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. All measured curves were compatible with our previously developed mathematical model, hinting to a potential common underlying mechanism of forgetting.

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. We consider two forms of the cost: a precision cost and an unpredictability cost; these penalize beliefs that are less entropic and less deterministic, respectively. We apply our framework to the case of a Bernoulli variable: the bias of a coin is inferred from a sequence of coin flips. Theoretical predictions are qualitatively different depending on the form of the cost. A precision cost induces overestimation of small probabilities, on average, and a limited memory of past observations, and, consequently, a fluctuating bias. An unpredictability cost induces underestimation of small probabilities and a fixed bias that remains appreciable even for nearly unbiased observations. The case of a fair (equiprobable) coin, however, is singular, with non-trivial and slow fluctuations in the inferred bias. The proposed framework of costly Bayesian inference illustrates the richness of a 'resource-rational' (or 'bounded-rational') picture of seemingly irrational human cognition.

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. The corresponding graph model can be solved analytically, resulting in a novel parameter-free prediction for the average number of memory items recalled (R) out of M items in memory: R=sqrt[3πM/2]. This prediction was verified with a specially designed experimental protocol combining large-scale crowd-sourced free recall and recognition experiments with randomly assembled lists of words or common facts. Our results show that human memory can be described by universal laws derived from first principles.

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. Moreover, observers often inspect different parts of a scene sequentially to form overall perception, suggesting that perceptual decoding requires working memory, yet few models consider how working-memory properties may affect decoding hierarchy. We probed decoding hierarchy by comparing absolute judgments of single orientations and relative/ordinal judgments between two sequentially presented orientations. We found that lower-level, absolute judgments failed to account for higher-level, relative/ordinal judgments. However, when ordinal judgment was used to retrospectively decode memory representations of absolute orientations, striking aspects of absolute judgments, including the correlation and forward/backward aftereffects between two reported orientations in a trial, were explained. We propose that the brain prioritizes decoding of higher-level features because they are more behaviorally relevant, and more invariant and categorical, and thus easier to specify and maintain in noisy working memory, and that more reliable higher-level decoding constrains less reliable lower-level decoding.

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. Small deviations from the desired dynamics due to error or inherent noise might have a dramatic effect in the future. A method to cope with these difficulties is thus needed. In this work we focus on recurrent networks with linear activation functions and binary output unit. We characterize its ability to reproduce a temporal sequence of actions over its output unit. We suggest casting the temporal learning problem to a perceptron problem. In the discrete case a finite margin appears, providing the network, to some extent, robustness to noise, for which it performs perfectly (i.e. producing a desired sequence for an arbitrary number of cycles flawlessly). In the continuous case the margin approaches zero when the output unit changes its state, hence the network is only able to reproduce the sequence with slight jitters. Numerical simulation suggest that in the discrete time case, the longest sequence that can be learned scales, at best, as square root of the network size. A dramatic effect occurs when learning several short sequences in parallel, that is, their total length substantially exceeds the length of the longest single sequence the network can learn. This model easily generalizes to an arbitrary number of output units, which boost its performance. This effect is demonstrated by considering two practical examples for sequence learning. This work suggests a way to overcome stability problems for training recurrent networks and further quantifies the performance of a network under the specific learning scheme.

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, ). Here we show that an attractor neural network model of place cells with connections endowed with short-term synaptic plasticity can account for this phenomenon. A memory trace of the recent history of network activity is maintained in the state of the synapses, allowing the network to temporarily reactivate the representation of the previous environment in the absence of the corresponding sensory cues. The model predicts that the number of flickering events depends on the amplitude of the ongoing theta rhythm and the distance between the current position of the animal and its position at the time of cue switching. We test these predictions with new analysis of experimental data. These results suggest a potential role of short-term synaptic plasticity in recruiting the activity of different cell assemblies and in shaping hippocampal activity of behaving animals.

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. The current idea is that to induce transitions in attractor neural networks, it is necessary to extinguish the current memory. We introduce a novel mechanism capable of inducing transitions between memories where similarities between memories are actively exploited by the neural dynamics to retrieve a new memory. Populations of neurons that are selective for multiple memories play a crucial role in this mechanism by becoming attractors on their own. The mechanism is based on the ability of the neural network to control the excitation-inhibition balance.

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. Moreover, some of them developed a number of consistent input-position-dependent recall strategies, in particular recalling words consecutively ("chaining") or in groups of consecutively presented words ("chunking"). The time course of acquisition and particular choice of positional grouping were variable among participants. Our results show that acquiring positional strategies plays a crucial role in improvement of recall performance.

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. The model predicts that different items stored in memory have different probability to be recalled depending on the size of their representation. Moreover, items with high recall probability tend to be recalled earlier and suppress other items. We performed an analysis of a large data set on free recall and found a highly specific pattern of statistical dependencies predicted by the model, in particular negative correlations between the number of words recalled and their average recall probability. Taken together, experimental and modeling results presented here reveal complex interactions between memory items during recall that severely constrain recall capacity.

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. We found that in the 10- to 100-Hz frequency range there was a significant reduction in the exponent χ of the 1/f(χ) component of the spectrum associated with neuronal activation. In a minority of electrodes showing particularly high activations the exponent reduction was associated with specific band-limited power modulations: emergence of a high gamma (80-100 Hz) and a decrease in the alpha (9-12 Hz) peaks. Importantly, the peaks' height was correlated with the 1/f(χ) exponent on activation. Control simulation ruled out the possibility that the change in 1/f(χ) exponent was a consequence of the analysis procedure. These results reveal a new global, cross-frequency (10-100 Hz) neuronal process reflected in a significant reduction of the power spectrum slope of the ECoG signal.

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. During immobility, hippocampus exhibits sharp irregular bursts of activity, with occasional rapid orderly activation of place cells expressing a possible trajectory of the animal. The mechanisms underlying this rich repertoire of dynamics are still unclear. We developed a novel recurrent network model that accounts for the observed phenomena. We assume that the network stores a map of the environment in its recurrent connections, which are endowed with short-term synaptic depression. We show that the network dynamics exhibits two different regimes that are similar to the experimentally observed population activity states in the hippocampus. The operating regime can be solely controlled by external inputs. Our results suggest that short-term synaptic plasticity is a potential mechanism contributing to shape the population activity in hippocampus.

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. In this paper, we present a new attractor network model that accounts for the conjunctive position-by-velocity selectivity of grid cells. Our network model is able to perform robust path integration even when the recurrent connections are subject to random perturbations.

Synaptic scaling enables dynamically distinct short- and long-term memory formation.

Memory storage in the brain relies on mechanisms acting on time scales from minutes, for long-term synaptic potentiation, to days, for memory consolidation. During such processes, neural circuits distinguish synapses relevant for forming a long-term storage, which are consolidated, from synapses of short-term storage, which fade. How time scale integration and synaptic differentiation is simultaneously achieved remains unclear. Here we show that synaptic scaling - a slow process usually associated with the maintenance of activity homeostasis - combined with synaptic plasticity may simultaneously achieve both, thereby providing a natural separation of short- from long-term storage. The interaction between plasticity and scaling provides also an explanation for an established paradox where memory consolidation critically depends on the exact order of learning and recall. These results indicate that scaling may be fundamental for stabilizing memories, providing a dynamic link between early and late memory formation processes.

Scaling laws of associative memory retrieval.

Most people have great difficulty in recalling unrelated items. For example, in free recall experiments, lists of more than a few randomly selected words cannot be accurately repeated. Here we introduce a phenomenological model of memory retrieval inspired by theories of neuronal population coding of information. The model predicts nontrivial scaling behaviors for the mean and standard deviation of the number of recalled words for lists of increasing length. Our results suggest that associative information retrieval is a dominating factor that limits the number of recalled items.

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.

Mapping dynamic memories of gradually changing objects.

Our brain is able to maintain a continuously updated memory representation of objects despite changes in their appearance over time (aging faces or objects, growing trees, etc.). Although this ability is crucial for cognition and behavior, it was barely explored. Here, we investigate this memory characteristic using a protocol emulating face transformation. Observers were presented with a sequence of faces that gradually transformed over many days, from a known face (source) to a new face (target), in presentations separated by other stimuli. This practice resulted in a drastic change in the memory and recognition of the faces. Although identification of the source and older face instances was reduced, recent face instances were increasingly identified as the source and rated as highly similar to the memory of the source. Using an object perturbation method, we estimated the corresponding memory shift, showing that memory patterns shifted from the source neighborhood toward the target. Our findings suggest that memory is updated to account for object changes over time while still keeping associations with past appearances. These experimental results are broadly compatible with a recently developed model of associative memory that assumes attractor dynamics with a learning rule facilitated by novelty, shown to hold when objects change gradually over short timescales.

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. However, a study, Ding, Cueva, Tsodyks, and Qian (2017), provided evidence against the assumption and proposed that visual decoding may often follow a high-to-low-level hierarchy in working memory, where higher-to-lower-level constraints introduce interactions among lower-level features. If two orientations on opposite sides of the fixation are both task relevant and enter working memory, then they should interact with each other. We indeed found the predicted cross-fixation interactions (repulsion and correlation) between orientations. Control experiments and analyses ruled out alternative explanations such as reporting bias and adaptation across trials on the same side of the fixation. Moreover, we explained the data using a retrospective high-to-low-level Bayesian decoding framework.

Neuronal population coding of parametric working memory.

Comparing two sequentially presented stimuli is a widely used experimental paradigm for studying working memory. The delay activity of many single neurons in the prefrontal cortex (PFC) of monkeys was found to be stimulus-specific, however, population dynamics of stimulus representation has not been elucidated. We analyzed the population state of a large number of PFC neurons during a somatosensory discrimination task. Using the tuning curves of the neurons, we derived a compact characterization of the population state. Stimulus representation by the population was found to degrade after stimulus termination, and emerge in a different form toward the end of the delay. Specifically, the tuning properties of neurons were found to change during the task. We suggest a mechanism whereby information about the stimulus is contained in activity-dependent synaptic facilitation of recurrent connections.

Intracellular dynamics of virtual place cells.

The pattern of spikes recorded from place cells in the rodent hippocampus is strongly modulated by both the spatial location in the environment and the theta rhythm. The phases of the spikes in the theta cycle advance during movement through the place field. Recently intracellular recordings from hippocampal neurons (Harvey, Collman, Dombeck, & Tank, 2009 ) showed an increase in the amplitude of membrane potential oscillations inside the place field, which was interpreted as evidence that an intracellular mechanism caused phase precession. Here we show that an existing network model of the hippocampus (Tsodyks, Skaggs, Sejnowski, & McNaughton, 1996 ) can equally reproduce this and other aspects of the intracellular recordings, which suggests that new experiments are needed to distinguish the contributions of intracellular and network mechanisms to phase precession.

Continuous attractors with morphed/correlated maps.

Continuous attractor networks are used to model the storage and representation of analog quantities, such as position of a visual stimulus. The storage of multiple continuous attractors in the same network has previously been studied in the context of self-position coding. Several uncorrelated maps of environments are stored in the synaptic connections, and a position in a given environment is represented by a localized pattern of neural activity in the corresponding map, driven by a spatially tuned input. Here we analyze networks storing a pair of correlated maps, or a morph sequence between two uncorrelated maps. We find a novel state in which the network activity is simultaneously localized in both maps. In this state, a fixed cue presented to the network does not determine uniquely the location of the bump, i.e. the response is unreliable, with neurons not always responding when their preferred input is present. When the tuned input varies smoothly in time, the neuronal responses become reliable and selective for the environment: the subset of neurons responsive to a moving input in one map changes almost completely in the other map. This form of remapping is a non-trivial transformation between the tuned input to the network and the resulting tuning curves of the neurons. The new state of the network could be related to the formation of direction selectivity in one-dimensional environments and hippocampal remapping. The applicability of the model is not confined to self-position representations; we show an instance of the network solving a simple delayed discrimination task.