At the start of a sequence, all neural activity is set to a uniform, low value (unless stated differently in the Results section). While an image is presented to the network, the lowest area representation neurons linearly reflect the pixel-wise intensity of the input (at the bottom of Figure 2B). Error neurons in area l receive excitatory input from the activity y l of associated representation neurons as shown in the one-to-one connections in Figure 2A, and are inhibited by the summed-up predictions y ⌢ l from the higher area:

where bold letters indicate vectors and matrices and W l ( t − 1 ) denotes the symmetric weight matrix between area l and area l + 1 from the previous time step (the weights will change during learning). Strictly symmetric weight matrices as frequently used in predictive coding models (Rao and Ballard, 1999; Dora et al., 2021) lead to a weight transport problem during learning. However, it has been shown that, in combination with weight decay, symmetric weights can be obtained by learning rule comparable to ours without explicitly enforcing symmetry (Alonso and Neftci, 2021), since the locally available pre- and postsynaptic activity that determine the weight change are identical (symmetric) for each pair of feedforward and feedback connections. Each representation neuron receives inhibitory input from one error neuron in the same area and excitatory input from the weighted bottom-up errors and thus changes its activation state at each time step (see “inference” in Alg S1):

This adjustment of neural activation state x l (akin to membrane potential) of representation neurons can be interpreted as matching top-down predictions better than before (and thus reducing activity of the associated error neuron) and sending down predictions that better match representation neuron activity in the area below (thus reducing errors there). The rate at which neuronal activation is changed is governed by the parameter ϵ inf = 0.05 referred to in the following as the inference rate. The activation state x l is now translated into an output firing rate y l :

where ϕ denotes the sigmoid activation function, and Δ x a constant lateral offset of the firing threshold. The saturation of the sigmoid for large inputs corresponds to a maximal firing rate of the representation neurons, in contrast to the more artificial (rectified) linear activation functions used in Rao and Ballard (1999) and Dora et al. (2021) that do not have an upper bound.

Before training, weights are initialized to random values from a Gaussian distribution centered at zero and with standard deviation of 0.5, clipped at zero to prevent negative weights and divided by the number of neurons in the next (higher) area. After 10 inference steps, long-term adaptation of synaptic weights is conducted in a Hebbian manner, strengthening synapses between active error neurons in area l and simultaneously active representation neurons in the area above (l + 1):

with learning rate ϵ l e a r n . Apart from not using weight decay, normalization or a gating mechanism, we thus use the same learning rule as Rao and Ballard (1999) and Dora et al. (2021). Based on the slower change of synaptic efficacy in comparison to membrane potential dynamics, weights are assumed to be constant between these updates. In Equation 4 , the sign of the prediction error controls the direction of the weight change. If the prediction is too large relative to the activity of the representation neurons in this area, the error is negative, and the weight mediating the prediction will be reduced. As a result, given the same prediction, the error in the consecutive time step will be smaller. This stabilizing effect on the response of error neurons is familiar from the work of Vogels et al. (2011) that showed how Hebbian plasticity regulates inhibitory input to reduce firing and achieve a balanced global state.

To summarize, both the balanced, excitatory-inhibitory wiring of the network and the unsupervised adaptation of weights based on remaining prediction errors lead to an alignment of representations and predictions, and thus a reduction in error neuron activity. The sum of squared prediction errors can then be seen as an implicit objective function, upon which the inference steps conduct an approximate gradient descent taking into account only the sign and not value of the derivative of the activation function, unlike (Whittington and Bogacz, 2017), and upon which learning conducts a precise gradient descent.

We trained the network on temporally dynamic inputs, using short video sequences. After validating network performance on moving horizontal and vertical bars, we switched to using 10 digits of the MNIST handwritten digits dataset (one per digit from 0 to 9). Each sequence contained six gradually transformed images, and separate datasets were created for translational motion, rotation, and scaling (Figure 3). For translational and rotational motion, two transformation speeds were used, differing in overlap between consecutive images. The examples shown in Figure 3 are from the dataset with larger step size (“fast” condition). To further examine robustness of the training paradigm under more realistic and less sparse inputs, random noise patterns were added to the image background during training. A last dataset consisted of five high-pass filtered images of toy objects (an airplane shown in the last row of Figure 3, a sports car, a truck, a lion and a tin man) from the smallNORB dataset (LeCun et al., 2004), undergoing a rotation.

The network was trained on the 10 (for the toy objects: five) sequences, each presenting a different digit, for multiple epochs. Each epoch consisted of 10 iterations of the same sequence (e.g., of a moving digit ‘6’) before switching to the next (of digit ‘7’). All hyperparameters are summarized in Supplementary material 1.1. This repetition of individual sequences drastically improved network performance and could be achieved by the brain through a replay or reactivation mechanism (observed in visual cortex by Ji and Wilson, 2007 and Xu et al., 2012, see also Wilson and McNaughton, 1994; Lansink et al., 2009). For laterally moving stimuli, repeated presentation can also be achieved by object-tracking saccades that lead to repeated motion across the same photoreceptors on the retina. As the most information-neutral state, the activity was reset to uniform, low values at the beginning of each sequence. This assumption is justified for objects that are seen independently of each other; for instance, not every ‘6’ is followed by a ‘7’ (but see Supplementary material 1.15 for how this assumption can be relaxed). For each image, multiple inference-learning cycles (Equation 1–4) were conducted before switching to the next image in the sequence. A training epoch consisted of an iteration through all sequences from the dataset. Supplementary material 1.2 contains the pseudocode for the nested training loops.

To quantify to what extent the network learned representations that are invariant to transformation, while at the same time retaining meaningful information about sample identity, we combined representational similarity analysis (Kriegeskorte et al., 2008) with linear decoding. The distance d between two representations r 1 and r 2 , vectors of neural activity in a model area, was measured via cosine dissimilarity:

Linear decoding was conducted by mapping the inferred representations through a fully connected layer to a layer with one neuron per class label. We implemented this via the linear model class and fitting function of the sklearn library in Python.¹ Decodability was then measured by the classification accuracy on representations that the decoder had not been presented with before. How well the decoder generalized from representations of a subset of samples from each sequence to the other views of the object is a direct measure of downstream usefulness in the scenario outlined in Figure 1.

We found that neurons in network area 3 became tuned to samples in a position-invariant manner. To quantify invariance, we analyzed the neural representations in the highest area of trained networks (Figure 2) under changes of inputs. More specifically, inference was run on still images from the training datasets until convergence was reached (see Supplementary material 1.3 for a description of convergence). Then, pairwise comparison of inferred area 3 representations measured in cosine distance quantified representational dissimilarity between representations of the same sample, e.g., a digit (within-sequence) or different samples (across-sequence). All pairwise values were plotted in Representational Dissimilarity Matrices (RDMs, Kriegeskorte et al., 2008) in Figure 4.

Indicating invariance, RDMs of trained networks showed high similarity within sequences; for instance, Digit “1”, “2”, etc. was represented by highly similar activity patterns in area 3, irrespective of position. Representations of samples from different sequences, such as digit “1” and digit “2” at the same position were distinct, as indicated by a high dissimilarity in matrix elements off the block diagonal. The same held true for the rotating and scaling digits (Figures 4B,E) as well as for the five rotating toy objects (Figure 4F). Supplementary material 1.9 contains a proof of principle demonstration of learning multiple transformations in the same network. Noise (shown for the translational motion in Figure 4D versus the noiseless motion in Figure 4C) slightly degraded clarity of the RDM but preserved the overall structure well. Additionally, the structure of the RDM proved to be quite tolerant to smaller weight initialization (Supplementary material 1.7).

Invariance of representations was a consequence of learning from inputs that are transformed continuously in the temporal domain as evidenced by the RDMs of the untrained network that showed very little structure (Figure 4A, note the different color scale, cosine distance below 0.001). Networks trained on the static frames of the sequences, in which activity was reset after each frame also lacked a block-diagonal structure (Supplementary Figure S2), illustrating the role of continuous motion in the training paradigm, which is to provide the necessary temporal structure in which subsequent inputs can be assumed to be caused by the same objects. Interestingly, we did not find an influence of sequence order on decoding accuracy (Supplementary Figure S11), suggesting that only temporal (as shown by the comparison to the static training paradigm), but not spatial continuity of the input transformations was necessary for successful representation learning. The Hebbian learning rule thus groups together consecutive inputs in a manner reminiscent of contrastive, self-supervised methods (Van Den Oord et al., 2019; Illing et al., 2021; Halvagal and Zenke, 2022) that explicitly penalize dissimilarity in the loss function. Here, the higher-level representation from the previous timestep provides a target for the consecutive inputs reminiscent of implementations of supervised learning with local learning rules (Lee et al., 2015; Whittington and Bogacz, 2017; Haider et al., 2021).

Area 3-representations were informative about the identity of the sample moving in sequence as decodability improved with training (Figures 5A,B). In addition to its behavioral relevance, decodability of representations quantifies the learned within-sequence invariance. A biologically plausible way to make high-level object representations available to downstream processes (such as action selection, Figure 1) is a layer of weighted synaptic connections, i.e., a linear decoder, to infer object identity. We simulated this through a linear mapping of the converged area 3-activity vectors that were obtained as above to 10 object identity-encoding neurons (digits “0”, “1”, …, “9”). After fitting the decoding model to 2/3 of the representations, evaluation was conducted on the remaining 1/3 in a stratified k-fold manner (with k = 3). Compared to the information content in the input signal, as measured by the accuracy of a linear decoder, as well as k-means clustering, area 3 representations achieved better decoding performance after around five training epochs (Figure 5A). The model also outperformed linear Slow Feature Analysis (SFA) (Wiskott and Sejnowski, 2002) of the raw inputs (for details see Supplementary material 1.12). This was confirmed across almost all used datasets (Table 1) and even increased as the transformation step size was increased, resulting in smaller overlap between consecutive images (“fast” conditions in Table 1, shown in the first and third row of Figure 3). Across the hierarchy, higher network areas developed more invariant representations than lower areas (Supplementary Figure S9).

Decodability of network representations was maintained when the dataset size was significantly increased. We tested this by training networks on up to 20 random digits per digit class (totaling 200 sequences of the fast translations). As shown in Figure 5C, the network maintained above 60% linear decoding accuracy of digit class while an enlarged version of the network shown in cyan further improved this. On the other hand, increasing dataset size negatively affected the invariance structure of the RDMs (Supplementary material 1.8). putatively due to the limitations discussed in section 4.4.

Lastly, generalization performance for the remaining MNIST dataset was measured by decoding accuracy on previously unseen digits. Here, accuracy was above 60% when more than 100 training sequences were used (Figure 5D). In the enlarged network, decoding accuracy rose above 75% (the blue line in Figure 5D), confirming the network’s capacity to generalize. The small standard deviation between randomly initialized runs indicates the representativeness of the chosen validation subset.

The continuous training paradigm improved decoding performance in comparison to networks trained on static inputs. There, decoding performance dropped from the initial value and was consistently more than 20 percentage points worse than in the continuously trained network (Figure 5B and Table 1). This can partially be explained by the learning of more sample-specific and thus less invariant representations in the static training paradigm, where activity was not carried over from one image to the next (Supplementary Figure S2).

Without explicitly integrated constraints, the network developed a hierarchy of timescales in which representations in higher network areas decorrelated more slowly over inference time than in lower areas. We quantified this by measuring the autocorrelation R during presentation of rotating digits. It is defined as

where ∆ is the time lag measured in inference steps between the points to be compared, T is the duration of each sequence (consisting of 6,000 inference steps), N the number of neurons in the subpopulation and z (t) the activity vector in the subpopulation (averaged across 10 inference steps). High values indicate similar, non-zero activities and thus high temporal stability. The resulting autocorrelation curves for time lags between 0 and the length of an individual sequence are shown in Figures 6A,B, averaged across the 10 rotation sequences. From these curves, decay constants were inferred by measuring the time until decay to 1/e. If that value was not reached until the sequence end, we extrapolated by using a linear continuation through the values at Δ = 0 and Δ = 6,000 time steps. Additionally, we varied the stimulus timescale by dividing the number of inference steps on each frame by the rotation speed. The resulting decay constants showed a clear and robust hierarchy across network areas, as well as a positive correlation with the stimulus timescale (Figure 6C). A significant difference was found between representation neurons in area 3 and area 1 (mean difference at speed one: 7377 time steps, p = 1.61e-2). p-values were determined by a Games-Howell post-hoc test (an extension of the familiar Tukey post-hoc test that does not assume equal variances) succeeding rejection of the null hypothesis across the six populations in a Welch’s ANOVA, as described in more detail in Supplementary material 1.16. A smaller, but significant difference was observed between representation neurons in area 2 and area 1 (4,996 time steps, p = 9.68e-4). In error-coding neurons, the hierarchy was less pronounced, but area 0 and area 2 nonetheless showed a significant difference (p = 9.50e-5). Comparison to a statically trained network with the same architecture which failed to develop a temporal hierarchy in representations (Supplementary material 1.4) showed that the temporal hierarchy was not built into the model architecture, but instead is an emergent property of the model under the continuous training paradigm. This is underlined by the fact that the same inference rate was used in all network areas. The hierarchy in representational dynamics as well as the positive correlation with stimulus dynamics is in agreement with experimental findings in rat visual cortex (Piasini et al., 2021). There, the authors computed neuronal timescales for the decay of autocorrelation in a similar manner and found more stable activity patterns in higher areas of rat visual cortex (Figure 6D).

The decay speed of autocorrelation also allowed us to differentiate between quickly decorrelating error neurons and more persistent representation neurons in higher network areas. Error-coding neurons in area 2 showed a shorter activity timescale than representation neurons within the same area. The difference equaled 4,991 time steps (p = 9.88e-4), compared to only 211 time steps in the statically trained network (Supplementary Figure S3). In this context Piasini et al. (2021) discussed the following scenario: when perceiving a continuously moving object, its identity is predictable over time. Thus, one could expect a diminishing firing rate in neurons representing this object, in contrast to their evidence on larger timescales in higher visual areas. Our results reconcile the framework of predictive coding with these empirical observations by differentiating between quickly decorrelating error-signals and persistent representations. Remarkably, this prediction about the consequences of predictive coding circuitry for the activity autocorrelation timescales of error- and representation neurons has, to our knowledge, not been proposed before. Here it is important to mention the extensive literature on the analysis of different frequency bands in cortical feedforward and feedback signal propagation [summarized in Bastos et al. (2012) from a predictive coding perspective]. These sources did, however, not speak about temporal stability and the two concepts are not easily connected. It is, for instance, conceivable to have low-frequency signals that quickly decorrelate or high-frequency signals that are maintained over time.

The network learned a generative model of the visual inputs as shown by successful input-reconstruction through the network’s top-down pathway (Figure 7). Since areas further up in the ventral processing stream of the cerebral cortex are thought to encode object identity, it is interesting to ask, in how far they are to be able to encode fully detailed scene information, or whether they contain only reduced information (such as object identity). To examine the functioning of this reverse pathway under the continuous transformation training paradigm, we investigated the representational content in each area by reconstructing sensory inputs in a top-down manner. After training, a static input image was presented until network activity converged (Supplementary material 1.3). Then, the input was blanked out and the inferred activity pattern (representation) from a selected area was propagated back down to the input neurons via the top-down weights. Area by area, activity y l of representation neurons was installed by the descending predictions y ⌢ l (see Supplementary material 1.5 for details).

As shown in Figure 7A, the accuracy of reconstruction strongly depended on the area it was initiated from. While predictions from latent representations in area 1 gave rise to reconstructions that resembled the original inputs and achieved low reconstruction errors (Figure 7B), higher areas were less accurate. From there, reconstructions were either blurry or showed the stimulus in a different position, rotational angle, or scale than presented prior to construction (e.g., the “0” from area 3 in the second row of Figure 7). This logically follows from the invariance achieved in these higher areas, from where a single generalized representation cannot suffice to regenerate many specific images. Despite this limitation in obtaining precise reconstructions, which resulted from training on extended sequences instead of individual frames, area 1-representation neurons in all networks contained enough information to regenerate the inputs, thus confirming that the model had learned a generative model of the dataset.

The generative capacity of the network’s top-down pathway was further confirmed by its ability to reconstruct whole objects from partially occluded sequences as shown in Figure 8. A behaviorally relevant use of a generative pathway is the ability to fill in for missing information, such as when guessing what the whole scene may look like and planning an action toward occluded parts of an object. To investigate filling-in in the model, we presented occluded test sequences to the network trained on laterally moving digits (the same as before). After inference on each frame of the test dataset, the predictions sent down to the lowest network area were normalized and plotted retinotopically in Figure 8. Details on the reconstruction process can be found in Supplementary material 1.6. Indeed, predictions sent toward the lowest area carried information about the occluded parts (Figure 8A).

As the input deteriorated, predictions also visibly degraded, resulting in a rising MSE (Figure 8B). The continuously trained network consistently achieved slightly, but significantly better reconstructions than its counterpart trained on static images (for a more detailed analysis see Supplementary material 1.6). An independent t-test resulted in p < 6e-4 for all sequence frames except for the first, unoccluded frame where the difference was non-significant. That the difference was small can be explained by two opposing mechanisms: on the one hand memorization of specific frames putatively aids reconstruction in the static network (Supplementary Figure S2). On the other hand, availability of invariant object identity from the temporal context, which can be expected to improve reconstruction in the continuously trained network. Overall, the availability of top-down information in occluded fields of network area 0 is comparable to the presence of concealed scene information observed in early visual areas of humans (Smith and Muckli, 2010) that cannot be explained by purely feedforward models of perception. Unlike auto-associative models of sequential pattern-completion (Herz et al., 1989), our network forms hierarchical representations comparable to Illing et al. (2021).

We have shown how networks that minimize local prediction errors learn object representations invariant to the precise viewing conditions in higher network areas (Figure 4), while acquiring a generative model in which especially lower areas are able to reconstruct specific inputs (Figures 7, 8). The learned high-level representations distinguish between different objects, as linear decoding accuracy of object identity was high (Figure 5). Comparison to considerably worse decoding performance in networks trained on static images underlined the importance of temporally continuous transformation for the learning process (Figure 5A), noting that spatially ordered sequences (as in, e.g., visual object motion) are not strictly necessary (Supplementary Figure S11). Focusing on the implications for neural dynamics, learning from temporally continuous transformations such as continuous motion led to a hierarchy of timescales in representation neurons that showed more slowly changing activity in higher areas, where they notably differed from the more quickly varying error neurons (Figure 6).

Without the need for explicit data labels, the model developed meaningful, decodable representations purely by Hebbian learning. Linking slowly varying predictions in higher areas to more quickly changing inputs in lower areas lead to emergence of temporally stable representations without the need for an explicit constraint for slowness as used for example in Wiskott and Sejnowski (2002). At the same time, the model acquired generative capacity that enables reconstruction of partially occluded stimuli, in line with retinotopic and content-carrying feedback connections to V1 (Smith and Muckli, 2010; Marques et al., 2018), see also (Pennartz et al., 2019) for a review of predictive feedback mechanisms. Other neuron-level models of invariance-learning (LeCun et al., 1989; Földiák, 1991; Rolls, 2012; Halvagal and Zenke, 2022) neither account for such feedback nor experimentally observed explicit encoding of mismatch between prediction and observation (Zmarz and Keller, 2016; Leinweber et al., 2017) and used considerably more complex learning rules requiring a larger set of assumptions (Halvagal and Zenke, 2022). Conversely, auto-associative Hopfield-type models that learn dynamic pattern completion from local learning rules (Herz et al., 1989; Brea et al., 2013) do not learn hierarchical invariant representations like the proposed model does. By solving the task of invariance learning in agreement with the generativity of sensory cortical systems, the claim for predictive coding circuits as fundamental building blocks of the brain’s perceptual pathways is strengthened.

We argue that the model generalizes predictive coding to moving stimuli in a biologically more plausible way than other approaches (Lotter et al., 2016, 2020; Ali et al., 2021) that rely on error backpropagation, which is non-local (Rumelhart et al., 1985) or the equivalently non-local backpropagation through time (BPTT, Ali et al., 2021). BPTT achieves global gradient descent and thus generally offers performance benefits over Hebbian learning rules. However, it is not straightforward to combine BPTT with invariance learning from temporal structure and direct comparison is thus difficult. As our network is based on the principles developed by Rao and Ballard (1999), its basic neural circuitry is shared with other implementations of predictive coding with local learning rules derived from it Whittington and Bogacz (2017) and Dora et al. (2021). In terms of scope of the current model, focusing on representational invariance and investigating the consequences of training on dynamic inputs clearly distinguishes the present approach from Dora et al. (2021). Mechanistic differences are biologically motivated, such as omissionof a gating term used by Dora et al. (2021) that depended on the partial derivative with respect to presynaptic neuronal activity. This minimizes the set of necessary assumptions compared to other implementations that require such a term in inference (Whittington and Bogacz, 2017; Dora et al., 2021) and/or learning (Dora et al., 2021). Unlike (Dora et al., 2021), the present implementation also does not require weight regularization that depends on information not readily available at the synapses.

Although sufficient for learning of invariant representations on the datasets considered here, the fully connected architecture we used can be expected to limit the degree of representation invariance (as visible, e.g., in the structure of the RDMs) for more complex datasets. However, it has been shown that the lack of inductive bias in fully connected models can be compensated for by training on larger amounts of data (Bachmann et al., 2023). Here, the self-supervised nature of our model is an advantage, as it does not require labeled data. Another interesting extension of the model will be to investigate other common types of transformation such as rotation of three-dimensional objects into the plane. Based on the model’s ability to deal with the scaling transformation and 3D toy objects, we do not expect any fundamental obstacle: the temporal structure of the transformation is important, not the way that it affects the image.

Fully connected areas may also restrict performance on out-of-sample testing. Here, combination of receptive field-like local filters with a pooling mechanism (Riesenhuber and Poggio, 1999) may be helpful to become tolerant to the varying configurations of individual features comprising the objects from the same class. Using a weakly supervised paradigm could improve decoding accuracy even further. It has been shown that under constraints which would be out of the scope of this paper to discuss, inversely connected predictive coding networks can do exact backpropagation when clamping the highest layer activities in a supervised manner (Whittington and Bogacz, 2017; Salvatori et al., 2021).

Input reconstructions from higher network areas degraded as representations became more invariant. This is a direct consequence of Equation 7: each element from the set of area 3-representations casts a unique prediction to the area below. Consequently, multiple different (not invariant) area 3 patterns would be necessary to fully reconstruct a sequence of inputs. Thus, either the invariance in area 3 or the faithfulness of the reconstruction suffers. Nevertheless, the network as a whole appeared to strike a good balance in the trade-off of memorizing information to reconstruct individual samples in lower areas (hence the better reconstruction accuracy from area 1 in Figure 7) and abstracting over the sequence, where area 3 represents object identity invariantly (Figure 5), fitting theoretical descriptions of multilevel perception (ch. 9 in Pennartz, 2015). The more detailed and sample-specific information may provide useful input to the action-oriented dorsal processing stream (Goodale and Milner, 1992), whereas the hierarchy of the ventral visual cortex extracts object identity and relevant concepts (Mishkin et al., 1983).

The model captures neural response properties in early and high-level areas of the visual cortical hierarchy. Retinotopic (Marques et al., 2018) and information carrying (Smith and Muckli, 2010) feedback to early visual areas (cf. Figures 7, 8) as well as invariant (Logothetis et al., 1995; Freiwald and Tsao, 2010) and object-specific representations (cf. Figure 4) in the temporal lobe (Desimone et al., 1984; Haxby et al., 2001; Quiroga et al., 2005) are captured by the simulation results. While there is ample evidence for a hierarchy of timescales in the visual processing streams of humans (Hasson et al., 2008), primates (Murray et al., 2014) and rodents (Piasini et al., 2021), with larger temporal stability in higher areas, the compatibility with deep predictive coding is debated (Piasini et al., 2021). Our simulation results of increasingly large timescales further up in the network hierarchy may help to reconcile predictive coding with the experimental evidence. Coincidentally, this was also found to be true in a recently developed predictive coding model, albeit with only two layers and without explicit error representations (Jiang and Rao, 2022). Compared to emergence of temporal hierarchies purely as a result of dynamics in spiking neurons (van Meegen and van Albada, 2021) or large-scale models (Chaudhuri et al., 2015; Mejias and Wang, 2022), our model provides a complementary account, postulating development of the temporal hierarchy as a consequence of a functional computation: learning invariance by local error minimization.

What novel insights can be extracted about the brain’s putative use of predictive algorithms? Theories of predictive coding range from limiting it to a few functions [such as subtraction of corollary discharges to compensate for self-motion (Leinweber et al., 2017)] and input reconstruction (Rao and Ballard, 1999) to claiming extended versions of it as the most important organizational principle of the brain (Friston, 2010), namely the free energy principle. PC models provide a critical step to make theories of perception and imagery quantitative and falsifiable as well as to guide experimental research (Pennartz et al., 2019). Based on the simulation results, error neurons in higher visual areas operate on a much shorter activity timescale than their representational counterparts. This comparison of distinct subpopulations may provide an additional angle to measuring neural correlates of prediction errors [for a review see (Walsh et al., 2020)], as representation neuron responses have been barely considered in experimental work so far. In combination with work on encoding of errors in superficial, and representations in deep cortical layers (Bastos et al., 2012; Keller and Mrsic-Flogel, 2018; Pennartz et al., 2019; Jordan and Keller, 2020), area- and layer-wise recordings of characteristic timescales could lead to a better understanding of cortical microcircuits underlying predictive coding. Layer-wise investigations also show distinct patterns of feedforward and feedback connectivity (Markov et al., 2014) and information processing (Oude Lohuis et al., 2022). Only with knowledge about these microcircuits, models of finer granularity can be constructed.