimension in this space can be explained in terms of elementary features elicited directly from human subjects in publicly available norms.

Original: Given this converging evidence, we conclude that dimensions represent distinct types of information, from taxonomic (indicators of category membership) to functional or perceptual.
Revised: Given this converging evidence, we conclude that dimensions represent distinct types of information, from taxonomic (indicators of category membership) to functional or perceptual.

Original: As the representations were estimated solely from behavioral data, this suggests a simple model of decision making in the triplet task.
Revised: As the representations were estimated solely from behavioral data, this suggests a simple model of decision making in the triplet task.

Original: This can be viewed in terms of the distinction discussed in
Revised: This can be viewed in terms of the distinction discussed in

Original: Navarro & Lee (2004) for judging concept similarity from semantic feature vectors.
Revised: Navarro & Lee (2004) for judging concept similarity from semantic feature vectors.

Original: They distinguish a dimensional approach for representing stimuli (each feature is a continuous value, each concept is a point in a high-dimensional space, and similarity corresponds to proximity in the space), and a featural approach (each feature is binary, or discrete, and similarity is a function of the number of features that are common to both concepts, or that distinguish them).
Revised: They distinguish a dimensional approach for representing stimuli (each feature is a continuous value, each concept is a point in a high-dimensional space, and similarity corresponds to proximity in the space), and a featural approach (each feature is binary, or discrete, and similarity is a function of the number of features that are common to both concepts, or that distinguish them).

Original: More reﬁned schemes use modiﬁed distance metrics (dimensional) or combine commonality and distinctiveness (featural).
Revised: More reﬁned schemes use modiﬁed distance metrics (dimensional) or combine commonality and distinctiveness (featural).

Original: The use of sparsity and positivity in the SPoSE representation, and the vector dot product for computing concept similarity, blends the featural and dimensional approaches when making decisions about a triplet of concepts.
Revised: The use of sparsity and positivity in the SPoSE representation, and the vector dot product for computing concept similarity, blends the featural and dimensional approaches when making decisions about a triplet of concepts.

Original: First, if any two concepts share a semantic category, and the other one does not, the two concepts will likely be grouped together.
Revised: First, if any two concepts share a semantic category, and the other one does not, the two concepts will likely be grouped together.

Original: Because of sparsity, the dot product between concepts will be driven primarily by the number of features are shared between the two concepts in the same category, versus the different one.
Revised: Because of sparsity, the dot product between concepts will be driven primarily by the number of features are shared between the two concepts in the same category, versus the different one.

Original: Second, if any three concepts share a semantic category, they also share most, if not all of their non-zero features.
Revised: Second, if any three concepts share a semantic category, they also share most, if not all of their non-zero features.

Original: The decision becomes a function of the values of the features shared between them, and hence dimensional rather than featural.
Revised: The decision becomes a function of the values of the features shared between them, and hence dimensional rather than featural.

Original: Third, if all concepts belong to different categories, there may be very few features in common between any two of them.
Revised: Third, if all concepts belong to different categories, there may be very few features in common between any two of them.

Original: The results will likely be determined by which of those few features takes a higher value.
Revised: The results will likely be determined by which of those few features takes a higher value.

Original: Results might be idiosyncratic, e.g. two objects grouped because their pictures are both very red, while the alternative grouping would be because they are both string-like, and the former feature is more salient.
Revised: Results might be idiosyncratic, e.g. two objects grouped because their pictures are both very red, while the alternative grouping would be because they are both string-like, and the former feature is more salient.

Original: This is another reason why our features are unbounded: their scale can reﬂect their importance in decision making.
Revised: This is another reason why our features are unbounded: their scale can reﬂect their importance in decision making.

Original: This is akin to learning a distance metric in dimensional approaches.
Revised: This is akin to learning a distance metric in dimensional approaches.

Original: Our object representations capture the information that is necessary to explain subject behavior in the triplet task.
Revised: Our object representations capture the information that is necessary to explain subject behavior in the triplet task.

Original: Obviously, subjects have a lot more information about each concept that is not necessary or relevant for task performance.
Revised: Obviously, subjects have a lot more information about each concept that is not necessary or relevant for task performance.

Original: A promising direction for further work is to sample additional triplets so as to obtain more ﬁne-grained, within-category distinctions.
Revised: A promising direction for further work is to sample additional triplets so as to obtain more ﬁne-grained, within-category distinctions.

Original: Beyond this, we have also considered the possibility of there being information inﬂuencing behavior that might be too infrequent to be estimated from this type of data, or elicited from human subjects.
Revised: Beyond this, we have also considered the possibility of there being information inﬂuencing behavior that might be too infrequent to be estimated from this type of data, or elicited from human subjects.

Original: Yet another possible extension is to consider different types of similarity judgments (Veit et al., 2017), e.g. resulting from asking subjects to group objects based on a speciﬁc attribute (size, color, etc.).
Revised: Yet another possible extension is to consider different types of similarity judgments (Veit et al., 2017), e.g. resulting from asking subjects to group objects based on a speciﬁc attribute (size, color, etc.).

Original: One avenue for trying to identify this type of information is to predict synset vectors from SPoSE vectors and/or semantic features elicited from subjects, and represent the residuals in terms of a dictionary of new sparse, positive concept features.
Revised: One avenue for trying to identify this type of information is to predict synset vectors from SPoSE vectors and/or semantic features elicited from subjects, and represent the residuals in terms of a dictionary of new sparse, positive concept features.

Original: These could then be used as a complement to SPoSE dimensions.
Revised: These could then be used as a complement to SPoSE dimensions.

Original: A CKNOWLEDGEMENTS
Revised: A CKNOWLEDGEMENTS

Original: This research was possible thanks to the support of the National Institute of Mental Health Intramural Research Program (ZIA-MH-002909) and a Feodor-Lynen fellowship of the Humboldt foundation awarded to MNH.
Revised: This research was possible thanks to the support of the National Institute of Mental Health Intramural Research Program (ZIA-MH-002909, ZIC-MH002968) and a Feodor-Lynen fellowship of the Humboldt foundation awarded to MNH.

Original: Portions of this study used the high-performance computational capabilities of the Biowulf Linux cluster at the National Institutes of Health, Bethesda, MD (biowulf.nih.gov).
Revised: Portions of this study used the high-performance computational capabilities of the Biowulf Linux cluster at the National Institutes of Health, Bethesda, MD (biowulf.nih.gov).

Original: We would like to thank Alex Martin and Patrick McClure for their feedback and suggestions
Revised: We would like to thank Alex Martin and Patrick McClure for their feedback and suggestions.

Original: S PARSITY PROPERTIES
Revised: S PARSITY PROPERTIES

Original: Empirically, we ﬁnd that when the model is initialized with too many dimensions, SPoSE does not use all of the dimensions: it leaves many of them to be close to zero.
Revised: Empirically, we ﬁnd that when the model is initialized with too many dimensions, SPoSE does not use all of the dimensions: it leaves many of them to be close to zero.

Original: (The reason they are not exactly zero is due to noise from stochastic optimization.)
Revised: (The reason they are not exactly zero is due to noise from stochastic optimization.)

Original: Our explanation of this property is that the SPoSE objective encourages multiple similar dimensions to be merged.
Revised: Our explanation of this property is that the SPoSE objective encourages multiple similar dimensions to be merged.

Original: Let X be the p × m embedding matrix, and write X i for i th row of X .
Revised: Let X be the p × m embedding matrix, and write X i for i th row of X .

Original: Suppose that the SPoSE model is well-speciﬁed and that there exist two highly similar dimensions in the true object space, X 1 and X 2 , in the sense that ∆ =
Revised: Suppose that the SPoSE model is well-speciﬁed and that there exist two highly similar dimensions in the true object space, X 1 and X 2 , in the sense that ∆ =

Original: X 1 − X 2 is very small.
Revised: X 1 − X 2 is very small.

Original: Since the true similarity S is deﬁned as
Revised: Since the true similarity S is deﬁned as

Original: [Equation]
Revised: [Equation]

Original: the contribution of these two dimensions to the true similarity matrix is X
Revised: the contribution of these two dimensions to the true similarity matrix is X

Original: [Equation]
Revised: [Equation]

Original: Rather than ﬁnd these two dimensions from the data, SPoSE may ﬁnd a single dimension
Revised: Rather than ﬁnd these two dimensions from the data, SPoSE may ﬁnd a single dimension

Original: [Equation]
Revised: [Equation]

Original: This is because ˆ X 1 closely approximates the contribution of X 1 and X 2 to the true similarity matrix S ,
Revised: This is because ˆ X 1 closely approximates the contribution of X 1 and X 2 to the true similarity matrix S ,

Original: [Equation]
Revised: [Equation]

Original: But the L1 norm of ˆ X 1 is a smaller by the factor √ 2 / 2 than the combined L1 norms of X 1 and X 2 .
Revised: But the L1 norm of ˆ X 1 is a smaller by the factor √ 2 / 2 than the combined L1 norms of X 1 and X 2 .

Original: Therefore, if the approximation error to the empirical log-likelihood from using ˆ X 1 is small relative to the L1 penalty λ
Revised: Therefore, if the approximation error to the empirical log-likelihood from using ˆ X 1 is small relative to the L1 penalty λ

Original: ( || X 1 || 

Revised: ( || X 1 ||

Original: + ||
Revised: + ||

Original: X 2 || 1 ) , SPoSE will combine the two dimensions into one dimension.
Revised: X 2 || 1 ) , SPoSE will combine the two dimensions into one dimension.

Original: Note that the choice of L regularization is critical for this property: under the squared L2 norm, ˆ X 1 incurs approximately the same penalty as X 1 and X 2 combined so that there is no incentive to merge.
Revised: Note that the choice of L regularization is critical for this property: under the squared L2 norm, ˆ X 1 incurs approximately the same penalty as X 1 and X 2 combined so that there is no incentive to merge.

Original: This property has disadvantages and practical advantages.
Revised: This property has disadvantages and practical advantages.

Original: A possible disadvantage is that multiple dimensions in the data may be agglomerated if they are too similar.
Revised: A possible disadvantage is that multiple dimensions in the data may be agglomerated if they are too similar.

Original: However, depending on the application, this may be an advantage rather than a disadvantage since a few agglomerated dimensions may be more easy to interpret than many seemingly redundant dimensions.
Revised: However, depending on the application, this may be an advantage rather than a disadvantage since a few agglomerated dimensions may be more easy to interpret than many seemingly redundant dimensions.

Original: The disadvantage is also not as much of a disadvantage when one considers that dimensions that are too similar may be impossible to disentangle based on empirical data anyways, so SPoSE does not fare worse in this regard than other methods.
Revised: The disadvantage is also not as much of a disadvantage when one considers that dimensions that are too similar may be impossible to disentangle based on empirical data anyways, so SPoSE does not fare worse in this regard than other methods.

Original: This property of SPoSE allows for automatic dimensionality selection and also increases the reproducibility of the embedding.
Revised: This property of SPoSE allows for automatic dimensionality selection and also increases the reproducibility of the embedding.