## Abstract

Perceptual constancy requires the brain to maintain a stable representation of sensory input. In the olfactory system, activity in primary olfactory cortex (piriform cortex) is thought to determine odour identity^{1,2,3,4,5}. Here we present the results of electrophysiological recordings of single units maintained over weeks to examine the stability of odour-evoked responses in mouse piriform cortex. Although activity in piriform cortex could be used to discriminate between odorants at any moment in time, odour-evoked responses drifted over periods of days to weeks. The performance of a linear classifier trained on the first recording day approached chance levels after 32 days. Fear conditioning did not stabilize odour-evoked responses. Daily exposure to the same odorant slowed the rate of drift, but when exposure was halted the rate increased again. This demonstration of continuous drift poses the question of the role of piriform cortex in odour perception. This instability might reflect the unstructured connectivity of piriform cortex^{6,7,8,9,10,11,12}, and may be a property of other unstructured cortices.

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## Data availability

Data will be made available upon reasonable request to the corresponding authors.

## Code availability

Code will be made available upon reasonable request to the corresponding authors.

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## Acknowledgements

We thank L. F. Abbott, S. R. Datta, S. Fusi, J. W. Krakauer, A. Kumar, M. A. Long, A. M. Michaiel, and S. L. Pashkovski for comments on the manuscript; G. W. Johnson and T. Tabachnik for assistance with instrumentation; G. Buzsáki and members of the Buzsáki laboratory, D. A. Gutnisky, and C. C. Rodgers for experimental advice; the instructors of the 2015 Advanced Course in Computational Neuroscience at the Champalimaud Foundation for instruction; D. F. Albeanu and members of the Albeanu laboratory, D. Aronov, K. A. Bolding, R. Costa, J. P. Cunningham, J. T. Dudman, W. M. Fischler, K. M. Franks, M. E. Hasselmo, V. Jayaraman, A. Y. Karpova, E. Marder, J. A. Miri, C. Poo, D. Rinberg and members of the Rinberg laboratory, E. S. Schaffer, and D. D. Stettler for comments; M. Gutierrez, C. H. Eccard, P. J. Kisloff, and A. Nemes for general laboratory support; and the Howard Hughes Medical Institute and the Helen Hay Whitney Foundation for financial support.

## Author information

### Affiliations

### Contributions

This work is the result of a close collaboration between C.E.S. and A.J.P.F., who conceived the study and designed the experiments. Experiments were performed by C.E.S., S.N.O. and A.J.P.F. The data were analysed and the manuscript was written by C.E.S, R.A. and A.J.P.F.

### Corresponding authors

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

**Peer review information** *Nature* thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Longitudinal tracking of single units in piriform cortex.

**a**, Chronic silicon probe implantation in anterior piriform cortex (green). Anatomical image and structure designations from the Allen Mouse Brain Atlas^{60} (http://www.brain-map.org). Inset, probe diagram with relative positions of the 32 recording electrodes; red, DiI marking probe position; black, cell bodies (NeuroTrace). Diagrams not to scale. **b**, Number of single units retained as a function of recording interval duration. Mean ± s.d. with individual data points; blue dotted line, linear regression; blue shading, 95% CI. *ρ* = −0.41, *P* = 1.2 × 10^{−3}, *n* = 24 recordings across 8 days, *n* = 18 recordings across 16 days, *n* = 12 recordings across 24 days, *n* = 6 recordings across 32 days, all from 6 mice. **c**, Single-unit yield for single-day record sessions. Left, per recording session as a function of time since probe implantation. Blue dotted line, linear regression; blue shading, 95% CI. *ρ* = −0.12, *P* = 0.23. Right, single-unit yields across all single-day recording sessions (*n* = 97 recording sessions in 16 mice). **d**, Left, probability density of waveform similarities for all pairs of single units simultaneously recorded within each day. Red dashed line indicates inclusion criterion (0.93, the distribution’s 99th percentile) for rejection of candidate single units recorded across multiple days. Right, probability density of refractory period violations (refractory period is defined as an inter-spike interval <1.5 ms). **e**, Average waveforms for a representative single unit recorded at each of the recording sites of the silicon probe. Waveforms from all days (0–32) are superimposed with each day plotted as a separate colour (colour scheme maintained throughout). Inset **e**,**i**, mean waveforms for days 0, 8, 16, 24, and 32 for a subset of recording sites, indicated by the grey box. Inset **e**,**ii**, mean waveforms for days 0 to 32, superimposed for a single recording site (dashed grey box). **f**, Waveform correlations for each single unit across days 0 and 32 (red) and across all single units within-day (grey); within-unit, across-days versus within-day, across-units, *P* = 4.8 × 10^{−246}, Wilcoxon rank-sum, *n* = 379 single units from 6 mice. The grey distribution is replotted from **d** (left). **g**, Single-unit waveform centroids across a 32-day interval from a representative mouse (centroid computed using spatial average across electrode positions weighted by the squared mean waveform amplitude at each electrode). Centroid for each single unit isolated on day 0 (blue circles) and days 8, 16, 24, and 32 (red circles, columns 1–4, respectively; days 0 versus 8, *n* = 100 single units; days 0 versus 16, *n*= 94 single units; days 0 versus 24, *n* = 84 single units; days 0 versus 32, *n* = 77 single units). Grey circles indicate the positions and sizes of the probe’s 32 electrode sites. **h**, Mean displacement of single-unit centroids from this mouse between day 0 (blue circle, defined at origin) and days 8, 16, 24, and 32 (red circles, columns 1–4, respectively). Grey contours indicate quintile boundaries of the distribution of centroid position displacement for the population. **i**, Top, cumulative distribution of within-unit centroid displacement (red) between day 0 and days 8, 16, 24, and 32 (columns 1–4, respectively) and across-unit centroid displacement within day (black) for this mouse. Median on day 0 versus 8 within-unit = 1.8 μm (Q1 = 1.1 μm, Q3 = 2.9 μm), across-unit = 63.5 μm (Q1 = 31.5 μm, Q3 = 107 μm); day 0 versus 16 within-unit = 2.1 μm (Q1 = 1.3 μm, Q3 = 3.2 μm), across-unit = 64.2 μm (Q1 = 32.0 μm, Q3 = 108 μm); day 0 versus 24 within-unit = 2.6 μm (Q1 = 1.5 μm, Q3 = 3.5 μm), across-unit = 64.4 μm (Q1 = 32.2 μm, Q3 = 108 μm); day 0 versus 32 within-unit = 2.8 μm (Q1 = 2.2 μm, Q3 = 4.2 μm), across-unit = 64.5 μm (Q1 = 32.1 μm, Q3 = 108 μm); for all comparisons *P* < 9.5 × 10^{−51}, Wilcoxon rank-sum, *n* as in **g**. Inset at bottom, *x*-axis 0 to 10 μm.

### Extended Data Fig. 2 Assessing the stability of single units recorded across multiple days.

**a**, **b**, Experiment time courses for 16-day (**a**) and 32-day (**b**) interval protocols. ‘Recovery’, period following headplate attachment and stereotactic targeting before silicon probe implantation to allow full recovery; ‘settling’, minimum five-week period after probe implantation to permit tissue settling and signal stabilization; ‘monitor’, minimum ten-day period during which neural signals were recorded daily to assess signal stability. Experiments began only once single units could be reliably tracked across days. ‘Record’, experiment protocol (Figs. 1a, 4a, c). ‘Familiarization’ (16-day interval experiments in **a** only), daily odorant presentation for experiments described in Fig. 4c, d and Extended Data Fig. 10d–h. **c**, For single units held during 16-day interval experiments, waveform similarity (left; Pearson’s correlation), centroid displacement (middle), and spike time ACG distance (right; Euclidean norm between normalized ACGs) measured between day 0 and subsequent days (red, ‘within-unit, across-day’) and across all single units within each day (black, ‘across-unit, within-day’). Dotted lines, median. Shading, boundaries of top and bottom quartiles (*n* = 690 single units from 7 mice). **d**, As in **c** but for single units held during 32-day interval experiments (*n* = 379 single units from 6 mice). **e**, Example spike–time autocorrelograms from two single units recorded in the same mouse on five separate days. **f**, Density heatmap showing ACG distance of pairs of simultaneously recorded single units plotted against waveform similarity (left) and distance between their centroids (right) for those pairs. Top, 16-day interval experiments (*n* = 1,248,216 pairs of single units from 7 mice on 17 days); bottom, 32-day interval experiments (*n* = 841,138 pairs of single units from 6 mice on 33 days). This shows that waveform-based features (waveform similarity and centroid distance) vary independently of the similarity of the spike–time ACGs. Thus, ACG distance is a measure of single-unit stability to which the spike-sorting pipeline is insensitive. **g**, Waveform similarity (top), centroid distance (middle), and ACG distance (bottom) for a given single unit between days 0 and 32, plotted against the same metric applied to the same single unit versus the most similar other simultaneously recorded single unit. Dashed line, unity. **h**, Mean single unit spontaneous firing rate on an individual day (baseline firing rate) compared across intervals of 8 days (*ρ* = 0.89, *n* = 2,177 single units), 16 days (*ρ* = 0.82, *n* = 1,412 single units), 24 days (*ρ* = 0.74, *n* = 816 single units) and 32 days (*ρ* = 0.68, *n* = 379 single units) from 6 mice. For all correlations, *P* < 4.0 × 10^{−52}. Each plot shows a random subset of 379 single units, to match the number of single units recorded across the 32-day interval (right). Black dashed line, unity; blue dotted line, linear regression; blue shading, 95% CI. **i**, Odour response similarity plotted against change in mean spontaneous firing rate on a symlog scale (left; *ρ* = −0.041, *P* = 0.43) and absolute spontaneous firing rate on a log scale (right; *ρ* = 0.087, *P* = 0.09) across a 32-day interval (*n* = 379 single units from 6 mice). Blue dotted line, linear regression; blue shading, 95% CI. **j**, For single units held during 16-day interval experiments, waveform similarity (left), centroid displacement (middle) and ACG distance (right) measured between days 0 and 16, plotted against odour response similarity of that same single unit (Pearson’s correlation of pairs of vectors computed on the two days, consisting of the response magnitudes for each odorant of a panel); black circles, individual units; blue dotted line, linear regression; blue shading, 95% CI. **k**, As in **j** but for single units held during 32-day interval experiments, plotting these features measured between days 0 and 32.

### Extended Data Fig. 3 A single unit is more similar to itself across days than to any other single unit on the probe.

**a**, Bottom, single unit recorded on day 32 (red, same as shown in Extended Data Fig. 1e) overlaid with the five most similar single units to it recorded on the same day (black), as measured by waveform similarity (Pearson’s correlation between waveforms). Top, spike–time cross correlograms between the example single unit and each of the five most similar single units. The absence of a dip in cross correlogram amplitude at the 0-ms time lag (refractory period violations) indicates that the example single unit and each of the five most similar single units correspond to distinct neurons. **b**, Top, for single units held across days, waveform similarity measured on day 0 versus subsequent days (red; within-unit, across-days), and waveform similarity measured between a given single unit and the ten single units most similar to it within a given day (blue; across-units, within-day). Dotted line, median. Shading, top and bottom quartiles. Bottom, cumulative distributions (left, full distribution; inset at right, expanded *x*-axis) within-unit for day 0 versus day 16 (red), ten most similar single units within a day (blue), one most similar single unit within a day (cyan). Median within-unit waveform similarity between day 0 and day 16, 0.98 (Q1 = 0.97, Q3 = 0.99); median across-unit waveform similarity with the ten most similar, 0.86 (Q1 = 0.80, Q3 = 0.90); median across-unit waveform similarity with the one most similar, 0.94 (Q1 = 0.91, Q3 = 0.95). **c**, **d**, Same analysis as in **b** but for centroid displacement and spike–time ACG distance (Euclidean norm between normalized ACGs), respectively. **c**, Median within-unit displacement between day 0 and day 16, 2.9 μm (Q1 = 1.6 μm, Q3 = 5.0 μm); median across-unit distance from the ten most similar, 11.2 μm (Q1 = 6.9 μm, Q3 = 16.5 μm); median across-unit distance from the one most similar, 6.1 μm (Q1 = 3.6 μm, Q3 = 9.3 μm). **d**, Median within-unit ACG distance between day 0 and day 16, 0.018 (Q1 = 0.012, Q3 = 0.028); median across-unit ACG distance for the ten most similar, 0.047 (Q1 = 0.031, Q3 = 0.069); median across-unit ACG distance for the one most similar, 0.044 (Q1 = 0.030, Q3 = 0.064). **e**–**g**, As in **b**–**d** but for the experiments performed across a 32-day interval. **e**, Median within-unit waveform similarity between day 0 and day 32, 0.97 (Q1 = 0.96, Q3 = 0.98); median across-unit waveform similarity with the ten most similar, 0.87 (Q1 = 0.82, Q3 = 0.91); median across-unit waveform similarity with the one most similar, 0.93 (Q1 = 0.91, Q3 = 0.96). **f**, Median within-unit displacement between day 0 and day 32, 3.5 μm (Q1 = 2.1 μm, Q3 = 5.6 μm); median across-unit distance from ten most similar, 11.2 μm (Q1 = 6.9 μm, Q3 = 16.7 μm); median across-unit distance from one most similar, 7.3 μm (Q1 = 4.6 μm, Q3 = 10.7 μm). **g**, Median within-unit ACG distance between day 0 and day 32, 0.024 (Q1 = 0.016, Q3 = 0.038); median across-unit ACG distance for the ten most similar, 0.048 (Q1 = 0.032, Q3 = 0.072); median ACG distance for the one most similar, 0.050 (Q1 = 0.030, Q3 = 0.077). All within-unit metrics are significantly different from across-unit metrics (*P* < 1.4 × 10^{−60}, Wilcoxon rank-sum), for both the one most and ten most similar comparisons, across both the 16-day (*n* = 690 single units from 7 mice) and 32-day (*n* = 379 single units from 6 mice) interval experiments. Thus, a single unit is more similar to itself across days than it is even to those single units most similar to it recorded within a given day. **h**–**j**, Receiver operator characteristic (ROC) curves showing the true positive rate versus the false positive rate for waveform similarity (**h**), centroid displacement (**i**) and ACG distance (**j**) for both 16-day and 32-day intervals for the ten most (blue) and one most (cyan) similar units. When computing the ROC, ‘signal’ was defined as the distribution with the higher mean. Dashed line corresponds to unity.

### Extended Data Fig. 4 Evoked responses in single units across days.

**a**, Activity of eight single units across a 32-day interval selected to illustrate the diversity of odour-evoked response profiles across single units within each day and within individual single units across days. Columns separate test odorants (chemical names, top). Spike rasters (rows: 7 trials per day) and PSTHs are coloured by day as indicated. Horizontal black bars, 4-s odorant stimulus epochs. The single-unit responses to individual stimuli shown in Fig. 1b are replotted here alongside responses for those single units to the seven other stimuli in the panel: Fig. 1b, left: unit 1, stimulus 7 (linalool oxide); Fig. 1b, middle: unit 2, stimulus 5 (nerol); Fig. 1b, right: unit 3, stimulus 2 (geranyl nitrile). **b**, *z*-scored odour-evoked activity of 300 randomly selected odour–unit pairs during the 4-s odorant stimulus epoch (black bars), ordered differently in each panel. Left, ordered by odour response magnitude on day 0 (replotted from Fig. 1c); middle, ordered by odour response magnitude on day 32; right, ordered by odour response magnitude individually on each day.

### Extended Data Fig. 5 Selective odour responses with stable within-day statistics and across-day drift in piriform cortex.

**a**, **b**, Fraction of single units that exhibit a significant modulation (**a**) and an increase (red) or decrease (blue) (**b**) in firing rate during the odorant stimulus epoch in response to 0–8 odorants (Wilcoxon rank-sum on firing rate during the odorant stimulus epoch versus spontaneous baseline firing rate, *α* = 0.001). **c**, Cumulative distributions (left) and mean coefficient of variation (*c*_{v}; right) of response magnitude computed on each odour test day across all trials for each odour–unit pair. Mean (95% CI) across days, *c*_{v} = 0.88 (0.87, 0.89), *n* = 19,356 odour–unit pairs. **d**, Cumulative distributions (left) and mean fraction of responses preserved per responsive single unit (right) across 8–32-day intervals (8 days: 35.0% (27.3%, 42.5%), 16 days: 19.8% (13.5%, 27.5%), 24 days: 16.9% (10.3%, 26.7%), 32 days: 6.6% (1.9%, 17.5%); *ρ* = –0.25, *P* = 5 × 10^{−6}, *n* = 318 single units). Non-responsive and broadly responsive single units were excluded from the analysis by setting a threshold on lifetime sparseness (0.65). **e**, Left, fraction of preserved responses per single unit across 32 days versus lifetime sparseness threshold. Right, fraction of single units stable across 32 days versus lifetime sparseness threshold. A single unit was considered stable over 32 days if all significantly modulated responses to the odorant panel were preserved. These quantities do not depend on lifetime sparseness threshold (0.2–0.65, 40th–95th percentile across all single units). **f**, Classification accuracy (8-way, SVM, linear kernel, L2 regularization, trained and tested on data stitched across 3 mice, random draws of 231 single unit subsets from 286 total single units to avoid saturation, 1-s sliding window, 250-ms steps). Grey box, 4-s odorant stimulus epoch; vertical dotted line, onset of odour response at odour port (mean time across all stimuli at which the PID signal reached 5% of maximum); horizontal dashed line, chance performance for 8-way classification. **g**, Classification performance for fifteen temporal binnings of the odour response epoch, measured by maximum classification accuracy (top) and number of single units required to reach 50% of maximum accuracy (bottom) (*n* = 286 single units recorded within-day, stitched across 3 mice). Black shading, binning used for all subsequent classification and for computation of pairwise population vector correlations, angles and drift rate, unless otherwise indicated. For classification using single bins, the window start was set to 500 ms after stimulus initiation so the quantification windows did not begin before odorant stimulus onset as measured by the PID signal. **h**, Classification accuracy as a function of number of single units used, using the highest performance binning in **g** (four 2-s bins). Dashed arrow, number (21) of single units required to achieve >50% classification accuracy. **i**, Classification accuracy for a classifier trained on earlier days and tested on later days (‘Forward’, replotted from Fig. 2b) compared with a model trained on later days and tested on earlier day (‘Reverse’). Dotted lines, mean; shading, s.d.; limit of 41 single units per animal with 100 permutations. **j**, Classification accuracy of a classifier trained on responses on day 24 alone (all 56 trials) and tested on day 32 compared with a model trained on 75 random subsets of 56 trials drawn from days 0–24 and tested on day 32; *P* = 2.6 × 10^{−5}, Wilcoxon rank-sum, 100 random subsets of 23 single units per mouse. A classifier trained on concatenated data from days 0–24 will assign high weights to single units with stable (less variable) responses across all days and low weights to single units whose responses varied. Thus, if there is a special population of neurons whose responses are informative about stimulus class and are more stable than others, a model trained on a concatenation of days 0 through 24 ought to perform better when tested on day 32 than a model trained on day 24 alone. However, we do not observe this: thus, it is not possible to establish single units that are most informative about odour identity on day 32 based on their responses across days 0–24. This finding argues against the presence of an informative stable subpopulation. **k**, Representational drift between a pair of days can be estimated by measuring the difference in odour-evoked population responses across days after correcting for within-day variability^{25}. Top left, variability across days (across-day drift + within-day variability), estimated by computing the angle (*θ*_{p,q}) between trial-averaged population vectors **u**_{p} and **u**_{q} for each odour across each pair of days *p* and *q*. Bottom left, variability within a day (noise), estimated by measuring the mean of the angle between the trial-averaged population vectors (\(\bar{\theta }\)) for each odour within each day on odd trials versus even trials (*θ*_{k}, over all days *k*). Right, the drift rate (*r*_{p,q}) is the corrected angle \(({\theta }_{p,q}-\,\bar{\theta }\)) divided by the time between days *p* and *q* (Δ*t*_{p,q}). **l**, Cumulative distributions (left) and mean angles (right) between trial-averaged population vectors within-day and across 8–32-day intervals (*n* = 180, *n* = 144, *n* = 108, *n* = 72 and *n* = 36 pairs, respectively). Blue dotted line, exponential regression fit with \(\theta \,=\,C\,-\,(C-R)\,{e}^{\frac{-t}{\tau }}\), where \(\theta \) is the variability (angle), *C* the asymptote, *R* the intercept at *t* = 0 (within-day variability), and *τ* the time constant of the exponential in days. The mean rate of change of the exponential fit over the 32-day interval is 1.0 ° per day. **m**, Cumulative distributions (left) and mean within-day angles (right) between trial-averaged population vectors (*n* = 72 pairs per day). No pair of within-day angles differs significantly (*P* ≥ 0.56 for all pairs, Wilcoxon rank-sum). Black crosses, mean ± 95% CI; blue dotted line, linear regression; blue shading, 95% CI. Classification performed on the three mice presented with an eight-odorant panel. Otherwise, *n* = 6 mice.

### Extended Data Fig. 6 Odorant stimuli.

**a**, PID signals for an example odorant (anisole) across a 32-day interval from a single experiment. Black traces, individual trials; red traces, within-day mean (*n* = 7 trials). **b**, Example PID traces for all other odorant stimuli used in this study. Black traces, individual trials on one day; red, mean (*n* = 7 trials). **c**, Mean PID amplitude across all intervals for experiments in which odorants were presented every 8 days. PID amplitude for a given odorant stimulus is highly correlated across sessions (8-day interval, *ρ* = 0.99, *P* = 6.9 × 10^{−276}, *n* = 288 comparisons; 16-day interval, *ρ* = 0.99, *P* = 7.9 × 10^{−166}, *n* = 208 comparisons; 24-day interval, *ρ* = 0.98, *P* = 6.2 × 10^{−94}, *n* = 128 comparisons; 32-day interval, *ρ* = 0.98, *P* = 3.7 × 10^{−46}, *n* = 64 comparisons). **d**, Left, coefficient of variation of PID amplitude across all trials for each odorant for experiments in which odorants were presented every 8 days (median across all odorants: *c*_{v} = 0.02, (Q1 = 0.01, Q3 = 0.04), *n* = 400 mean odorant stimulus pulses computed across 2,800 individual trials for 12 distinct odorants). Middle, rise time (median across all odorants 0.47 s (Q1 = 0.21, Q3 = 1.0 s)). Right, decay time of PID signal (median across odorants 0.51 s (Q1 = 0.21 s, Q3 = 1.3 s)). PID signal onset was defined as the time required to reach 5% of maximum on each trial. PID rise time was defined as the time between onset and 66% of maximum on each trial; PID decay time was defined as the time between 95% and 33% of maximum after stimulus offset. Anisole *n* = 350 trials, 50 days; isopentyl acetate *n* = 231 trials, 33 days; ethyl *trans*-3-hexenoate *n* = 350 trials, 50 days; octanal *n* = 245 trials, 35 days; linalool oxide 231 trials, 33 days; *cis*-3-hexen-1-ol *n* = 245 trials, 35 days; geranyl nitrile *n* = 168 trials, 24 days; cuminaldehyde *n* = 168 trials, 24 days; R-(−)-carvone *n* = 63 trials, 9 days; methyl salicylate *n* = 63 trials, 9 days; decanal *n* = 231 trials, 33 days; nerol *n* = 231 trials, 33 days. Grey bars, mean across all experiments by odorant; black bars, 95% CI. **e**, Corrected angle as a function of interval for each odorant stimulus used in 32-day interval experiments. Black crosses, mean ± 95% CI. Decanal: corrected angle correlation across intervals, *ρ* = 0.63, *P* = 3.5 × 10^{−6} and drift rate, 0.8 (0.5 – 1.1)° per day (*n* = 45 population vector pairs from 3 mice). Isopentyl acetate: corrected angle correlation across intervals, *ρ* = 0.63, *P* = 2.3 × 10^{−11} and drift rate, 1.0 (0.8 – 1.3)° per day (*n* = 90 population vector pairs from 6 mice). *cis*-3-Hexen-1-ol: corrected angle correlation across intervals, *ρ* = 0.87, *P* = 1.7 × 10^{−14} and drift rate, 1.0 (0.7 – 1.3)° per day (*n* = 45 population vector pairs from 3 mice). Ethyl *trans*-3-hexenoate: corrected angle correlation across intervals, *ρ* = 0.766, *P* = 1.3 × 10^{−9} and drift rate, 1.3 (1.1 – 1.6)° per day (*n* = 45 population vector pairs from 3 mice). Linalool oxide: corrected angle correlation across intervals, *ρ* = 0.70, *P* = 1.7 × 10^{−14} and drift rate, 1.5 (1.2 – 1.8)° per day (*n* = 90 population vector pairs from 6 mice). Nerol: corrected angle correlation across intervals, *ρ* = 0.78, *P* = 2.6 × 10^{−10} and drift rate, 1.5 (1.1 – 1.9)° per day (*n* = 90 population vector pairs from 6 mice). Cuminaldehyde: corrected angle correlation across intervals, *ρ* = 0.57, *P* = 4.2 × 10^{−5} and drift rate, 1.5 (1.1 – 2.2)° per day (*n* = 45 population vector pairs from 3 mice). Octanal: corrected angle correlation across intervals, *ρ* = 0.78, *P* = 2.6 × 10^{−10} and drift rate, 1.6 (1.3 – 1.9)° per day (*n* = 45 population vector pairs from 3 mice). Anisole: corrected angle correlation across intervals, *ρ* = 0.69, *P* = 1.7 × 10^{−7} and drift rate, 1.6 (1.2 – 2.1)° per day (*n* = 45 population vector pairs from 3 mice). **f**, Drift rate for each odorant stimulus used in 32-day interval experiments. Red dotted line, mean drift rate across all experiments (from distribution in Fig. 2e). **g**, Odorants used in this study. Numbers indicate the number of experimental replicates in which each odorant molecule was used for each experiment type. **h**, Mean, normalized PID signal recorded simultaneous to the neural signals that were used to classify odorant stimuli using a linear SVM (superimposed, reproduced from Extended Data Fig. 5f).

### Extended Data Fig. 7 Drift during the early phase of the odour response.

**a**, Mean local field potential over all 32 electrodes (filtered 0.1–20 Hz) from an example trial. We estimated the time of first sniff onset following stimulus onset by detecting the first peak of this oscillation on each trial. Only spikes that occurred within the 190 ms after and 10 ms before the detection of sniff onset were analysed (first sniff epoch). Arrowhead, estimated sniff onset. Grey bar, 4-s odorant stimulus epoch. **b**, Red, classification accuracy (4-way, SVM, linear kernel, L2 regularization) of single-trial *z*-scored population vectors as a function of interval using only the 200-ms window during the first sniff (as estimated by the first peak in the local field potential) in this mouse (*n* = 71 single units). Classification performance on day 0 computed using leave-one-out cross-validation. For all other intervals the model was trained on all responses from the earlier day and tested on all responses from the later day, as in Fig. 2b. Black, performance with stimulus labels shuffled; mean ± s.d. **c**–**e**, As in Fig. 2c–e, but for only the first sniff epoch in this mouse (8-day interval, *n* = 32 pairs of trial-averaged population vectors; 16-day interval, *n* = 24 pairs; 24-day interval, *n* = 16 pairs; 32-day interval, *n* = 8 pairs; within day, all days *n* = 40 pairs). **f**, Top, odour–odour correlation matrices computed on each day during the first sniff epoch in this mouse; middle, bottom, matrices computed using complementary splits of the trials recorded on each day. **g**, Correlation matrix dissimilarity (scaled Frobenius norm; see Methods). **h**, **i**, As in Fig. 3b, c but for only the first sniff epoch in this mouse. **h**, Edge angle matrices; **i**, edge angle matrix dissimilarity (scaled Frobenius norm; see Methods). Black crosses, mean ± 95% CI; blue dotted line, linear regression; blue shading, 95% CI.

### Extended Data Fig. 8 Drift in response geometry under diverse similarity metrics and temporal binnings.

**a**, Top, odour–odour correlation matrices computed within each odour test day using all trials (from same mouse as in Fig. 3b); middle, bottom, computed using splits of three trials per stimulus (middle) and the complementary four trials per stimulus (bottom) recorded on that day. Odour–odour correlation matrices were computed from trial-averaged population response vectors to eight odorant stimuli recorded on each of the five days. **b**, Correlation matrix dissimilarity (Frobenius norm; see Methods) from the same mouse as in **a** (mean ± 95% CI). Grey dashed line, top, matrix dissimilarity computed using shuffled stimulus identities; bottom, matrix dissimilarity computed within all individual days; grey shading, 95% CI. *ρ* = 0.43, *P* = 4.0 × 10^{−25}. Both within- and across-day matrix dissimilarity were calculated using odour–odour correlation matrices based on trial-averaged population vectors taken across all combinations of 3-trial/4-trial splits of the data for a given odorant on a given session. Within-day differences in odour response geometry measures (odour–odour correlation matrix dissimilarity) are significantly lower than differences measured across days (*P* < 1.2 × 10^{−34} for all measures and intervals from all three mice that were presented with a panel of eight stimuli). **c**, Correlation matrix dissimilarity averaged across all three mice, after scaling results from each subject between 0 (mean within-day matrix dissimilarity) and 1 (mean shuffle matrix dissimilarity). Blue dotted line, linear regression; blue shading, 95% CI. Within-day, 525 pairs; across days, 1,050 pairs. Correlation matrix dissimilarity increases significantly for: left, raw odour–odour correlations; second from left, odour–odour correlations computed using responses projected onto the data’s first six principal components (computed separately on each day); second from right, raw cosine distances; and right, cosine distances computed using responses projected onto the data’s first six principal components (computed separately on each day). **d**, Left, correlation coefficients of normalized matrix dissimilarity versus time interval (using odour–odour correlations measured in the full neural space; that is, Pearson’s correlation *ρ* such as that reported in **c**, left), computed at 250-ms steps using a 1-s sliding window along the odour response epoch. Grey box, 4-s odorant stimulus epoch; vertical dotted line, onset of odour response at odour port (mean time across all stimuli at which the PID signal reached 5% of max). Right, correlation coefficients for normalized matrix dissimilarity versus time interval computed using 15 temporal binnings of the odour response epoch. **e**, As in **d** but using edge angles rather than correlations. This effect also holds when using responses projected onto the data’s first six principal components, as well as using cosine distance rather than Pearson’s correlation (data not shown).

### Extended Data Fig. 9 Drift in response geometry in the odour coding subspace.

**a**, Left, percentage of total variance explained by each demixed principal component (dPC)^{28} from an example mouse; middle, fraction of total stimulus (red) and condition-independent (blue) variance explained for this example mouse; right, total variance explained by stimulus dPCs (red, 78.4% (95% CI 76.0%, 79.8%)) and condition-independent dPCs (blue, 21.6% (95% CI 20.2%, 23.7%)) for the *n* = 3 mice shown a panel of 8 odorant stimuli. Dark red, variance explained by the first ten dPCs that were primarily stimulus coding (45% (41.8%, 48.6%)). Error bars, 95% CI. **b**, Odour–odour correlation matrices from the example mouse computed after projecting responses onto the data’s first ten stimulus-coding dPCs, computed separately on each day (top row) and then (bottom two rows) using complementary splits of the trials recorded on each day. **c**, Correlation matrix dissimilarity (scaled Frobenius norm; see Methods) for all mice, using responses projected onto the data’s first ten stimulus-coding dPCs. **d**, Edge angle matrices from the example mouse computed after projecting responses onto the data’s first ten stimulus-coding dPCs. **e**, Across-day edge angle matrix dissimilarity (scaled Frobenius norm; see Methods) for all mice, using responses projected onto the data’s first ten stimulus-coding dPCs. Black crosses, mean ± 95% CI; blue dotted line, linear regression; blue shading, 95% CI.

### Extended Data Fig. 10 Effect of fear conditioning and familiarity on drift.

**a**, Conditioning experiment. Day −1: present one odorant paired with shock (CS+) and a second without shock (CS−) in a conditioning chamber. Days 0 and 16: administer conditioned (CS+ and CS−) and four additional neutral odorants to head-fixed mouse while recording neural signals and measuring behavioural responses in a virtual burrow assay^{29}. Days 1–15: record neural signals in head-fixed mouse without test odorant administration. **b**, Behaviour. Left, trial-averaged ingress amplitude (*n* = 5 mice) across time on days 0 and 16 on trial blocks 2–7 (shading, 95% CI). Grey bar, 4-s odorant stimulus epoch. Right, mean ± 95% CI ingress amplitude during the final second of the odorant epoch on blocks 2–7. For days 0 and 16, CS+ vesus CS− and CS+ versus neutral, *P* < 1.4 × 10^{−3}, Wilcoxon rank-sum. **c**, Neurophysiology. Left, scatter plots showing single-unit response magnitude for all three stimulus classes (mean spontaneous baseline-subtracted evoked responses computed during the odorant stimulus epoch) of odour–unit pairs on day 0 versus day 16 (CS+: *n* = 148 odour–unit pairs, CS−: *n* = 129 odour–unit pairs, neutral stimuli: *n* = 482 odour–unit pairs, data pooled across 5 mice). Black dashed line, unity; blue dotted line, linear regression; blue shading, 95% CI. Regression was performed across all odour–unit pairs that showed a significantly modulated response on at least one of the two days (Wilcoxon rank-sum, *α* = 0.001). Middle, cumulative distributions; right, mean ± 95% CI (*n* = 5 mice) of corrected angles for all three classes of stimulus. For all comparisons, *P* > 0.05 (Wilcoxon rank-sum). We note that classical conditioning reduces within-day variability (unpublished observations). Thus, the odour–unit pair response correlations reported here, which are not corrected for within-day variability, are higher than in other experiments (for example, Fig. 2a), but measures that correct for within-day variability, such as corrected angle or drift rate, are comparable. **d**, Familiarity experiment. Mice were presented with a panel of four neutral odorants daily over a 32-day interval (days −16 to 16; familiar). Starting on day 0, a panel of unfamiliar odorants was presented at 8-day intervals. **e**, Mean odour-evoked response magnitude (spontaneous baseline-subtracted, computed during the odorant stimulus epoch) of odour–unit pairs across intervals of 8 days (left, familiar odorants: *n* = 741 odour–unit pairs, unfamiliar odorants: *n* = 1,137 odour–unit pairs) and 16 days (right, familiar odorants: *n* = 371 odour–unit pairs, unfamiliar odorants: *n* = 570 odour–unit pairs), data pooled across 5 mice. Black dashed line, unity; blue dotted line, linear regression; blue shading, 95% CI. Regression was performed across all odour–unit pairs that showed a significantly modulated response on at least one of the two days (Wilcoxon rank-sum, *α* = 0.001). **f**, Across-day classification accuracy (4-way, SVM, linear kernel, L2 regularization, scaled between chance and maximum within-day performance to account for slight differences in within-day performance between the two conditions). Solid lines, mean; shading, 95% CI. **g**, **h**, Cumulative distribution (**g**) and mean ± 95% CI (**h**) of corrected angles from *n* = 5 mice. Unfamiliar, *ρ* = 0.48, *P* = 1.0 × 10^{−4}; familiar, *ρ* = 0.23, *P* = 0.08.

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Schoonover, C.E., Ohashi, S.N., Axel, R. *et al.* Representational drift in primary olfactory cortex.
*Nature* **594, **541–546 (2021). https://doi.org/10.1038/s41586-021-03628-7

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