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Communicating emotional intensity plays a vital ecological role because it provides valuable information about the nature and likelihood of the sender's behavior. 1 , 2 Yet how this complex signaling task is achieved remains unknown. We addressed this question using a perception-based, data-driven method to mathematically model the specific facial movements that receivers use to classify the six basic emotions-"happy," "surprise," "fear," "disgust," "anger," and "sad"-and judge their intensity in two distinct cultures (East Asian, Western European; total n = 120). In both cultures, receivers expected facial expressions to dynamically represent emotion category and intensity information over time, using a multi-component compositional signaling structure. Specifically, emotion intensifiers peaked earlier or later than emotion classifiers and represented intensity using amplitude variations. Emotion intensifiers are also more similar across emotions than classifiers are, suggesting a latent broad-plus-specific signaling structure. Cross-cultural analysis further revealed similarities and differences in expectations that could impact cross-cultural communication. Specifically, East Asian and Western European receivers have similar expectations about which facial movements represent high intensity for threat-related emotions, such as "anger," "disgust," and "fear," but differ on those that represent low threat emotions, such as happiness and sadness. Together, our results provide new insights into the intricate processes by which facial expressions can achieve complex dynamic signaling tasks by revealing the rich information embedded in facial expressions., 3 For example, attack often follows signals of intense aggression if receivers fail to retreat. 4 , 5 Humans regularly use facial expressions to communicate such information. 6 , 7 , 8 , 9 , 10 , 11 Yet how this complex signaling task is achieved remains unknown. We addressed this question using a perception-based, data-driven method to mathematically model the specific facial movements that receivers use to classify the six basic emotions-"happy," "surprise," "fear," "disgust," "anger," and "sad"-and judge their intensity in two distinct cultures (East Asian, Western European; total n = 120). In both cultures, receivers expected facial expressions to dynamically represent emotion category and intensity information over time, using a multi-component compositional signaling structure. Specifically, emotion intensifiers peaked earlier or later than emotion classifiers and represented intensity using amplitude variations. Emotion intensifiers are also more similar across emotions than classifiers are, suggesting a latent broad-plus-specific signaling structure. Cross-cultural analysis further revealed similarities and differences in expectations that could impact cross-cultural communication. Specifically, East Asian and Western European receivers have similar expectations about which facial movements represent high intensity for threat-related emotions, such as "anger," "disgust," and "fear," but differ on those that represent low threat emotions, such as happiness and sadness. Together, our results provide new insights into the intricate processes by which facial expressions can achieve complex dynamic signaling tasks by revealing the rich information embedded in facial expressions., Competing Interests: Declaration of interests P.G.S. is on the advisory board of this Current Biology., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Models are the hallmark of mature scientific inquiry. In psychology, this maturity has been reached in a pervasive question-what models best represent facial expressions of emotion? Several hypotheses propose different combinations of facial movements [action units (AUs)] as best representing the six basic emotions and four conversational signals across cultures. We developed a new framework to formalize such hypotheses as predictive models, compare their ability to predict human emotion categorizations in Western and East Asian cultures, explain the causal role of individual AUs, and explore updated, culture-accented models that improve performance by reducing a prevalent Western bias. Our predictive models also provide a noise ceiling to inform the explanatory power and limitations of different factors (e.g., AUs and individual differences). Thus, our framework provides a new approach to test models of social signals, explain their predictive power, and explore their optimization, with direct implications for theory development.

Human facial expressions are complex, multi-component signals that can communicate rich information about emotions, 1-5 including specific categories, such as "anger," and broader dimensions, such as "negative valence, high arousal." 6-8 An enduring question is how this complex signaling is achieved. Communication theory predicts that multi-component signals could transmit each type of emotion information-i.e., specific categories and broader dimensions-via the same or different facial signal components, with implications for elucidating the system and ontology of facial expression communication. 9 We addressed this question using a communication-systems-based method that agnostically generates facial expressions and uses the receiver's perceptions to model the specific facial signal components that represent emotion category and dimensional information to them. 10-12 First, we derived the facial expressions that elicit the perception of emotion categories (i.e., the six classic emotions 13 plus 19 complex emotions 3 ) and dimensions (i.e., valence and arousal) separately, in 60 individual participants. Comparison of these facial signals showed that they share subsets of components, suggesting that specific latent signals jointly represent-i.e., multiplex-categorical and dimensional information. Further examination revealed these specific latent signals and the joint information they represent. Our results-based on white Western participants, same-ethnicity face stimuli, and commonly used English emotion terms-show that facial expressions can jointly represent specific emotion categories and broad dimensions to perceivers via multiplexed facial signal components. Our results provide insights into the ontology and system of facial expression communication and a new information-theoretic framework that can characterize its complexities., Competing Interests: Declaration of interests The authors declare no competing interests., (Crown Copyright © 2021. Published by Elsevier Inc. All rights reserved.)

Real-world studies show that the facial expressions produced during pain and orgasm-two different and intense affective experiences-are virtually indistinguishable. However, this finding is counterintuitive, because facial expressions are widely considered to be a powerful tool for social interaction. Consequently, debate continues as to whether the facial expressions of these extreme positive and negative affective states serve a communicative function. Here, we address this debate from a novel angle by modeling the mental representations of dynamic facial expressions of pain and orgasm in 40 observers in each of two cultures (Western, East Asian) using a data-driven method. Using a complementary approach of machine learning, an information-theoretic analysis, and a human perceptual discrimination task, we show that mental representations of pain and orgasm are physically and perceptually distinct in each culture. Cross-cultural comparisons also revealed that pain is represented by similar face movements across cultures, whereas orgasm showed distinct cultural accents. Together, our data show that mental representations of the facial expressions of pain and orgasm are distinct, which questions their nondiagnosticity and instead suggests they could be used for communicative purposes. Our results also highlight the potential role of cultural and perceptual factors in shaping the mental representation of these facial expressions. We discuss new research directions to further explore their relationship to the production of facial expressions., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

Understanding the cultural commonalities and specificities of facial expressions of emotion remains a central goal of Psychology. However, recent progress has been stayed by dichotomous debates (e.g. nature versus nurture) that have created silos of empirical and theoretical knowledge. Now, an emerging interdisciplinary scientific culture is broadening the focus of research to provide a more unified and refined account of facial expressions within and across cultures. Specifically, data-driven approaches allow a wider, more objective exploration of face movement patterns that provide detailed information ontologies of their cultural commonalities and specificities. Similarly, a wider exploration of the social messages perceived from face movements diversifies knowledge of their functional roles (e.g. the 'fear' face used as a threat display). Together, these new approaches promise to diversify, deepen, and refine knowledge of facial expressions, and deliver the next major milestones for a functional theory of human social communication that is transferable to social robotics., (Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Visual categorization is the brain computation that reduces high-dimensional information in the visual environment into a smaller set of meaningful categories. An important problem in visual neuroscience is to identify the visual information that the brain must represent and then use to categorize visual inputs. Here we introduce a new mathematical formalism-termed space-by-time manifold decomposition-that describes this information as a low-dimensional manifold separable in space and time. We use this decomposition to characterize the representations used by observers to categorize the six classic facial expressions of emotion (happy, surprise, fear, disgust, anger, and sad). By means of a Generative Face Grammar, we presented random dynamic facial movements on each experimental trial and used subjective human perception to identify the facial movements that correlate with each emotion category. When the random movements projected onto the categorization manifold region corresponding to one of the emotion categories, observers categorized the stimulus accordingly; otherwise they selected "other." Using this information, we determined both the Action Unit and temporal components whose linear combinations lead to reliable categorization of each emotion. In a validation experiment, we confirmed the psychological validity of the resulting space-by-time manifold representation. Finally, we demonstrated the importance of temporal sequencing for accurate emotion categorization and identified the temporal dynamics of Action Unit components that cause typical confusions between specific emotions (e.g., fear and surprise) as well as those resolving these confusions.