Mathematical models of learning and what can be learned from them.

Learning is a multi-faceted phenomenon of critical importance and hence attracted a great deal of research, both experimental and theoretical. In this review, we will consider some of the paradigmatic examples of learning and discuss the common themes in theoretical learning research, such as levels of modeling and their corresponding relation to experimental observations and mathematical ideas common to different types of learning.

Forgetting dynamics for items of different categories.

How the dynamic evolution of forgetting changes for different material types is unexplored. By using a common experimental paradigm with stimuli of different types, we were able to directly cross-examine the emerging dynamics and found that even though the presentation sets differ minimally by design, the obtained curves appear to fall on a discrete spectrum. We also show that the resulting curves do not depend on physical time but rather on the number of items shown.

Cross-fixation interactions of orientations suggest high-to-low-level decoding in visual working memory.

Sensory encoding (how stimuli evoke sensory responses) is known to progress from low- to high-level features. Decoding (how responses lead to perception) is less understood but is often assumed to follow the same hierarchy. Accordingly, orientation decoding must occur in low-level areas such as V1, without cross-fixation interactions.

Effects of order on memory of event times.

Memorizing time of an event may employ two processes (1) encoding of the absolute time of events within an episode, (2) encoding of its relative order. Here we study interaction between these two processes. We performed experiments in which one or several items were presented, after which participants were asked to report the time of occurrence of items.

Biases and Variability from Costly Bayesian Inference.

When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are updated as a function of sequential observations. We introduce a theoretical framework in which biases and variability emerge from a trade-off between Bayesian inference and the cognitive cost of carrying out probabilistic computations.

Multiscale representation of very large environments in the hippocampus of flying bats.

Hippocampal place cells encode the animal's location. Place cells were traditionally studied in small environments, and nothing is known about large ethologically relevant spatial scales. We wirelessly recorded from hippocampal dorsal CA1 neurons of wild-born bats flying in a long tunnel (200 meters).

Retroactive interference model of forgetting.

Memory and forgetting constitute two sides of the same coin, and although the first has been extensively investigated, the latter is often overlooked. A possible approach to better understand forgetting is to develop phenomenological models that implement its putative mechanisms in the most elementary way possible, and then experimentally test the theoretical predictions of these models. One such mechanism proposed in previous studies is retrograde interference, stating that a memory can be erased due to subsequently acquired memories.

Fundamental Law of Memory Recall.

Human memory appears to be fragile and unpredictable. Free recall of random lists of words is a standard paradigm used to probe episodic memory. We proposed an associative search process that can be reduced to a deterministic walk on random graphs defined by the structure of memory representations.

Emergence of hierarchical organization in memory for random material.

Structured information is easier to remember and recall than random one. In real life, information exhibits multi-level hierarchical organization, such as clauses, sentences, episodes and narratives in language. Here we show that multi-level grouping emerges even when participants perform memory recall experiments with random sets of words.

Optimal dynamic coding by mixed-dimensionality neurons in the head-direction system of bats.

Ethologically relevant stimuli are often multidimensional. In many brain systems, neurons with "pure" tuning to one stimulus dimension are found along with "conjunctive" neurons that encode several dimensions, forming an apparently redundant representation. Here we show using theoretical analysis that a mixed-dimensionality code can efficiently represent a stimulus in different behavioral regimes: encoding by conjunctive cells is more robust when the stimulus changes quickly, whereas on long timescales pure cells represent the stimulus more efficiently with fewer neurons.

Stabilizing patterns in time: Neural network approach.

Recurrent and feedback networks are capable of holding dynamic memories. Nonetheless, training a network for that task is challenging. In order to do so, one should face non-linear propagation of errors in the system.

Visual perception as retrospective Bayesian decoding from high- to low-level features.

When a stimulus is presented, its encoding is known to progress from low- to high-level features. How these features are decoded to produce perception is less clear, and most models assume that decoding follows the same low- to high-level hierarchy of encoding. There are also theories arguing for global precedence, reversed hierarchy, or bidirectional processing, but they are descriptive without quantitative comparison with human perception.

Memory States and Transitions between Them in Attractor Neural Networks.

Human memory is capable of retrieving similar memories to a just retrieved one. This associative ability is at the base of our everyday processing of information. Current models of memory have not been able to underpin the mechanism that the brain could use in order to actively exploit similarities between memories.

A theory of working memory without consciousness or sustained activity.

Working memory and conscious perception are thought to share similar brain mechanisms, yet recent reports of non-conscious working memory challenge this view. Combining visual masking with magnetoencephalography, we investigate the reality of non-conscious working memory and dissect its neural mechanisms. In a spatial delayed-response task, participants reported the location of a subjectively unseen target above chance-level after several seconds.

Theta-paced flickering between place-cell maps in the hippocampus: A model based on short-term synaptic plasticity.

Hippocampal place cells represent different environments with distinct neural activity patterns. Following an abrupt switch between two familiar configurations of visual cues defining two environments, the hippocampal neural activity pattern switches almost immediately to the corresponding representation. Surprisingly, during a transient period following the switch to the new environment, occasional fast transitions between the two activity patterns (flickering) were observed (Jezek, Henriksen, Treves, Moser, & Moser, ).

Feature Detection in Visual Cortex during Different Functional States.

Cortical activity exhibits distinct characteristics in different functional states. In awake behaving animals it shows less synchrony, while in rest or sleeping state cortical activity is most synchronous. Previous studies showed that switching between functional states can change the efficiency of flowing sensory information.

Synaptic Correlates of Working Memory Capacity.

Psychological studies indicate that human ability to keep information in readily accessible working memory is limited to four items for most people. This extremely low capacity severely limits execution of many cognitive tasks, but its neuronal underpinnings remain unclear. Here we show that in the framework of synaptic theory of working memory, capacity can be analytically estimated to scale with characteristic time of short-term synaptic depression relative to synaptic current time constant.

Practice makes perfect in memory recall.

A large variability in performance is observed when participants recall briefly presented lists of words. The sources of such variability are not known. Our analysis of a large data set of free recall revealed a small fraction of participants that reached an extremely high performance, including many trials with the recall of complete lists.

Neural Network Model of Memory Retrieval.

Human memory can store large amount of information. Nevertheless, recalling is often a challenging task. In a classical free recall paradigm, where participants are asked to repeat a briefly presented list of words, people make mistakes for lists as short as 5 words.

A unifying principle underlying the extracellular field potential spectral responses in the human cortex.

Electrophysiological mass potentials show complex spectral changes upon neuronal activation. However, it is unknown to what extent these complex band-limited changes are interrelated or, alternatively, reflect separate neuronal processes. To address this question, intracranial electrocorticograms (ECoG) responses were recorded in patients engaged in visuomotor tasks.

Effects of long-term representations on free recall of unrelated words.

Human memory stores vast amounts of information. Yet recalling this information is often challenging when specific cues are lacking. Here we consider an associative model of retrieval where each recalled item triggers the recall of the next item based on the similarity between their long-term neuronal representations.

Word length effect in free recall of randomly assembled word lists.

In serial recall experiments, human subjects are requested to retrieve a list of words in the same order as they were presented. In a classical study, participants were reported to recall more words from study lists composed of short words compared to lists of long words, the word length effect. The world length effect was also observed in free recall experiments, where subjects can retrieve the words in any order.

Short-term plasticity based network model of place cells dynamics.

Rodent hippocampus exhibits strikingly different regimes of population activity in different behavioral states. During locomotion, hippocampal activity oscillates at theta frequency (5-12 Hz) and cells fire at specific locations in the environment, the place fields. As the animal runs through a place field, spikes are emitted at progressively earlier phases of the theta cycles.

Continuous attractor network model for conjunctive position-by-velocity tuning of grid cells.

The spatial responses of many of the cells recorded in layer II of rodent medial entorhinal cortex (MEC) show a triangular grid pattern, which appears to provide an accurate population code for animal spatial position. In layer III, V and VI of the rat MEC, grid cells are also selective to head-direction and are modulated by the speed of the animal. Several putative mechanisms of grid-like maps were proposed, including attractor network dynamics, interactions with theta oscillations or single-unit mechanisms such as firing rate adaptation.

Working models of working memory.

Working memory is a system that maintains and manipulates information for several seconds during the planning and execution of many cognitive tasks. Traditionally, it was believed that the neuronal underpinning of working memory is stationary persistent firing of selective neuronal populations. Recent advances introduced new ideas regarding possible mechanisms of working memory, such as short-term synaptic facilitation, precise tuning of recurrent excitation and inhibition, and intrinsic network dynamics.