This is how the Neocortex Learns — part 1/3
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This is how the Neocortex Learns Randall C. O'Reilly Astera Institute; Department of Psychology Center for Neuroscience, University of California Davis correspondence: oreilly@ucdavis.edu June 7, 2026, Version: 1 https.//compcogneuro.org/oreilly-2026-cortlearn Abstract: A sufficient account of how the neocortex learns must meet three criteria: 1. Computationally, it must approximate a powerful, general-purpose learning algorithm known to scale to human-level intelligence; 2. Algorithmically, it must be implementable using known, well-established neural circuits within the neocortex and associated brain structures; 3. Implementationally, there must be a detailed account for how all of the algorithmic mechanisms actually function at a neurochemical level. At present, there is only one framework that meets all of these criteria: error-driven predictive learning via temporal derivatives, driven by corticothalamic circuits, based on competitive kinase synaptic plasticity induction mechanisms. This has been implemented in the Axon neural simulation framework using spiking neurons, and demonstrated to learn across a wide range of challenging cognitively motivated tasks. Introduction Understanding how the neocortex learns is perhaps the single most important step in understanding human intelligence, because our cognitive functions emerge over years of experience-driven learning within this brain structure, which is unique to mammals and is most greatly expanded in primates, especially humans. Following Marr (1982), there are three levels at which any theory of neocortical learning can be evaluated: computational, algorithmic, and implementational. The deliberately provocative conclusion of this paper is that only one current theory, which we label the temporal derivative model (Jang et al., 2026), provides a sufficient account across these three levels, and thus represents the most viable working hypothesis for how the neocortex learns. Computational Is there a mathematically proven basis for understanding why the neocortical learning mechanism should be capable in principle of accomplishing human-level intelligence through experience-driven learning? Have implementations of this learning mechanism actually demonstrated this capacity? There is only one learning mechanism that meets this criterion: error backpropagation (Rumelhart et al., 1986; Widrow & Hoff, 1960; Werbos, 1974), which drives learning in modern-day large-language models (LLMs) based on the transformer architecture (Vaswani et al., 2017), along with essentially every other type of modern powerful neural network model. This is essentially an open-and-shut case at this point: nothing else even comes close. This is how the Neocortex Learns 2 There have been many proposals for ways of augmenting, simplifying, or approximating error backpropagation, but in practice, nothing else has managed to dethrone the stochastic gradient descent (SGD) procedure, which remains the effectively universal standard for current state-of-the-art (SOTA) models. Furthermore, gradient descent can also be applied to more complex probabilistic models through the variational inference approach (Blei et al., 2017), reinforcing the idea that this is perhaps a uniquely efficient way to search through combinatorially large parameter spaces. Recent work provides a more general overarching framework for understanding all of these gradient-based learning mechanisms (Khan & Rue, 2023; Vastola et al., 2026). Since the skeptical publication of Crick (1989), there has been a widespread and persistent belief among many scientists that error backpropagation is fundamentally incompatible with the biology of the brain. However, in fact there are various longstanding proposals that show how the brain could accomplish backpropagation, which we discuss next. Algorithmic Can the computational-level mechanism be implemented algorithmically in a way that is in principle compatible with known neurobiological mechanisms, at the circuit and structural level? There have been various proposals for how to implement error backpropagation using known neocortical circuits (see Lillicrap et al., 2020 for a recent review, and Discussion below for more details), but only one provides a comprehensive fit with known neocortical (and thalamocortical) properties, while also satisfying the final implementational criterion described next. The temporal derivative algorithm is based on the representation of the backpropagated error gradient implicitly as the temporal derivative (difference) between two distinct activation states that emerge over time (Figure 1), instead of requiring a distinct population of neurons to explicitly represent the gradient in terms of their firing rates. The idea of using two different states or phases of neural activity to compute error gradients originated with the Boltzmann Machine (Ackley et al., 1985), and a direct derivation from the error backpropagation formalism was first provided by the GeneRec (Generalized Recirculation) algorithm (O’Reilly, 1996), which generalized the original Recirculation model of Hinton & McClelland (1988). Other derivations were subsequently developed (Xie & Seung, 2003; Scellier & Bengio, 2017). By representing the error gradient implicitly as a difference between two activation states, this algorithm avoids the significant additional complexity required for maintaining two distinct populations of neurons coding for the feedforward activity and the backpropagated error signal, with a third distinct population representing their difference. Instead, under this temporal derivative framework, all of the neurons in the neocortex are always encoding a positive, mutually compatible representation of the current state, through bidirectional excitatory connections that are a well-established and relatively unique property of the neocortex (Markov et al., 2013; Van Essen & Maunsell, 1983). In one phase, this current state reflects a prediction, which is then followed by an outcome that may differ from the prior prediction, with any difference in corresponding activation states throughout the network providing a close approximation to the error gradient between outcome and prediction. This is how the Neocortex Learns 3 Figure 1: How bidirectional activation propagation can communicate error signals, in the simplest case of a three-layer network mapping from a Sensory Input to a Prediction output, with the Actual Outcome driving the Prediction layer only in the later plus phase, after an initial minus phase when the prediction is generated. The Error is the temporal difference between the (plus – minus) activity levels. There is just one network with three bidirectionally connected units, as shown at the left; the networks shown further to the right are snapshots of the activity state of this network at different points in time, which evolves from left to right. The thick colored lines also show the activation level of each of the three neurons over time, both in terms of the line height and the brightness and warmth of the color gradient. Initially, each neuron is inactive (blue). Then, external Sensory Input arrives, and a wave of bottom-up excitation propagates upward through the Hidden and Prediction layers. Critically, the Prediction and Hidden neurons mutually excite each other via bidirectional connections, which contributes to each of their activity levels. The snapshot of the network in the middle shows the neural activity at the end of the minus phase. Then, at the start of the plus phase, the Actual Outcome arrives, which is more active than the Prediction, and it therefore drives more activity in the Prediction neuron. This propagates top-down to the Hidden neuron as well, which is the key mechanism by which bidirectional connectivity communicates error signals, causing the Hidden neuron to have a (plus – minus) activity difference, reflecting the top-down influence from the Prediction layer. This temporal-difference based Error signal provides a good approximation to the error backpropagation error gradient (O’Reilly, 1996). This is how the Neocortex Learns 4 Figure 2: Connectivity between the neocortex and the pulvinar nucleus of the thalamus, in the case of primary and secondary visual areas, that is uniquely well-suited for driving predictive error-driven learning. The numerous and relatively weaker projections from layer 6 (VI) neurons activate a prediction over the pulvinar, that integrates the signals from multiple cortical areas and neurons to synthesize the prediction, which improves over the course of learning throughout the neocortex and in these final projections into the pulvinar. By contrast, the strong, focal driver inputs from layer 5 (V) intrinsic bursting (5IB) neurons can activate an outcome representation that is essentially an unlearned copy of the activity pattern in lower cortical layers (e.g., V1 trains V2 predictions in this case). The periodic bursting of the 5IB neurons ensures that this outcome activity is only phasically present (i.e., the plus phase), with a complete prediction – outcome learning cycle occurring within roughly 200 ms (i.e., theta frequency, 5 Hz). Diagram based on Sherman & Guillery (2006). The thalamocortical connectivity of the neocortex directly supports the generation of these two states, within an overall predictive learning framework, which is learning to predict what happens next based on what just happened (O’Reilly et al., 2021). Specifically, thalamic relay cells (TRCs) in the higher-order pulvinar (for posterior cortex) and mediodorsal (for frontal cortex) nuclei of the thalamus receive two distinct inputs (Figure 2; Sherman & Guillery, 2006; Usrey & Sherman, 2018): 1. A large number of normal-strength inputs onto more distal dendritic arbors from a wide range of higher- level neocortical brain areas. 2. A much smaller number (even just one) of abnormally strong driver inputs originating from the layer 5b intrinsic bursting (5IB) neurons in hierarchically lower neocortical areas, which burst roughly every 100-200 ms (i.e., at the alpha or theta rhythm), and are otherwise inactive. This constellation of properties creates phasic alternations between a prediction state driven exclusively by the first pathway, and an outcome state that reflects the strong impact of the driver inputs, which only occurs phasically. Critically, the pulvinar neurons do not compute the difference between these two inputs and send that as their output, instead they merely reflect these two different inputs in their activity levels across time. The TRCs send extensive excitatory reciprocal projections back to the same areas that send the prediction- generating inputs, thereby communicating the temporal difference between the prediction and outcome states back into the neocortex, where local synaptic plasticity is driven by this temporal derivative. Furthermore, bidirectional connectivity within the neocortex effectively computes the partial derivative of these error signals relative to sending neural activity coming from other areas, thereby accomplishing the critical error backpropagation credit assignment learning process between neocortical layers (O’Reilly, 1996). This is how the Neocortex Learns 5 There is a wealth of detailed neuroscience data that is consistent with this overall framework, as reviewed in O’Reilly et al. (2021) (e.g., Fiebelkorn & Kastner, 2021; Sherman & Guillery, 2006; Sherman & Usrey, 2024). Implementational Going down a level of neurobiological detail, how could the algorithmic property of a temporal derivative between prediction and outcome states actually drive synaptic plasticity locally at all of the neocortical and thalamic synapses? Mathematically, the temporal derivative can be computed as the difference between fast minus slow integrals of a common driving input signal. Intuitively, the fast integral more closely reflects the more recent outcome state, while the slow integral still retains more of the trace from the earlier prediction state. See temporal derivative on compcogneuro.org for an interactive demonstration of this principle. Neurochemically, the difference between LTP (long term potentiation, i.e., synaptic weight increase) versus LTD (long term depression, weight decrease) is determined in part by a competition between two different kinases, CaMKII (calcium calmodulin kinase II) and DAPK1 (death-associated protein kinase 1), both of which are driven by calcium-activated calmodulin (CaM) (Goodell et al., 2017; Goodell et al., 2021; Cook et al., 2021; Tullis & Bayer, 2023; Bayer & Giese, 2025). If CaMKII has a faster overall integration of the common CaM driver, and DAPK1 a slower such integration, then this would implement the necessary temporal derivative mechanism. Figure 3: Results from Jang et al. (2026), which are consistent with the predictions of the temporal derivative learning mechanism. A Pre- and postsynaptic neurons were stimulated to either 25 Hz or 50 Hz across the two 100 ms halves (prediction, outcome) of a 200 ms theta cycle. B All 4 cells of the 2x2 combination of prediction, outcome frequencies were tested. C The progression of probe EPSP amplitudes surrounding the stimulation protocol at time 0, showing that the increasing temporal derivative (25 to 50 Hz for both the pre and postsynaptic neurons, in orange) resulted in LTP, while the decreasing temporal derivative (50 to 25 Hz, in blue) resulted in LTD. Both flat profiles (constant 25 Hz or 50 Hz) resulted in no net synaptic efficacy change. D, E Summary showing all cell values (open circles) and averages (bars) for the individual conditions at different times after stimulation, with statistically significant results highlighted with asterisks (** = P < .01, *** = P < .001).