Understanding the neural bases of subjective experience remains one of the great challenges of the natural sciences. Higher-order theories of consciousness are typically defended by assessments of neural activity in higher cortical regions during perception, often with disregard to the nature of the neural computations that these regions execute. We have sought to refocus the problem toward identification of those neural computations that are necessary for subjective experience with the goal of defining the sorts of neural architectures that can perform these operations. This approach removes reliance on behaviour and brain homologies for appraising whether non-human animals have the potential to subjectively experience sensory stimuli. Using two basic principles—first, subjective experience is dependent on complex processing executing specific neural functions and second, the structure-determines-function principle—we have reasoned that subjective experience requires a neural architecture consisting of stacked forward models that predict the output of neural processing from inputs. Given that forward models are dependent on appropriately connected processing modules that generate prediction, error detection and feedback control, we define a minimal neural architecture that is necessary (but not sufficient) for subjective experience. We refer to this framework as the hierarchical forward models algorithm. Accordingly, we postulate that any animal lacking this neural architecture will be incapable of subjective experience.