This is how the Neocortex Learns — part 2/3

Cleaned-text code points [13963, 28384). Bibliography omitted here; source.md includes it.

This is how the Neocortex Learns 6
There is now direct experimental evidence consistent with this prediction (Jang et al., 2026). Specifically, 
pre and postsynaptic pyramidal neurons in a widely-used in vitro synaptic plasticity preparation were 
driven by different temporal patterns of activity over a 200 ms theta-cycle window, with one activity level 
for the first 100 ms (i.e., reflecting the prediction state), and another activity level for the second 100 ms 
(the outcome state).
After 10 repeated presentations of these different temporal patterns, the resulting changes from baseline 
synaptic efficacy strength matched the predictions of the temporal derivative learning mechanism (Figure 
3). Specifically, when there was a rising pattern between prediction and outcome (25 Hz to 50 Hz), LTP 
resulted. When this pattern went the opposite direction (50 Hz to 25 Hz), LTD resulted. Finally, and 
critically, for both of the stable conditions (25 Hz to 25 Hz and 50 Hz to 5 Hz), no net synaptic efficacy 
change occurred. This latter condition directly contradicts the standard Hebbian-style account of synaptic 
plasticity, because the 50-50 case has the most overall synaptic activity, and yet it did not result in LTP, 
whereas the 25-to-50 case did. Furthermore the 25-to-50 and 50-to-25 cases both have the same net amount 
of synaptic activity, just organized differently across time.
Summary
Thus, the strong conclusion from this summary evaluation is that the temporal derivative form of error-
driven predictive learning is unique in providing a consistent and empirically supported account for how 
the neocortex learns, across all three relevant levels of analysis. Furthermore, this theory has been 
implemented in large-scale spiking neural networks, in the Axon framework, described extensively at 
compcogneuro.org. That website provides many examples of these models that can be run through the web 
browser, using the WebGPU framework for GPU-based acceleration to provide reasonable performance. 
For further details, see the kinase algorithm.
Alternative frameworks
Various points of contrast with other possible learning algorithms are briefly discussed below, to clarify the 
relevant distinctions.
Explicit error and predictive coding
Various alternative proposals for implementing the error backpropagation algorithm (Lillicrap et al., 2020) 
and the classic Bayesian predictive coding framework (e.g., Rao & Ballard, 1999) both hypothesize that a 
sub-population of neurons directly represent the error, by subtracting a top-down prediction from the 
bottom-up actual outcome (Figure 4). Thus, different populations of neurons must be somehow segregated 
so that they can represent fundamentally distinct information. Furthermore, all three of these different 
signals (prediction, outcome, error) should in principle be communicated across layers, in different 
directions, requiring strongly segregated pathways.
By contrast, as emphasized above, the temporal derivative framework keeps the error gradient 
representation implicit, as the difference in activity states over time, which greatly simplifies the biological 
implementation required. Furthermore, it allows for all levels in the network to work together to drive 
parallel constraint satisfaction processing, integrating top-down and bottom-up constraints, to drive 
coherent interpretations of the current state (Hopfield & Tank, 1985; O’Reilly et al., 2013). This represents 
a powerful form of search through representation space, operating as a kind of inner-loop optimization 
within the outer-loop of error backpropagation search through synaptic weight space to improve the 
predictive accuracy of the system.

This is how the Neocortex Learns 7
Figure 4: Proposals for implementing error-driven learning that require explicit error signals and / or 
separate neural pathways for feedforward vs. prediction signals. Given the pervasive interconnectivity of 
all lamina and neurons in the neocortex, it is unlikely that such strict separation between such channels is 
sustained. A is from Rao & Ballard (1999) on predictive coding, where the error is explicitly represented in 
neural firing, as a difference between a top-down prediction and bottom-up signal. Note that the 
feedforward signal to higher layers is exclusively an error signal, not a positive representation of the input 
stimulus. B is the target-prop model from Le Cun (1986) (via Lillicrap et al., 2020), which has a separate 
feedforward pathway on the left, and top-down feedback on the right, with the difference between these 
two providing the error signal.

The available neural evidence is consistent with the coherent, synergistic, redundant encoding of 
information across all levels of the cortex, with no significant evidence of the kind of structural segregation 
required by the explicit error models (Walsh et al., 2020; Heilbron & Chait, 2018). Furthermore, the 
standard predictive coding framework only has error signals propagating forward beyond the first layer, 
which is inconsistent with the extensive evidence showing that higher cortical areas contain positive 
representations of the input stimulus, at various levels of abstraction.
Thus, the temporal derivative framework supports the widely accepted idea that the neocortex learns by 
generating top-down predictions of what will happen next, in a way that appears to be more compatible 
with available neural evidence at multiple levels of analysis.
Hebbian learning
The predominant computational-level interpretation of neocortical learning in the literature has generally 
focused on various forms of Hebbian learning, based on the well-established data demonstrating a 
relationship between the level of postsynaptic calcium, entering via NMDA receptors, and the direction and 
magnitude of synaptic plasticity (Lisman, 1989; Bear & Malenka, 1994). Specifically, low levels of 
calcium result in LTD, while higher levels result in LTP. This is generally consistent with the BCM 
(Bienenstock et al., 1982) version of a Hebbian learning algorithm.
Despite this seeming advantage at the implementational level, Hebbian learning is essentially a non-starter 
at the computational level, because it only has a local, heuristic function in terms of extracting statistical 
regularities of co-activation (Oja, 1982; Rumelhart & Zipser, 1985; Intrator & Cooper, 1992). Therefore, 
there is no reason to believe that Hebbian learning can effectively train deep layered networks like those 
present in the neocortex, whereas this is precisely the case where error backpropagation excels.

This is how the Neocortex Learns 8
The spike-timing dependent plasticity (STDP) (Bi & Poo, 1998) version of Hebbian learning has been a 
primary focus of computational models (e.g., Kheradpisheh et al., 2018; Diehl & Cook, 2015). However, it 
is now clear that the simple computationally compelling form of STDP originally described, which 
required a very particular stimulation protocol with individual pairs of spikes separated by 1 s intervals, is 
not generally applicable to more realistic patterns of neural activity (Debanne & Inglebert, 2023). Indeed 
the same BCM-like pattern emerges with more realistic, denser activity patterns (Shouval et al., 2010; 
Izhikevich & Desai, 2003). Thus, STDP lacks both implementational-level support and a coherent 
computational-level account for why it should be a powerful learning mechanism.
Eligibility traces and specialized output learning
There is increasing evidence for a form of learning that applies specifically to output neurons in the 
neocortex and the hippocampus, which may function somewhat like the output decoding neurons in 
reservoir computing networks (Verstraeten et al., 2007; Tanaka et al., 2019), where a complex internal 
dynamical state can be read out by only adapting a single layer of output neuron synapses. This has been 
termed behavioral timescale synaptic plasticity (BTSP), and extensively studied in area CA1, which is the 
output layer of the hippocampus (Magee, 2026; Bittner et al., 2015; Bittner et al., 2017).
In BTSP, elevated plateau potentials in distal dendrites provide the critical plasticity-inducing mechanism 
that establishes an eligibility trace that lasts for several seconds. In CA1, these distal plateau potentials are 
activated by entorhinal cortex layer 3 inputs, which thus serve as a special training signal for driving 
plasticity in the other major population of synaptic inputs, from area CA3. A similar mechanism has 
recently been described in layer 5 pyramidal neurons in neocortex, which also have a prominent distal 
dendritic tuft, and are the primary output neurons of the neocortex (Yaeger et al., 2025; Xiao et al., 2025).
In both of these BTSP cases, there is rapid learning driven by the distal dendritic inputs, with an inhibitory 
negative feedback loop that prevents overtraining (Campbell et al., 2026). There is evidence in the CA1 
neurons that this plasticity is generally transient, consistent with a fast mapping type of learning that can 
rapidly adapt to read out behaviorally-relevant signals from the more slowly-adapting internal 
representations of the relevant systems (hippocampus or neocortex) (Vaidya et al., 2025).
The driving target signal for plasticity in the layer 5 neocortical neurons remains unclear (Magee, 2026), 
but we do know that these neurons receive extensive thalamic input targeting the distal dendritic tuft in 
layer 1. The thalamic projections that target layer 1 are generally of the matrix type, which means they 
typically have broad axonal arbors targeting many different neurons across multiple cortical areas. A 
prominent and widespread source of such projections comes from the ventral anterior (VA) nucleus, which 
receives inputs from layer 5 neurons in motor cortical areas, and is also under disinhibitory control from 
the basal ganglia (Phillips et al., 2021; Xiao et al., 2009; Kuramoto et al., 2015; Economo et al., 2018). 
This would provide a way for direct motor-relevant target signals to drive the rapid tuning of neocortical 
output neurons across most of neocortex, even all the way down in area V1 (Yaeger et al., 2025; Kuramoto 
et al., 2015).
The temporally-extended nature of the eligibility-trace mechanism allows later outcome or motor action 
signals to drive learning from earlier state representations, providing a solution to the temporal version of 
the credit assignment process (this is what the behavioral timescale connotes). In other brain areas such as 
the basal ganglia, and recently in the neocortex, neuromodulatory signals including dopamine have been 
found to drive eligibility-trace learning mechanisms, bridging the temporal gap until reinforcement signals 
become available (He et al., 2015; Shouval & Kirkwood, 2025).

This is how the Neocortex Learns 9
The current evidence suggests that the BTSP-based eligibility-trace mechanisms are synergistic with the 
more slowly-accumulating and shorter time-scale plasticity mechanisms (Magee, 2026), which provide the 
initial biases and encodings upon which the fast BTSP learning builds. The logic is similar to the 
complementary learning systems framework for understanding how the hippocampus and neocortex are 
separately optimized for rapid episodic learning (hippocampus) and slow statistical learning (neocortex) 
(McClelland et al., 1995; O’Reilly et al., 2014): error-driven learning within the many layers of the 
neocortex slowly learns to extract systematic ways of representing the structure of the environment, while 
the rapid, output-focused BTSP mechanism provides a way to quickly decode the resulting complex 
internal states to satisfy the current behavioral demands.
Conclusion
Across the three levels considered here, the strongest constraint appears to come from the computational 
level, effectively narrowing the field to one viable type of learning: error backpropagation. If someone 
were to discover something even more generally powerful than error backpropagation, that would certainly 
represent an important advance across many fields, but given the massive amount of research that has been 
invested into exploring algorithms at the computational level, this is seeming increasingly unlikely.
This then puts more of the weight on the algorithmic and implementational-level arguments outlined 
above, which each now have significant empirical evidence to support them. Nevertheless, more extensive 
empirical research is essential to further test between the different possible algorithmic and 
implementational possibilities that have been advanced for accomplishing predictive error-driven learning.
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