Neural coding

How neural responses represent variables relevant to an organism. A coding claim specifies both which response features carry information and how a downstream system can use them.

Dependence of a neural response on combinations of task variables. A cell can carry information about an object in a context and at a sequence position rather than encode only one of these variables.

The number of recorded action potentials in a specified interval. A count is a nonnegative integer; a fitted firing rate or an expected count need not be an integer.

The number of action potentials per unit time, interpreted as an average over a stated window or as an intensity estimated from a spike train. Window size changes which temporal information remains visible.

A group of neurons whose coordinated activity and learned interactions can represent or participate in an experience. An assembly can overlap with assemblies for other events; it need not assign one private neuron to each memory.

Suppose storing activities $a_1,\dots ,a_T$ changes a matrix by $\Delta W=\eta {\sum }_{t=1}^T{a}_t{a}_t^T$. Any permutation of the activities leaves this sum unchanged. Therefore the update alone cannot distinguish an episode from its reversal. This is a restriction on the stated order-insensitive update, not on all Hebbian learning: trace learning, an evolving context or directed transitions can introduce order information.

An account of regional specialization in terms of the complexity and conjunctions represented, rather than a strict division between perception and memory. The feature-conjunction account of perirhinal cortex proposes object-level combinations that resolve shared-feature ambiguity; higher-order relations can require further interactions.^[ref]

A neuron active preferentially at a particular part of a temporally extended task or interval. Temporal selectivity can coexist with selectivity for location, behavior and sequence identity; it is not a claim that the cell is an isolated clock.

A representation of relations among locations or task states that can support inference beyond memorized stimulus–response pairs. The represented space need not be physically spatial. A cognitive-map hypothesis specifies which states and relations are encoded and what behaviour can use them.

A hippocampal population event involving a sharp wave and fast ripple oscillation, often associated with internally generated ensemble activity. Selective interruption can test its contribution to memory, but disrupting an event does not by itself identify the content or computational role of each participating sequence.^[ref]

A representation of position or orientation in an external reference frame. Transforming a retinal direction to a world location generally needs eye position, head orientation, self-location and depth or scene geometry. A label in world coordinates is a description of the code, not an explanation of how it develops.

A neuron selective for a viewed location in external space. In the primate recordings motivating the term, eye-position and locomotion measurements distinguished the looked-at part of the environment from the animal’s self-location and head direction.^[ref]

A neuron whose activity is spatially selective for the animal’s own location under specified conditions. Its field can depend on environment, task and sensory context; a visual view and self-location must be disentangled experimentally.

A change in a hippocampal spatial representation across environments or contexts. Models distinguish changes in firing rates, field locations and the relationships among simultaneously recorded units; visual cue changes need not produce one universal kind of response.

A neuron whose firing varies with the orientation of the head relative to the environment. Preferred direction must be distinguished from gaze direction and self-location. Landmark rotation and cue-removal experiments test the visual anchor of this code.^[ref]

Rhythmic variation in neural signals. Frequency-band averages can obscure brief events; the timing and duration of bursts can matter independently of mean spectral power.

A neural rhythm in the frequency range conventionally called theta. In rodent hippocampal experiments it provides a temporal reference for comparing the firing of local and remote cells. A matching rhythm does not alone identify the direction or necessity of communication.

A neural oscillation in the frequency band conventionally termed beta, below gamma. Its functional interpretation depends on task, site and temporal structure rather than on frequency alone.

A neural oscillation in a relatively high-frequency band conventionally termed gamma. Exact band boundaries vary by study and recording method.

An extracellular voltage reflecting weighted contributions from nearby and sometimes more distant neuronal currents. Its spatial sensitivity depends on anatomy, electrode placement and signal properties; it is not simply the firing rate of the nearest cell.

Inferring a stimulus, task state or behavior from neural measurements. Successful decoding demonstrates information accessible to the chosen decoder; it does not by itself establish the neural site's causal necessity, exclusive representation or downstream use.

Representation through the joint activity of multiple neurons. Information can reside in relative activity patterns even when the overall mean activity changes little. Neural decoding tests whether recorded patterns carry accessible information under a specified analysis.

Statistical dependence between neural responses remaining after the modeled task-related mean has been removed. Residual dependence can reflect shared state or omitted task variables as well as biological noise, so its interpretation depends on the conditioning model.

Coordinates describing the joint activity of a neural population, often using one coordinate per cell or fitted latent variable. A trajectory connects states over time. A useful reduced description requires evidence that it retains the neural and behavioral properties relevant to the intended claim.

In the observation model $y=Cz+b$, let $Q$ be an orthogonal matrix. Replacing $z$ by $Qz$ and $C$ by $C{Q}^T$ leaves $y$ unchanged because $Q^{T}Q=I$. Thus reconstruction alone does not give each latent axis a unique biological meaning. A particular stochastic model can restrict this symmetry through its prior and parameter constraints; the algebra does not claim every fitted latent model has every rotational ambiguity.

A proposed lower-dimensional set around which recorded population states are organized. The estimated dimension depends on sampling, noise, preprocessing and the scale of variation. A visually smooth embedding is not by itself proof of an intrinsic biological manifold.

The evolution of a population representation over time. A trajectory estimated after trial averaging or strong smoothing can differ from every individual-trial trajectory; this distinction matters for claims about neural dynamics.

Sustained neural activity outlasting a triggering input. Recurrent network dynamics can support persistent representations, but a sustained average signal can also conceal temporally variable events across trials or cells.

The region and stimulus features whose variation influences a sensory neuron's response. A visual receptive field may include spatially distinct ON and OFF regions; a linear receptive-field kernel is a signed weighting map, while the full response can be nonlinear and depend on stimulus history.

ON and OFF receptive-field subregions distinguish locations by response polarity. In the classic mapping experiment, a bright spot in an ON region increased firing during illumination; illumination in an OFF region suppressed maintained firing and/or evoked a discharge when the light disappeared. If maintained firing was very low, suppression could be hard to see. The recorded decrease alone did not distinguish direct inhibition at a synapse from reduced excitation. ^[ref] These are functional regions in visual space, not compartments of a cell body.

For the toy models here, visual contrast means brightness relative to a positive uniform background $L_0$: $C(x,y)=(L(x,y)-L_0)/L_0$. Positive values mean brighter than background, negative values darker, and zero unchanged. This convention separates spatial structure from the background level. A sinusoid $C=a\cos (\cdots )$ with $0\le a\le 1$ keeps $L=L_0(1+C)$ nonnegative. Different experimental conventions for visual contrast require their own definitions; the toy values below do not specify a historical stimulus intensity.

Representation by spike timing, latency, phase or relative timing across neurons, beyond a chosen count summary. Its interpretation requires a timing reference and a decoder capable of resolving the relevant precision.

A tendency for neural spikes to occur at preferred phases of a periodic stimulus. It supplies timing information without requiring one spike on every cycle. Its precision and usable frequency range depend on the cell population and conditions.

Representation by a neuron's firing frequency or the expected spike count in a chosen time window. The window length and averaging convention matter; equal counts do not imply equal temporal patterns.

A sequence of action potential times, represented mathematically as a point process or a sum of Dirac deltas. Its event counts, intervals and correlations summarize different aspects of neural activity.

An interspike interval is the elapsed time between consecutive action potentials in a spike train. Its probability distribution and dependence on previous activity can reveal a neuronal refractory period even when the average firing rate is unchanged.

For a correctly specified conditional rate, transformed interspike intervals have independent unit-exponential distributions, apart from observation-boundary censoring. Their transforms $1-e^{-z_i}$ should be uniform. Distributional checks and serial-correlation checks assess a fitted spike model on held-out data. A history-dependent model must include past spikes in its conditional rate; stimulus-only Poisson spike-train likelihood fitting cannot automatically capture refractoriness.