361,560 research outputs found

    Non-Bayesian updating: A theoretical framework

    Get PDF
    This paper models an agent in a multi-period setting who does not update according to Bayes' Rule, and who is self-aware and anticipates her updating behavior when formulating plans. Choice-theoretic axiomatic foundations are provided to capture updating biases that reflect excessive weight given to either prior beliefs, or alternatively, to observed data. A counterpart of the exchangeable Bayesian learning model is also described.Non-Bayesian updating, temptation and self-control, overreaction, underreaction, learning, law of small numbers

    Input-driven unsupervised learning in recurrent neural networks

    Get PDF
    Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is an attractor neural network with Hebbian learning (e.g. the Hopfield model). The model simplicity and the locality of the synaptic update rules come at the cost of a limited storage capacity, compared with the capacity achieved with supervised learning algorithms, whose biological plausibility is questionable. Here, we present an on-line learning rule for a recurrent neural network that achieves near-optimal performance without an explicit supervisory error signal and using only locally accessible information, and which is therefore biologically plausible. The fully connected network consists of excitatory units with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the patterns to be memorized are presented on-line as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs ('local fields'). Synapses corresponding to active inputs are modified as a function of the position of the local field with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. An additional parameter of the model allows to trade storage capacity for robustness, i.e. increased size of the basins of attraction. We simulated a network of 1001 excitatory neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction: our results show that, for any given basin size, our network more than doubles the storage capacity, compared with a standard Hopfield network. Our learning rule is consistent with available experimental data documenting how plasticity depends on firing rate. It predicts that at high enough firing rates, no potentiation should occu

    The Search for Invariance: Repeated Positive Testing Serves the Goals of Causal Learning

    Get PDF
    Positive testing is characteristic of exploratory behavior, yet it seems to be at odds with the aim of information seeking. After all, repeated demonstrations of one’s current hypothesis often produce the same evidence and fail to distinguish it from potential alternatives. Research on the development of scientific reasoning and adult rule learning have both documented and attempted to explain this behavior. The current chapter reviews this prior work and introduces a novel theoretical account—the Search for Invariance (SI) hypothesis—which suggests that producing multiple positive examples serves the goals of causal learning. This hypothesis draws on the interventionist framework of causal reasoning, which suggests that causal learners are concerned with the invariance of candidate hypotheses. In a probabilistic and interdependent causal world, our primary goal is to determine whether, and in what contexts, our causal hypotheses provide accurate foundations for inference and intervention—not to disconfirm their alternatives. By recognizing the central role of invariance in causal learning, the phenomenon of positive testing may be reinterpreted as a rational information-seeking strategy

    A three-threshold learning rule approaches the maximal capacity of recurrent neural networks

    Get PDF
    Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model has a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error signal, relying only upon locally accessible information. The fully-connected network consists of excitatory binary neurons with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the memory patterns are presented online as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs. Synapses corresponding to active inputs are modified as a function of the value of the local fields with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. We simulated and analyzed a network of binary neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction. The storage capacity obtained through numerical simulations is shown to be close to the value predicted by analytical calculations. We also measured the dependence of capacity on the strength of external inputs. Finally, we quantified the statistics of the resulting synaptic connectivity matrix, and found that both the fraction of zero weight synapses and the degree of symmetry of the weight matrix increase with the number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog

    Non-Bayesian Updating : A Theoretical Framework

    Get PDF
    This paper models an agent in an infinite horizon setting who does not update according to Bayes' Rule, and who is self-aware and anticipates her updating behavior when formulating plans. Choice-theoretic axiomatic foundations are provided. Then the model is specialized axiomatically to capture updating biases that reflect excessive weight given to (i) prior beliefs, or alternatively, (ii) the realized sample. Finally, the paper describes a counterpart of the exchangeable Bayesian model, where the agent tries to learn about parameters, and some answers are provided to the question "what does a non-Bayesian updater learn?"non-Bayesian updating, overreaction, underreaction, confirmatory bias, law of small numbers, gambler's fallacy, hot hand fallacy, temptation, self-control, learning, menus

    Prosodic cues enhance infants’ sensitivity to nonadjacent regularities

    Full text link
    In language, grammatical dependencies often hold between items that are not immediately adjacent to each other. Acquiring these nonadjacent dependencies is crucial for learning grammar. However, there are poten-tially infinitely many dependencies in the language input. How does the infant brain solve this computational learning problem? Here, we demonstrate that while rudimentary sensitivity to nonadjacent regularities may be present relatively early, robust and reliable learning can only be achieved when convergent statistical and per-ceptual, specifically prosodic cues, are both present, helping the infant brain detect the building blocks that form a nonadjacent dependency. This study contributes to our understanding of the neural foundations of rule learning that pave the way for language acquisition

    Reinforcing connectionism: learning the statistical way

    Get PDF
    Connectionism's main contribution to cognitive science will prove to be the renewed impetus it has imparted to learning. Learning can be integrated into the existing theoretical foundations of the subject, and the combination, statistical computational theories, provide a framework within which many connectionist mathematical mechanisms naturally fit. Examples from supervised and reinforcement learning demonstrate this. Statistical computational theories already exist for certainn associative matrix memories. This work is extended, allowing real valued synapses and arbitrarily biased inputs. It shows that a covariance learning rule optimises the signal/noise ratio, a measure of the potential quality of the memory, and quantifies the performance penalty incurred by other rules. In particular two that have been suggested as occuring naturally are shown to be asymptotically optimal in the limit of sparse coding. The mathematical model is justified in comparison with other treatments whose results differ. Reinforcement comparison is a way of hastening the learning of reinforcement learning systems in statistical environments. Previous theoretical analysis has not distinguished between different comparison terms, even though empirically, a covariance rule has been shown to be better than just a constant one. The workings of reinforcement comparison are investigated by a second order analysis of the expected statistical performance of learning, and an alternative rule is proposed and empirically justified. The existing proof that temporal difference prediction learning converges in the mean is extended from a special case involving adjacent time steps to the general case involving arbitary ones. The interaction between the statistical mechanism of temporal difference and the linear representation is particularly stark. The performance of the method given a linearly dependent representation is also analysed

    Input-driven unsupervised learning in recurrent neural networks

    Get PDF
    Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is an attractor neural network with Hebbian learning (e.g. the Hopfield model). The model simplicity and the locality of the synaptic update rules come at the cost of a limited storage capacity, compared with the capacity achieved with supervised learning algorithms, whose biological plausibility is questionable. Here, we present an on-line learning rule for a recurrent neural network that achieves near-optimal performance without an explicit supervisory error signal and using only locally accessible information, and which is therefore biologically plausible. The fully connected network consists of excitatory units with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the patterns to be memorized are presented on-line as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs (’local fields’). Synapses corresponding to active inputs are modified as a function of the position of the local field with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. An additional parameter of the model allows to trade storage capacity for robustness, i.e. increased size of the basins of attraction. We simulated a network of 1001 excitatory neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction: our results show that, for any given basin size, our network more than doubles the storage capacity, compared with a standard Hopfield network. Our learning rule is consistent with available experimental data documenting how plasticity depends on firing rate. It predicts that at high enough firing rates, no potentiation should occur
    • 

    corecore