Minimizing the Effect of Sleep Deprivation in the Forward-Forward Algorithm

Backpropagation (BP) powers modern deep learning, but it must hold every activation in memory until a global backward sweep consumes it, and that sweep locks each layer until the one above has finished. Forward-only algorithms, from Hinton's Forward-Forward (FF) through Cascaded Forward (CaFo) to Mono-Forward (MF), replace the global gradient with local learning signals and are promoted as more efficient on the basis of FLOP counts rather than measurements. We test that claim on hardware. Across almost 1000 runs on four vision benchmarks (MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100), we read energy, power and memory from an NVIDIA A100 GPU and compare each algorithm against a tuned BP baseline. Removing the backward pass does not by itself save energy: FF costs 4.1x to 6.3x BP's energy and CaFo 3.0x to 7.1x. Mono-Forward is the exception. Given the same number of data passes as BP, it uses 12.5% to 19.9% less energy and 24.6% to 27.5% less memory on the 3x2000 multilayer perceptrons, the largest configurations tested, at lower power and near-equal wall-clock time; on CIFAR-100 its test accuracy is statistically equivalent to BP's. A pre-registered ablation identifies gradient detachment, not MF's auxiliary losses, as the dominant factor tested. Trained to convergence, MF exceeds BP's test accuracy on CIFAR-10 and CIFAR-100 by 3.90 and 5.04 percentage points, but needs 3.5x to 4.5x as many passes and 3.2x to 4.0x the energy. Faster convergence is therefore the remaining target for an end-to-end gain.

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.

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.