Gravitating global defects: the gravitational field and compactification

We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater or equal 3. We will see that the general effect of a global defect is to introduce a deficit solid angle. We also show how the same kind of scalar field configurations can be used for spontaneous compactification of "n" extra dimensions on an n-sphere.Comment: Uses revte

Gravity of higher-dimensional global defects

Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the n extra dimensions. For Lambda = 0 and n > 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Lambda > 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Lambda < 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.Comment: 18 pages, no figures, uses revte

Integrating prediction errors at two time scales permits rapid recalibration of speech sound categories

Speech perception presumably arises from internal models of how specific sensory features are associated with speech sounds. These features change constantly (e.g. different speakers, articulation modes etc.), and listeners need to recalibrate their internal models by appropriately weighing new versus old evidence. Models of speech recalibration classically ignore this volatility. The effect of volatility in tasks where sensory cues were associated with arbitrary experimenter-defined categories were well described by models that continuously adapt the learning rate while keeping a single representation of the category. Using neurocomputational modelling we show that recalibration of natural speech sound categories is better described by representing the latter at different time scales. We illustrate our proposal by modeling fast recalibration of speech sounds after experiencing the McGurk effect. We propose that working representations of speech categories are driven both by their current environment and their long-term memory representations

Rhythmic modulation of prediction errors: a possible role for the beta-range in speech processing

Natural speech perception requires processing the current acoustic input while keeping in mind the preceding one and predicting the next. This complex computational problem could be handled by a multi timescale hierarchical inferential process that coordinates information flow up and down the language hierarchy. While theta and low-gamma neural frequency scales are convincingly involved in bottom-up syllable-tracking and phoneme-level speech encoding, the beta rhythm is more loosely associated with top-down processes without being assigned yet a specific computational function. Here we tested the hypothesis that the beta rhythm drives the precision of states during the speech recognition hierarchical inference process. We used a predictive coding model that recognizes syllables on-line in natural sentences, in which the precision of prediction errors is rhythmically modulated, resulting in alternating bottom-up vs. top-down processing regimes. We show that recognition performance increases with the rate of precision updates, with an optimal efficacy in the beta range (around 20 Hz). The model further performs when prediction errors pertaining respectively to syllable timing and syllable identity oscillate in antiphase. These results suggest that online syllable recognition globally benefits from the alternation of bottom-up and top-down dominant regime at beta rate, and that the gain is stronger when different features are also analyzed in alternation. These results speak to a discontinuous account of inferential operations in speech processing

Combining predictive coding and neural oscillations enables online syllable recognition in natural speech

On-line comprehension of natural speech requires segmenting the acoustic stream into discrete linguistic elements. This process is argued to rely on theta-gamma oscillation coupling, which can parse syllables and encode them in decipherable neural activity. Speech comprehension also strongly depends on contextual cues that help predicting speech structure and content. To explore the effects of theta-gamma coupling on bottom-up/top-down dynamics during on-line syllable identification, we designed a computational model (Precoss—predictive coding and oscillations for speech) that can recognise syllable sequences in continuous speech. The model uses predictions from internal spectro-temporal representations of syllables and theta oscillations to signal syllable onsets and duration. Syllable recognition is best when theta-gamma coupling is used to temporally align spectro-temporal predictions with the acoustic input. This neurocomputational modelling work demonstrates that the notions of predictive coding and neural oscillations can be brought together to account for on-line dynamic sensory processing

Prediction across sensory modalities: A neurocomputational model of the McGurk effect

The McGurk effect is a textbook illustration of the automaticity with which the human brain integrates audio-visual speech. It shows that even incongruent audiovisual (AV) speech stimuli can be combined into percepts that correspond neither to the auditory nor to the visual input, but to a mix of both. Typically, when presented with, e.g., visual /aga/ and acoustic /aba/ we perceive an illusory /ada/. In the inverse situation, however, when acoustic /aga/ is paired with visual /aba/, we perceive a combination of both stimuli, i.e., /abga/ or /agba/. Here we assessed the role of dynamic cross-modal predictions in the outcome of AV speech integration using a computational model that processes continuous audiovisual speech sensory inputs in a predictive coding framework. The model involves three processing levels: sensory units, units that encode the dynamics of stimuli, and multimodal recognition/identity units. The model exhibits a dynamic prediction behavior because evidence about speech tokens can be asynchronous across sensory modality, allowing for updating the activity of the recognition units from one modality while sending top-down predictions to the other modality. We explored the model's response to congruent and incongruent AV stimuli and found that, in the two-dimensional feature space spanned by the speech second formant and lip aperture, fusion stimuli are located in the neighborhood of congruent /ada/, which therefore provides a valid match. Conversely, stimuli that lead to combination percepts do not have a unique valid neighbor. In that case, acoustic and visual cues are both highly salient and generate conflicting predictions in the other modality that cannot be fused, forcing the elaboration of a combinatorial solution. We propose that dynamic predictive mechanisms play a decisive role in the dichotomous perception of incongruent audiovisual inputs

A deep hierarchy of predictions enables assignment of semantic roles in online speech comprehension

Understanding speech requires mapping fleeting and often ambiguous soundwaves to meaning. While humans are known to exploit their capacity to contextualize to facilitate this process, how internal knowledge is deployed on-line remains an open question. Here, we present a model that extracts multiple levels of information from continuous speech online. The model applies linguistic and nonlinguistic knowledge to speech processing, by periodically generating top-down predictions and incorporating bottom-up incoming evidence in a nested temporal hierarchy. We show that a nonlinguistic context level provides semantic predictions informed by sensory inputs, which are crucial for disambiguating among multiple meanings of the same word. The explicit knowledge hierarchy of the model enables a more holistic account of the neurophysiological responses to speech compared to using lexical predictions generated by a neural-network language model (GPT-2). We also show that hierarchical predictions reduce peripheral processing via minimizing uncertainty and prediction error. With this proof-of-concept model we demonstrate that the deployment of hierarchical predictions is a possible strategy for the brain to dynamically utilize structured knowledge and make sense of the speech input