Causes and consequences of representational drift

Abstract

The nervous system learns new associations while maintaining memories over long periods, exhibiting a balance between flexibility and stability. Recent experiments reveal that neuronal representations of learned sensorimotor tasks continually change over days and weeks, even after animals have achieved expert behavioral performance. How is learned information stored to allow consistent behavior despite ongoing changes in neuronal activity? What functions could ongoing reconfiguration serve? We highlight recent experimental evidence for such representational drift in sensorimotor systems, and discuss how this fits into a framework of distributed population codes. We identify recent theoretical work that suggests computational roles for drift and argue that the recurrent and distributed nature of sensorimotor representations permits drift while limiting disruptive effects. We propose that representational drift may create error signals between interconnected brain regions that can be used to keep neural codes consistent in the presence of continual change. These concepts suggest experimental and theoretical approaches to studying both learning and maintenance of distributed and adaptive population codes.

Figure 1:. Coding of spatial navigation in Posterior Parietal Cortex (PPC) drifts over days

(adapted from Driscoll et al. [4]). (A) Driscoll et al. [4] placed mice in a virtual reality environment, and required that subject remember visual cues to navigate to a target. Population activity was recorded with single-neuron resolution over days using calcium fluorescence imaging. (B) Raster plots showing average calcium signals from several hundred PPC neurons imaged over multiple days, with task location on the horizontal axis. Each row corresponds to a neuron, and mean activity is represented by color. Location-dependent activation drifted slowly over days: single neurons gained and lost location sensitivity or changed their tuning. Sorting cells by activation on any given day reveals population coding of maze location.

Figure 2:. Internal representations have unconstrained degrees of freedom that allow drift.

(A) Nonlinear dimensionality reduction of population activity recovers the low-dimensional structure of the T-maze in [4] (Figure 1a). Each point represents a single time-point of population activity, and is colored according to location in the maze. (B) Point clouds illustrate low-dimensional projections of neural activity as in (a). Although unsupervised dimensionality-reduction methods can recover the task structure on each day, the way in which this structure is encoded in the population can change over days to weeks. (C) Left: Neural populations can encode information in relative firing rates and correlations, illustrated here as a sensory variable encoded in the sum of two neural signals (y₁+y₂). Points represent neural activity during a repeated presentation of the same stimulus. Variability orthogonal to this coding axis does not disrupt coding, but could appear as drift in experiments if it occurred on slow timescales. Right: Such distributed codes may be hard to read-out from recorded sub-populations (e.g. y₁ or y₂ alone; black), especially if they entail correlations between brain areas. (D) Left: External covariates may exhibit context-dependent relationships. Each point here reflects a neural population state at a given time-point. The relationship between directions x₁ and x₂ changes depending on context (cyan vs. red). Middle: Internally, this can be represented a mixture model, in which different subspaces are allocated to encode each context, and the representations are linearly-separable (gray plane). Right: The expanded representation contains two orthogonal subspaces that each encode a separate, context-dependent relationship. This dimensionality expansions increases the degrees of freedom in internal representations, thereby increasing opportunities for drift.

Figure 3:. Local changes in recurrent networks have global effects, and global processes can compensate.

(A) The curved surfaces represent network configurations suitable for a given sensorimotor task, i.e. neural connections and tunings that generate a consistent behavior. Each axis represents different circuit parameters. Ongoing processes that disrupt performance must be corrected via error feedback to maintain overall sensorimotor accuracy (B) Colored dots represent projections of neural population activity onto task-relevant dimensions at various time-points. Activity is illustrated in three hypothetical areas, depicting a feed-forward transformation of a stimulus input into a motor output. (top) If the representation in one area changes (e.g. rotation of an internal sensory representation, ∆s, curved black arrow), downstream areas must also compensate to avoid errors (e.g. motor errors, ∆m, curved gray arrows). (bottom) Although the original perturbation was localized, compensation can be distributed over many areas. Each downstream area can adjust how it interprets its input. This is illustrated here as curved arrows, which denote a compensatory rotation that partially corrects the original perturbation. The distributed adjustment in neural tuning may appear as drift to experiments that examine only a local sub-population.