Energy-Efficient Deep Learning Without Backpropagation: A Rigorous Hardware-Validated Benchmarking Study of Forward-Only Algorithms

Training neural networks has traditionally relied on backpropagation (BP), a gradient-based algorithm that, despite its widespread success, suffers from key limitations in both biological and hardware perspectives. These include backward error propagation by symmetric weights, non-local credit assignment, and frozen activity during backward passes. We propose Forward Target Propagation (FTP), a biologically plausible and computationally efficient alternative that replaces the backward pass with a second forward pass. FTP estimates layerwise targets using only feedforward computations, eliminating the need for symmetric feedback weights or learnable inverse functions, hence enabling modular and local learning. We evaluate FTP on fully connected networks, CNNs, and RNNs, demonstrating accuracies competitive with BP on MNIST, CIFAR10, and CIFAR100, as well as effective modeling of long-term dependencies in sequential tasks. Moreover, FTP outperforms BP under quantized low-precision and emerging hardware constraints while also demonstrating substantial efficiency gains over other biologically inspired methods such as target propagation variants and forward-only learning algorithms. With its minimal computational overhead, forward-only nature, and hardware compatibility, FTP provides a promising direction for energy-efficient on-device learning and neuromorphic computing.

The Forward-Forward Algorithm (FFA) replaces backpropagation (BP) with layer-wise local contrastive objectives, eliminating the backward pass and the need to retain intermediate activations, yet suffers a persistent performance gap with BP that worsens with depth. This paper diagnoses two structural failure modes: an optimization floor arising from concurrent local updates; and a geometric collapse of layer representations driven by the local update mechanism. On the optimization side, we prove that the FFA loss satisfies the Polyak--Lojasiewicz inequality at each layer; however, simultaneous layer updates induce inter-layer representation-distribution drift, so each layer optimizes against a moving input distribution and incurs an error floor. On the representational side, the pairwise similarity kernel of layer representations contracts exponentially toward rank one as depth increases, collapsing the diversity of per-layer error signals. This collapse bounds FFA's effective learning capacity, which measures the diversity of gradient information across layers, independently of depth, whereas BP's chain-rule signal preserves per-layer diversity, yielding a capacity that scales with depth.

Forward-Forward (FF) learning [Hinton, 2022] replaces backpropagation with strictly layer-local goodness updates. Recent FF-CNN work has narrowed the gap to BP on 32x32 benchmarks, raising the question of whether layer-local training is becoming a viable alternative at realistic scale. To probe this rigorously, we develop DTG-FF -- dynamic temperature goodness, decoupled normalization, and multi-layer fusion -- as an instrument that sets FF-family state of the art across nine real-data benchmarks at the time of our submission (91.8% CIFAR-10 and an FF baseline at ImageNet-100 224x224), and use it to audit how far layer-local training actually scales. (1) Real-data scaling. Under identical recipe and backbone, an architecture-matched BP-DeepSup baseline beats DTG-FF by 2.40/5.93 pp on CIFAR-10/CIFAR-100, and the gap widens with class count. At 224x224 the same instrument reaches only 49.4% on ImageNet-100, versus 75.6% even for a self-supervised BP-trained ResNet-50 with linear evaluation [Tian et al., 2020] -- exposing a real-data ceiling invisible at 32x32. (2) Synthetic vs. real K-conflict. DTG-FF increasingly outperforms BP as class count K grows on synthetic teacher-student tasks, yet on real images the FF-BP gap reverses sign and widens with K. A within-dataset CIFAR-100 coarse vs. fine probe isolates label-hierarchy from image distribution: synthetic K-sweeps confound output dimensionality with fine-grained discrimination difficulty and thereby overstate FF transferability. (3) Systems audit. FF can be implemented without storing depth-wide activations, but on commodity 8 GB hardware standard BP+gradient-accumulation reaches 4.18 GB / 157 imgs/s versus DTG-FF's 7.90 GB / 138 imgs/s, so a memory-based justification for FF at this scale is not supported under fair baselines.