4,522 research outputs found

    The Small Number System

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    I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system

    A Neural Model of How the Brain Represents and Compares Multi-Digit Numbers: Spatial and Categorical Processes

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    Both animals and humans are capable of representing and comparing numerical quantities, but only humans seem to have evolved multi-digit place-value number systems. This article develops a neural model, called the Spatial Number Network, or SpaN model, which predicts how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the Inferior Parietal Cortex. Multi-digit numerical representations that obey a place-value principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. It is proposed that learned semantic categories that symbolize separate digits, as well as place markers like "tens," "hundreds," "thousands," etc., are associated through learning with the corresponding spatial locations of the Where representation, leading to a place-value number system as an emergent property of What-Where information fusion. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, it is proposed that transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. Neural mechanisms are defined which give rise to an ordered spatial numerical map ordering and Weber law characteristics as emergent properties. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream. The model's What-Where interactions can explain human psychophysical data, such as error rates and reaction times, about multi-digit (base 10) numerical stimuli, and describe how such a competence can develop through learning. The SpaN model and its explanatory range arc compared with other models of numerical representation.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333

    Stimulus Control by Timing in Pigeons

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    Timing has been widely studied in humans and animals across a variety of different timescales. The concept of time as a stimulus dimension, and how it is processed relative to other stimulus dimensions, has only recently been scrutinized. In the current work I present a review of interval timing as it relates to stimulus control, and discuss the role of attention in timing in the context of three sets of studies in pigeons. In the first set of studies, I analyzed whether the presence of a non-reinforced timed stimulus would disrupt timing of a stimulus reinforced on a fixed-interval schedule. In Experiment 1, half of the pigeons were trained on a 60-s fixed interval schedule of reinforcement signaled by onset of a sidekey; the other half of the birds had those same reinforced trials interspersed among trials in which the onset of a different sidekey signaled 60-s followed by non-reinforcement. Groups were reversed in the second phase of experimentation. Obtained peak-time curves showed flattened responding to the reinforced stimulus for birds which also received non-reinforced trials, suggesting that control by interval timing was overshadowed by the presence of a food/no food cue. Experiment 2 ruled out the possibility that this effect was caused by differences in reinforcement. Pigeons’ responding on this task was not controlled by timing because the visual discrimination based on food vs. no food was more salient than the temporal discrimination. In the second set of studies, I examined the ability of pigeons to track the identity of multiple stimuli presented in order across a temporal interval terminating in reinforcement. In Experiment 1A, pigeons responded to the final stimulus in a three-item sequence regardless of the preceding order of stimuli, or even if previous stimuli had not been presented, suggesting that the birds attended only to the reinforced stimulus and not to the order of stimuli. In Experiment 1B, pigeons were presented with baseline non-reinforced trials in which the order of the first two stimuli was reversed, and results showed that they responded differently to the third stimulus based on the order of stimuli. Experiment 2 extended these results with a five-stimulus sequence. Though birds showed only a weak appreciation of order, they nonetheless responded differentially based on temporal order. In the final study, I observed the tendency of pigeons to anticipate or perseverate after a mid-session reversal of response contingencies. The birds tended to make errors around the reversal point when the discrimination was a visually-based (red vs. green) task, and these errors were conclusively shown to be due to interval timing from the start of the session. However, when presented with a visual-spatial version of the same task, pigeons no longer made timing-induced errors and instead used a reinforcement-maximizing approach. The dimension of discrimination affected the strength of memory for the response and outcome of the previous trial, and in turn affected the tendency of birds to base their responding on an error-prone interval timing strategy

    Do not lose the details: reinforced representation learning for high performance visual tracking

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    This work presents a novel end-to-end trainable CNN model for high performance visual object tracking. It learns both low-level fine-grained representations and a high-level semantic embedding space in a mutual reinforced way, and a multi-task learning strategy is proposed to perform the correlation analysis on representations from both levels. In particular, a fully convolutional encoder-decoder network is designed to reconstruct the original visual features from the semantic projections to preserve all the geometric information. Moreover, the correlation filter layer working on the fine-grained representations leverages a global context constraint for accurate object appearance modeling. The correlation filter in this layer is updated online efficiently without network fine-tuning. Therefore, the proposed tracker benefits from two complementary effects: the adaptability of the fine-grained correlation analysis and the generalization capability of the semantic embedding. Extensive experimental evaluations on four popular benchmarks demonstrate its state-of-the-art performance
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