Searching for memories, Sudoku, implicit check bits, and the iterative use of not-always-correct rapid neural computation.

The algorithms that simple feedback neural circuits representing a brain area can rapidly carry out are often adequate to solve easy problems but for more difficult problems can return incorrect answers. A new excitatory-inhibitory circuit model of associative memory displays the common human problem of failing to rapidly find a memory when only a small clue is present. The memory model and a related computational network for solving Sudoku puzzles produce answers that contain implicit check bits in the representation of information across neurons, allowing a rapid evaluation of whether the putative answer is correct or incorrect through a computation related to visual pop-out. This fact may account for our strong psychological feeling of right or wrong when we retrieve a nominal memory from a minimal clue. This information allows more difficult computations or memory retrievals to be done in a serial fashion by using the fast but limited capabilities of a computational module multiple times. The mathematics of the excitatory-inhibitory circuits for associative memory and for Sudoku, both of which are understood in terms of energy or Lyapunov functions, is described in detail.

Encoding for computation: recognizing brief dynamical patterns by exploiting effects of weak rhythms on action-potential timing.

Many stimuli have meaning only as patterns over time. Most auditory and many visual stimuli are of this nature and can be described as multidimensional, time-dependent vectors. A simple neuron can encode a single component of the vector in a firing rate. The addition of a small subthreshold oscillatory current perturbs the action-potential timing, encoding the signal also in a timing relationship, with little effect on the coexisting firing rate representation. When the subthreshold signal is common to a group of neurons, the timing-based information is significant to neurons receiving inputs from the group. This information encoding allows simple implementation of computations not readily done with rate coding. These ideas are examined by using speech to provide a realistic input signal to a biologically inspired model network of spiking neurons. The output neurons of the two-layer system are shown to specifically encode short linguistic elements of speech.

Learning rules and network repair in spike-timing-based computation networks.

Plasticity in connections between neurons allows learning and adaptation, but it also allows noise to degrade the function of a network. Ongoing network self-repair is thus necessary. We describe a method to derive spike-timing-dependent plasticity rules for self-repair, based on the firing patterns of a functioning network. These plasticity rules for self-repair also provide the basis for unsupervised learning of new tasks. The particular plasticity rule derived for a network depends on the network and task. Here, self-repair is illustrated for a model of the mammalian olfactory system in which the computational task is that of odor recognition. In this olfactory example, the derived rule has qualitative similarity with experimental results seen in spike-timing-dependent plasticity. Unsupervised learning of new tasks by using the derived self-repair rule is demonstrated by learning to recognize new odors.

Simple networks for spike-timing-based computation, with application to olfactory processing.

Spike synchronization across neurons can be selective for the situation where neurons are driven at similar firing rates, a "many are equal" computation. This can be achieved in the absence of synaptic interactions between neurons, through phase locking to a common underlying oscillatory potential. Based on this principle, we instantiate an algorithm for robust odor recognition into a model network of spiking neurons whose main features are taken from known properties of biological olfactory systems. Here, recognition of odors is signaled by spike synchronization of specific subsets of "mitral cells." This synchronization is highly odor selective and invariant to a wide range of odor concentrations. It is also robust to the presence of strong distractor odors, thus allowing odor segmentation within complex olfactory scenes. Information about odors is encoded in both the identity of glomeruli activated above threshold (1 bit of information per glomerulus) and in the analog degree of activation of the glomeruli (approximately 3 bits per glomerulus).

What is a moment? Transient synchrony as a collective mechanism for spatiotemporal integration.

A previous paper described a network of simple integrate-and-fire neurons that contained output neurons selective for specific spatiotemporal patterns of inputs; only experimental results were described. We now present the principles behind the operation of this network and discuss how these principles point to a general class of computational operations that can be carried out easily and naturally by networks of spiking neurons. Transient synchrony of the action potentials of a group of neurons is used to signal "recognition" of a space-time pattern across the inputs of those neurons. Appropriate synaptic coupling produces synchrony when the inputs to these neurons are nearly equal, leaving the neurons unsynchronized or only weakly synchronized for other input circumstances. When the input to this system comes from timed past events represented by decaying delay activity, the pattern of synaptic connections can be set such that synchronization occurs only for selected spatiotemporal patterns. We show how the recognition is invariant to uniform time warp and uniform intensity change of the input events. The fundamental recognition event is a transient collective synchronization, representing "many neurons now agree," an event that is then detected easily by a cell with a small time constant. If such synchronization is used in neurobiological computation, its hallmark will be a brief burst of gamma-band electroencephalogram noise when and where such a recognition event or decision occurs.

What is a moment? "Cortical" sensory integration over a brief interval.

Recognition of complex temporal sequences is a general sensory problem that requires integration of information over time. We describe a very simple "organism" that performs this task, exemplified here by recognition of spoken monosyllables. The network's computation can be understood through the application of simple but generally unexploited principles describing neural activity. The organism is a network of very simple neurons and synapses; the experiments are simulations. The network's recognition capabilities are robust to variations across speakers, simple masking noises, and large variations in system parameters. The network principles underlying recognition of short temporal sequences are applied here to speech, but similar ideas can be applied to aspects of vision, touch, and olfaction. In this article, we describe only properties of the system that could be measured if it were a real biological organism. We delay publication of the principles behind the network's operation as an intellectual challenge: the essential principles of operation can be deduced based on the experimental results presented here alone. An interactive web site (http://neuron.princeton.edu/ approximately moment) is available to allow readers to design and carry out their own experiments on the organism.

From molecular to modular cell biology.

Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules. Understanding how modules work has depended on combining phenomenological analysis with molecular studies. General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints.

Odor space and olfactory processing: collective algorithms and neural implementation.

Several basic olfactory tasks must be solved by highly olfactory animals, including background suppression, multiple object separation, mixture separation, and source identification. The large number N of classes of olfactory receptor cells-hundreds or thousands-permits the use of computational strategies and algorithms that would not be effective in a stimulus space of low dimension. A model of the patterns of olfactory receptor responses, based on the broad distribution of olfactory thresholds, is constructed. Representing one odor from the viewpoint of another then allows a common description of the most important basic problems and shows how to solve them when N is large. One possible biological implementation of these algorithms uses action potential timing and adaptation as the "hardware" features that are responsible for effective neural computation.

All-or-none potentiation at CA3-CA1 synapses.

The molecular mechanisms underlying long-term potentiation in the hippocampus have received much attention because of the likely functional importance of synaptic plasticity for information storage and the development of neuronal connectivity. Surprisingly, it remains unclear whether activity modifies the strength of individual synapses in a digital (all-or-none) or analog (graded) manner. Here we characterize step-like all-or-none transitions from baseline synaptic transmission to potentiated states following protocols for inducing potentiation at putative single CA3-CA1 synaptic connections. Individual synapses appear to have all-or-none potentiation indicative of highly cooperative processes but different thresholds for undergoing potentiation. These results raise the possibility that some forms of synaptic memory may be stored in a digital manner in the brain.

Transforming neural computations and representing time.

Motifs of neural circuitry seem surprisingly conserved over different areas of neocortex or of paleocortex, while performing quite different sensory processing tasks. This apparent paradox may be resolved by the fact that seemingly different problems in sensory information processing are related by transformations (changes of variables) that convert one problem into another. The same basic algorithm that is appropriate to the recognition of a known odor quality, independent of the strength of the odor, can be used to recognize a vocalization (e.g., a spoken syllable), independent of whether it is spoken quickly or slowly. To convert one problem into the other, a new representation of time sequences is needed. The time that has elapsed since a recent event must be represented in neural activity. The electrophysiological hallmarks of cells that are involved in generating such a representation of time are discussed. The anatomical relationships between olfactory and auditory pathways suggest relevant experiments. The neurophysiological mechanism for the psychophysical logarithmic encoding of time duration would be of direct use for interconverting olfactory and auditory processing problems. Such reuse of old algorithms in new settings and representations is related to the way that evolution develops new biochemistry.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.

Pattern recognition computation using action potential timing for stimulus representation.

A computational model is described in which the sizes of variables are represented by the explicit times at which action potentials occur, rather than by the more usual 'firing rate' of neurons. The comparison of patterns over sets of analogue variables is done by a network using different delays for different information paths. This mode of computation explains how one scheme of neuroarchitecture can be used for very different sensory modalities and seemingly different computations. The oscillations and anatomy of the mammalian olfactory systems have a simple interpretation in terms of this representation, and relate to processing in the auditory system. Single-electrode recording would not detect such neural computing. Recognition 'units' in this style respond more like radial basis function units than elementary sigmoid units.

Decomposition of a mixture of signals in a model of the olfactory bulb.

We describe models for the olfactory bulb which perform separation and decomposition of mixed odor inputs from different sources. The odors are unknown to the system; hence this is an analog and extension of the engineering problem of blind separation of signals. The separation process makes use of the different temporal fluctuations of the input odors which occur under natural conditions. We discuss two possibilities, one relying on a specific architecture connecting modules with the same sensory inputs and the other assuming that the modules (e.g., glomeruli) have different receptive fields in odor space. We compare the implications of these models for the testing of mixed odors from a single source.

Olfactory computation and object perception.

Animals that are primarily dependent on olfaction must obtain a description of the spatial location and the individual odor quality of environmental odor sources through olfaction alone. The variable nature of turbulent air flow makes such a remote sensing problem solvable if the animal can make use of the information conveyed by the fluctuation with time of the mixture of odor sources. Behavioral evidence suggests that such analysis takes place. An adaptive network can solve the essential problem, isolating the quality and intensity of the components within a mixture of several individual unknown odor sources. The network structure is an idealization of olfactory bulb circuitry. The dynamics of synapse change is essential to the computation. The synaptic variables themselves contain information needed by higher processing centers. The use of the same axons to convey intensity information and quality information requires time-coding of information. Covariation defines an individual odor source (object), and this may have a parallel in vision.

Modeling the olfactory bulb and its neural oscillatory processings.

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35-60 Hz modulated activity which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transform between odor input and the bulbar output to olfactory cortex. There is significant correspondence between the model behavior and observed electrophysiology.

A molecular shift register based on electron transfer.

An electronic shift-register memory at the molecular level is described. The memory elements are based on a chain of electron-transfer molecules and the information is shifted by photoinduced electron-transfer reactions. This device integrates designed electronic molecules onto a very large scale integrated (silicon microelectronic) substrate, providing an example of a "molecular electronic device" that could actually be made. The design requirements for such a device and possible synthetic strategies are discussed. Devices along these lines should have lower energy usage and enhanced storage density.

Learning algorithms and probability distributions in feed-forward and feed-back networks.

Learning algorithms have been used both on feed-forward deterministic networks and on feed-back statistical networks to capture input-output relations and do pattern classification. These learning algorithms are examined for a class of problems characterized by noisy or statistical data, in which the networks learn the relation between input data and probability distributions of answers. In simple but nontrivial networks the two learning rules are closely related. Under some circumstances the learning problem for the statistical networks can be solved without Monte Carlo procedures. The usual arbitrary learning goals of feed-forward networks can be given useful probabilistic meaning.