Local learning methods offer an alternative to end-to-end backpropagation, but their unstructured local objectives can produce weak feature learning in deep networks. We study whether the order of hidden-state optimization can address this limitation. We propose a boundary-first inference schedule that partitions a model into chunks, first coordinates hidden states at chunk boundaries, and then refines representations within each chunk. We instantiate this schedule in predictive coding networks (PCNs), a local-learning framework in which hidden activities and prediction errors are explicitly exposed during inference. On CIFAR-10, the resulting boundary-first predictive-coding instantiation improves accuracy over standard predictive coding by $9.77\%$ under a standard parametrization and by $5.51\%$ under a $μ$-parametrization. Diagnostic analyses further show more non-trivial early-layer updates, lower initial-to-final CKA, and more diverse layerwise gradients, consistent with stronger feature learning. These results support boundary-first, chunk-based inference as a practical design principle for predictive-coding training and motivate its study in broader local-learning systems.
We introduce CMP (Cognitive Memory Primitive), a continual-learning architecture that repre?sents inputs as sparse relational codes, stores them in a two-tier competitive memory, and learns through local updates without end-to-end backpropagation through its feature-generating system. We investigate whether combining sparse representations, local learning, and persistent memory can reduce catastrophic forgetting relative to conventional backpropagation-based continual?learning approaches. On a controlled domain-incremental byte-level language modeling protocol, CMP demonstrates substantially lower backward transfer than a parameter-matched Trans?former trained with online Elastic Weight Consolidation (EWC). Across a three-seed replicated 15-domain experiment, CMP exhibits stable forgetting behavior, while separate head-to-head comparisons and domain-order analyses show consistently lower forgetting than the evaluated Transformer baseline under the reported experimental settings. We report these findings alongside a substantial single-domain accuracy gap relative to the Transformer, a null result on a vision benchmark, and a documented failure to combine CMP with an independent accuracy-improving mechanism, reflecting our commitment to reporting both positive and negative outcomes. These results suggest that the combination of sparse representations, local learning, and persistent memory is a promising direction for continual learning, while motivating further investigation into the respective roles of learning rules, representations, and architectural design in mitigating catastrophic forgetting.
Houman Safaai, Varun Reddy, Bernardo L. Sabatinics.LG cs.NE q-bio.NC
Direct feedback alignment (DFA) trains hidden layers with fixed random projections of the output error, avoiding the transposed-weight backward pass of backpropagation (BP). We study a failure mode of DFA training that is distinct from feedback quality: the local weight update is calculated by an outer product, so anisotropy can enter through either its presynaptic-activity factor or its local-error factor. Our analyses with controlled synthetic regimes isolate the first failure mode and show an approximately 40-percentage-point activity-conditioning gain when high-variance directions contain task-irrelevant nuisance. Three clean confirmations isolate a different regime: error conditioning improves raw DFA by 1.77--7.53 percentage points, and combining independently selected activity and error factors adds 0.40--0.90 points over activity conditioning. The signs hold for tanh/one-vs-rest MNIST and preregistered Fashion-MNIST, and replicate on eight fresh seeds in a ReLU/softmax MNIST model. This factorization yields a symmetric block-local family of normalized DFA (nDFA): activity nDFA right-preconditions by an inverse activity second moment, error nDFA left-preconditions by an inverse local-error second moment, and K-nDFA applies both factors with separately tuned damping. A linearized post-alignment calculation gives an exact input-side spectral identity and a Kronecker-factor motivation for the two-sided rule, whereas norm matching rules out a scalar step-size explanation. The error factor is fragile when under-damped, BatchNorm is a strong activity-side alternative, and convnet gains remain partial. We therefore frame conditioned DFA as a factor-level study of when local outer-product rules fail, not as a general replacement for BP or a solution to all-layer convolutional credit assignment.
We introduce CMP (Cognitive Memory Primitive), an architecture that represents inputs as sparse relational codes, stores them in a two-tier competitive memory, and learns entirely through local, gradient-free updates, with no backpropagation anywhere in the network. We use this architecture to test a specific hypothesis: that catastrophic forgetting, usually treated as a training-time defect to be patched with replay or regularization, is instead a structural consequence of how backpropagation assigns credit and that a learning rule that is local and sparse by construction should resist it without a patch. On a controlled domain-incremental protocol across 15 text domains, three-seed replicated, CMP's backward transfer is 15-19x better than a matched-size Transformer trained with online EWC, and the result survives a domain-order control (reported as a range, +0.24 to +0.44, rather than a single figure). We report this alongside a real, substantial accuracy gap versus the Transformer baseline, a null result on a recognized vision benchmark, and a diagnosed, unresolved failure attempting to combine this architecture with a separate mechanism that improves raw accuracy, disclosed because an honest negative result is more useful than an omitted one. The central claim is narrow and falsifiable: local, sparse, non-backpropagation learning measurably resists catastrophic forgetting better than backpropagation with its standard fix, under conditions we state precisely.
Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC. We show that this dependency is largely avoidable. For any layer $f(x)=\mathrm{Act}(\mathrm{Norm}(L(x)))$ with frozen normalization statistics, the exact $J^\top$ factors into three locally available terms, $J^\top v = L^\top(s \odot σ'(z) \odot v)$, where $σ'$ is the activation derivative, $z$ is the pre-activation, and $s=γ/σ_{\mathrm{run}}$ is the normalization gain. Prior weight-feedback methods omitted both corrections; restoring them closes the transport gap for this layer class. Locality here holds up to three assumptions, which we state upfront: weight symmetry ($L^\top$ mirrors the forward operator, as assumed by all PC), a soft spectral-norm control that is not synapse-local, and a nearest-neighbour approximation for MaxPool. Substituting the identity into PC yields WF-Act-PC, which removes the autograd backward pass from error transport. On CIFAR-10/100 (50 epochs, 5 seeds), WF-Act-PC is the only PC method whose accuracy improves with depth, surpassing iPC - the strongest classical PC baseline - by 2.7-22.3 pp on CIFAR-10. With both methods tuned per architecture, it matches or exceeds a comparably-tuned backpropagation baseline on the deeper CIFAR-10 architectures (VGG-9: 93.57% vs. 92.43%; ResNet-18: 92.76% vs. 91.54%) and on the harder Tiny-ImageNet benchmark, while trailing tuned BP on the deeper CIFAR-100 VGG cells. Our WF-Act-PC implementation is publicly available at https://github.com/jlshen025/pcax
We prove that two canonical local synaptic learning rules, the potentiation arm of spike-timing-dependent plasticity (STDP$^+$) and homeostatic plasticity (instantiated here via flashlight granule-cell-like neurons), together can implement the exact gradient of a SIGReg-like self-supervised learning objective. The equivalence requires no gradient calculations, no global error signals, no weight transport, and no label information: the only inputs are pre- and post-synaptic firing rates, local firing statistics, and the temporal contiguity of natural sensory streams. On a synthetic clustering task designed to probe whether class structure can be recovered from temporal ordering of inputs alone, ordered presentation raised cluster separation (CSR) to 2.49 while random ordering left it near baseline (0.83), a roughly threefold ($\approx 3.5σ$) separation attributable solely to input ordering. On temporally ordered MNIST, a two-layer network trained entirely with these rules achieved 87.3% linear-probe accuracy, showing that the mechanism functions end-to-end.
Backpropagation-trained dense neural networks are powerful function approximators, but they couple learning across many parameters and can overwrite previous associations when tasks conflict. This paper describes Local Pheromone Network, a small research prototype for sparse, local, manually updated neural networks. In Local Pheromone Network, each output unit reads only a fixed local neighborhood of input units subject to geometric distance and molecular-tag compatibility. Each synapse stores a weight, a short-term pheromone trace, a long-term pheromone trace, and an optional consolidation state. Training does not call automatic differentiation. Instead, every layer performs a pheromone-weighted Hebbian-style update on a budgeted subset of local synapses selected from local error and co-activity. The update budget adapts online: it shrinks when loss improves and expands toward recently active neighborhoods when loss worsens. Optional mechanisms add structural plasticity, local replay, output masks for partitioned learning, and a target-free local contrastive step. We present the implementation, learning rule, and preliminary experiments on synthetic regression, partitioned memory, conflicting memory, consolidated conflict, structural plasticity, replay, and a synthetic long-context hybrid memory task. The prototype learns local linear rules, preserves partitioned memories through tags and masks, reduces forgetting under consolidation, and uses replay under conflict.
Amirhossein Mohammadi, Alexander G. Ororbiacs.LG cs.NE
Predictive coding networks (PCNs) offer a biologically-plausible, local-learning alternative to back-propagation of errors (backprop). Nevertheless, they have remained largely confined to shallow architectures and evaluated on simple machine intelligence benchmarks. A central obstacle to scaling PCNs is that the learning signal decays rapidly as it propagates away from the clamped boundaries, leaving interior layers effectively unchanged. To directly counter this problem, we propose highway error propagation (HEP), a scheme that augments the free energy function underlying predictive coding (PC) by altering its neural structure with feedback matrices $V_{L\to i}$ that couple selected hidden states directly to the clamped output error. Since this coupling is linear in the hidden state, the highway pathway delivers a correction at every inference step whose magnitude is independent of depth, in contrast to vanilla PC where the output error reaches the $i$-th hidden layer with attenuation that decays exponentially in depth. This bypasses the Jacobian chain while preserving the local PC synaptic update rule. On MNIST and Fashion-MNIST, we show that HEP effectively trains MLPs of up to 128 layers with accuracy that is robust with respect to depth.
This work proposes a hybrid ANN-SNN pipeline that effectively leverages the rich embeddings of pretrained artificial neural networks (ANNs) to enable high-performance spiking neural networks (SNNs). The architecture couples a pretrained EfficientNet encoder with a CoLaNET spiking classifier. We convert the encoder's activations into spike trains via rate-coding and train the subsequent SNN classifier using local, biologically inspired learning rules, bypassing end-to-end gradient propagation. This approach achieves 99.09% accuracy on a 64-class ImageNet benchmark, demonstrating performance on par with conventional deep networks. The work presents a biologically plausible and efficient framework for adapting powerful pretrained encoders to downstream spiking neural network tasks.
The Forward-Forward (FF) algorithm offers a computationally efficient and biologically plausible alternative to backpropagation (BP) by training neural networks through purely local, layer-wise optimization. However, FF is inherently designed for classification via contrastive positive-negative sample pairs, and extending it to regression poses fundamental challenges: continuous target space lack natural "opposites" for contrastive learning, and the standard goodness function carries no information about target magnitude or ordering. We propose FFR (Forward-Forward for Regression), to our knowledge, the first framework to extend FF to real-world regression and demonstrate competitive performance across diverse real-world datasets. FFR introduces three key innovations: (1) an ordinal competitive goodness function that replaces contrastive pairs with competitive learning between partitioned neuron groups under distance-aware ordinal supervision; (2) a stratified ladder architecture where shallow layers learn coarse ordinal discrimination and deeper layers refine into fine-grained regression, with multi-scale feature aggregation for inter-layer collaboration; and (3) hierarchical prediction with uncertainty estimation, where multi-scale predictors jointly provide robust predictions and prediction confidence as a free-lunch. Extensive experimental results show FFR recovers on average 98.6% of BP's accuracy across five real-world regression benchmarks while reducing peak training memory to only 27% of BP's at depth 8 and 8% at depth 32, with per-iteration time around 72% of BP's, and substantially outperforms all BP-free competitors.
Hengyu Shi, Tianyang Han, Peizhe Wang +3cs.CL cs.LG
LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose \textbf{LoPT}: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT