In July 2041, T. Amankwah (Centre for Adaptive Systems, University of Sussex) and L. Gustafsson (Independent Research Collective, Ålife Working Group) published a theoretical paper arguing that gradient-based training is not a general account of learning but a solution to one specific problem, and that the field’s decade-long failure to reproduce it on non-differentiable substrates is a consequence of having misidentified which problem that is. The paper reframes an engineering difficulty as a set of unnecessary preconditions, and states the objection to its own proposal without answering it.
The Assumption
The paper opens by naming something it claims is almost never stated outright. Work on adaptive systems in the post-correction period begins, near-universally, from the position that adaptive capacity requires two things: a scalar objective, and a procedure for attributing the objective’s current value to the parameters responsible for producing it. The authors describe this as an assumption rather than a finding, on the grounds that it has rarely been tested against an architecture designed without it.
Their characterization of what gradient descent actually does is the paper’s load-bearing claim:
“Backpropagation is not a learning rule. It is a solution to a problem that arises only when three conditions hold at once: the system is evaluated against a single scalar objective, that objective is computed at an output remote from the parameters, and the mapping between them is deep enough that no parameter can be corrected on local information alone. Every one of those conditions is a design decision. The field has been treating the solution as the requirement.”
Why the Port Has Failed
The paper surveys the previous decade’s attempts to bring gradient methods to spiking and MORSe substrates and reports them as uniformly unsuccessful on their own terms. On the device side it defers entirely to the account in Bhaskaran et al. (2036): asymmetric potentiation and depression, write nonlinearity, and finite endurance.
Its own contribution is the claim that those are not the binding constraint. The authors argue that even a substrate with ideal, perfectly linear, infinitely enduring switching would fail the port, because the port presupposes an objective, and an embodied system under development has no output at which error could be observed. They note the consequence for how the failure has been interpreted:
“A decade of negative results has been read as evidence that the substrate is inadequate. It is equally consistent with the possibility that we have been trying to satisfy a precondition we did not need to accept.”
When Credit Assignment Is Unnecessary
This is the pivot the paper is remembered for. Working from the three conditions listed above, the authors observe that a system satisfying none of them has nothing for a credit-assignment procedure to operate on. The problem does not become harder in that case. It ceases to exist.
They offer two existence proofs that adaptive behaviour arises without an objective. Qian et al. (2037) produced directed, adaptive foraging in variable-resource environments from composed Physarum and Lenia dynamics, with no objective function anywhere in the system. Sorokina et al. (2026) reported generalization to novel environment configurations in cortical organoid arrays under closed-loop feedback, which is not gradient training and cannot be. Neither result is a demonstration of general cognition. Both are demonstrations that the assumption is not universal.
What Replaces It
The paper’s positive proposal is deliberately narrow. An update rule, it argues, should be permitted to depend only on quantities available at the site of the update: the recent activity of the cells on either side of a connection, and nothing else. No target, no error signal, no information routed from elsewhere in the graph.
It then states the objection to this proposal in its own voice, and declines to resolve it:
“The obvious objection is that local rules cannot produce globally coherent structure. A graph whose every region optimizes on its own information has no mechanism by which one region’s organization becomes consistent with another’s, and the result should be a collection of locally sensible arrangements that do not add up to a system. We do not have an answer to this. We think it is the correct next question, and we think it is a question about constraints rather than about rules.”
A Prediction
The paper closes with three consequences it says are checkable rather than rhetorical. A system built to these commitments would develop without a loss function present anywhere in it. Its capability would be a function of the sequence it was exposed to rather than of an objective it optimized, which would make benchmark comparison the wrong instrument and longitudinal case study the right one. And its developmental history would be specific to the instance, since a local rule accumulates along whatever path the activity took.
Institutional Context
The work was supported by a UK research council grant and by the Ålife Working Group’s own open-release arrangement, with no industrial partner. The paper is explicit that the Sussex group and the Ålife collective came to the problem from different directions, evolutionary robotics and artificial life respectively, and that the collaboration was the first between them.
The 2045 Connection
Amankwah’s objection was answered two years later, in Solheim and Amankwah (2043), and the answer became the architecture of the 2045 neural core: a fixed global resource budget whose constant total supplies the coupling that a global objective would otherwise provide, with no objective anywhere in the system.
T. Amankwah appears on the Fennimore et al. (2045) preprint byline. The 2041 paper’s third prediction, that developmental history would be instance-specific, was later given a physical basis in Bhaskaran et al. (2036) rather than the logical one argued here.