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Geometry of concept learning
Understanding Human ability to learn novel concepts from just a few sensory experiences is a fundamental problem in cognitive neuroscience. I will describe a recent work with Ben Sorcher and Surya Ganguli (PNAS, October 2022) in which we propose a simple, biologically plausible, and mathematically tractable neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learned from few examples are defined by tightly circumscribed manifolds in the neural firing-rate space of higher-order sensory areas. Discrimination between novel concepts is performed by downstream neurons implementing ‘prototype’ decision rule, in which a test example is classified according to the nearest prototype constructed from the few training examples. We show that prototype few-shot learning achieves high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network (DNN) models of these representations. We develop a mathematical theory that links few-shot learning to the geometric properties of the neural concept manifolds and demonstrate its agreement with our numerical simulations across different DNNs as well as different layers. Intriguingly, we observe striking mismatches between the geometry of manifolds in intermediate stages of the primate visual pathway and in trained DNNs. Finally, we show that linguistic descriptors of visual concepts can be used to discriminate images belonging to novel concepts, without any prior visual experience of these concepts (a task known as ‘zero-shot’ learning), indicated a remarkable alignment of manifold representations of concepts in visual and language modalities. I will discuss ongoing effort to extend this work to other high level cognitive tasks.
Theory-driven probabilistic modeling of language use: a case study on quantifiers, logic and typicality
Theoretical linguistics postulates abstract structures that successfully explain key aspects of language. However, the precise relation between abstract theoretical ideas and empirical data from language use is not always apparent. Here, we propose to empirically test abstract semantic theories through the lens of probabilistic pragmatic modelling. We consider the historically important case of quantity words (e.g., `some', `all'). Data from a large-scale production study seem to suggest that quantity words are understood via prototypes. But based on statistical and empirical model comparison, we show that a probabilistic pragmatic model that embeds a strict truth-conditional notion of meaning explains the data just as well as a model that encodes prototypes into the meaning of quantity words.
The Gist of False Memory
It has long been known that when viewing a set of images, we misjudge individual elements as being closer to the mean than they are (Hollingworth, 1910) and recall seeing the (absent) set mean (Deese, 1959; Roediger & McDermott (1995). Recent studies found that viewing sets of images, simultaneously or sequentially, leads to perception of set statistics (mean, range) with poor memory for individual elements. Ensemble perception was found for sets of simple images (e.g. circles varying in size or brightness; lines of varying orientation), complex objects (e.g. faces of varying emotion), as well as for objects belonging to the same category. When the viewed set does not include its mean or prototype, nevertheless, observers report and act as if they have seen this central image or object – a form of false memory. Physiologically, detailed sensory information at cortical input levels is processed hierarchically to form an integrated scene gist at higher levels. However, we are aware of the gist before the details. We propose that images and objects belonging to a set or category are represented as their gist, mean or prototype, plus individual differences from that gist. Under constrained viewing conditions, only the gist is perceived and remembered. This theory also provides a basis for compressed neural representation. Extending this theory to scenes and episodes supplies a generalized basis for false memories. They seem right, match generalized expectations, so are believable without challenging examination. This theory could be tested by analyzing the typicality of false memories, compared to rejected alternatives.
Analogies, Games and the Learning of Mathematics
Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.
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