Advances in neural computation have predominantly relied on the gradient
backpropagation algorithm (BP). However, the recent shift towards
non-stationary data modeling has highlighted the limitations of this heuristic,
exposing that its adaptation capabilities are far from those seen in biological
brains. Unlike BP, where weight updates are computed through a reverse error
propagation path, Hebbian learning dynamics provide synaptic updates using only
information within the layer itself. This has spurred interest in biologically
plausible learning algorithms, hypothesized to overcome BP's shortcomings. In
this context, Hinton recently introduced the Forward-Forward Algorithm (FFA),
which employs local learning rules for each layer and has empirically proven
its efficacy in multiple data modeling tasks. In this work we argue that when
employing a squared Euclidean norm as a goodness function driving the local
learning, the resulting FFA is equivalent to a neo-Hebbian Learning Rule. To
verify this result, we compare the training behavior of FFA in analog networks
with its Hebbian adaptation in spiking neural networks. Our experiments
demonstrate that both versions of FFA produce similar accuracy and latent
distributions. The findings herein reported provide empirical evidence linking
biological learning rules with currently used training algorithms, thus paving
the way towards extrapolating the positive outcomes from FFA to Hebbian
learning rules. Simultaneously, our results imply that analog networks trained
under FFA could be directly applied to neuromorphic computing, leading to
reduced energy usage and increased computational speed.

通过对神经计算的进一步研究，我们证明了当使用平方欧几里得范数作为驱动局部学习的好度函数时，Forward-Forward Algorithm（FFA）等同于新赫布学习规则，并通过比较两个版本的 FFA 在模拟网络和脉冲神经网络中的训练行为，证实了生物学习规则与当前使用的训练算法之间的关联，并为将 FFA 的积极结果推广到赫布学习规则铺平了道路。同时，我们的结果暗示在 FFA 下训练的模拟网络可以直接应用于神经形态计算，从而实现能源消耗的降低和计算速度的增加。

前向学习中新兴的 NeoHebbian 动态：对神经形态计算的意义

Emerging NeoHebbian Dynamics in Forward-Forward Learning: Implications  for Neuromorphic Computing

The search for "biologically plausible" learning algorithms has converged on
the idea of representing gradients as activity differences. However, most
approaches require a high degree of synchronization (distinct phases during
learning) and introduce substantial computational overhead, which raises doubts
regarding their biological plausibility as well as their potential utility for
neuromorphic computing. Furthermore, they commonly rely on applying
infinitesimal perturbations (nudges) to output units, which is impractical in
noisy environments. Recently it has been shown that by modelling artificial
neurons as dyads with two oppositely nudged compartments, it is possible for a
fully local learning algorithm named ``dual propagation'' to bridge the
performance gap to backpropagation, without requiring separate learning phases
or infinitesimal nudging. However, the algorithm has the drawback that its
numerical stability relies on symmetric nudging, which may be restrictive in
biological and analog implementations. In this work we first provide a solid
foundation for the objective underlying the dual propagation method, which also
reveals a surprising connection with adversarial robustness. Second, we
demonstrate how dual propagation is related to a particular adjoint state
method, which is stable regardless of asymmetric nudging.

通过将梯度表示为活动差异的方法进行生物合理性学习算法的搜索，提出了名为 “双向传播” 的完全本地学习算法，弥补了与反向传播的性能差距，无需分离的学习阶段或无穷小的盯人，在稳定性方面仍然与对称盯人无关。