The Bayesian Brain and Predictive Processing: A Critique, #3.

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4. Conclusion

Bayesian brain and predictive processing frameworks have generated valuable research and theoretical insights, but face substantial challenges that should temper enthusiasm about their status as fundamental theories of brain function. Computational intractability, implementation mysteries, explanatory flexibility, alternative explanations for supporting evidence, and philosophical difficulties all raise serious questions.

Rather than universal theories, these approaches may be most useful as heuristic frameworks for specific domains where probabilistic inference over generative models is appropriate. Claims that prediction error minimization explains all brain function, from basic perception to consciousness and psychopathology, overreaches current evidence.

The field would benefit from greater recognition of these frameworks’ limitations, more rigorous empirical testing against well-specified alternatives, and openness to pluralistic approaches that acknowledge mechanistic diversity in neural systems. Bayesian and predictive processing theories have contributed importantly to cognitive neuroscience, but their ultimate scope and validity remain open questions requiring continued critical examination rather than uncritical acceptance.

Appendix: Computational Intractability in Bayesian Brain and Predictive Processing Frameworks

As we have seen, a central claim of the Bayesian brain hypothesis and predictive processing framework, is that predictive processing provides a computationally tractable neural implementation of Bayesian inference. As Andy Clark put it,

It is thus a major virtue of the hierarchical predictive coding account that it effectively implements a computationally tractable version of the so-called Bayesian Brain Hypothesis. (Clark, 2013)

This tractability claim has been crucial for the framework’s appeal, suggesting that the rich Bayesian models developed in cognitive science might finally have a plausible neural implementation story. However, the computational complexity analysis by Kwisthout and van Rooij (2020) demonstrates that this central claim is fundamentally mistaken. Their rigorous mathematical proofs reveal that each key subcomputation postulated by predictive processing is computationally intractable, and that the standard appeals to “approximation” fail to resolve these intractability problems. This critique strikes at the heart of predictive processing’s claims to provide a unified theory of cortical computation.

The Core Intractability Results

Kwisthout and van Rooij’s analysis begins by formalizing the key computational transformations that predictive processing frameworks postulate. These include prediction (computing expected sensory inputs from hierarchical hypotheses), error computation (calculating discrepancies between predictions and observations), and explaining away prediction errors through various mechanisms including hypothesis updating, model revision, active inference, and adding observations. By characterizing these computations at Marr’s computational level—specifying their input-output transformations independent of implementation details—the authors can apply computational complexity theory to determine their inherent tractability.

The results are devastating for claims about predictive processing’s computational efficiency. Prediction, the computation of marginal probability distributions over prediction variables given distributions over hypothesis variables, is proven NP-hard even when restricted to networks with only single binary hypothesis and prediction variables. This means that no algorithm can compute predictions in polynomial time for all possible inputs, unless the widely accepted computational complexity assumption that P ≠ NP is false. The hierarchical structure that predictive processing emphasizes does not alleviate this intractability—it merely distributes intractable computations across multiple levels of the hierarchy.

Hypothesis updating, whether formalized as belief updating (computing full posterior distributions via Bayesian conditioning) or belief revision (revising hypotheses to minimize prediction error), is similarly intractable. The proof demonstrates NP-hardness for both interpretations and for both “SUM” variants (computing probability distributions) and “MAX” variants (computing most probable joint value assignments). Crucially, the intractability of belief revision persists even when the prediction error is arbitrarily small. This undermines a common intuition in the predictive processing literature that small prediction errors should make inference easier—the mathematical reality is that minimizing even tiny prediction errors remains computationally intractable.

Model revision, the process of adjusting parameters in generative models to accommodate unexpected observations, is proven NP-hard even when only a single parameter probability is subject to revision. This result challenges claims about how brains might learn hierarchical generative models through experience, as the computational problem of determining which parameter adjustments minimize prediction error is itself intractable. Similarly, active inference (selecting actions to minimize prediction error) and adding observations (choosing which aspects of the environment to sample) are both proven NP-hard, even with highly restricted action repertoires or observation spaces. These results collectively demonstrate that every major mechanism postulated by predictive processing for explaining away prediction errors faces fundamental computational barriers.

Why Approximation Fails to Rescue the Theory

A natural response to these intractability results might be that brains implement approximate rather than exact Bayesian inference, and that approximation could render the computations tractable. Indeed, proponents of predictive processing frequently invoke approximation as the key to neural plausibility. However, Kwisthout and van Rooij systematically dismantle this defense by demonstrating that approximation itself does not guarantee tractability.

The critical insight is that approximate Bayesian inference is also provably intractable in general. Previous work by Kwisthout et al. (2011) and Dagum and Luby (1993) established that approximate inference in Bayesian networks remains NP-hard, meaning that even computing approximate posteriors cannot be done in polynomial time for arbitrary networks. This includes the sampling-based approximation methods commonly invoked in discussions of neural implementation. While sampling algorithms can approximate Bayesian inference under certain assumptions, they require super-polynomial time in the worst case and frequently in typical cases for complex networks.

Heuristic approximation methods such as Laplace approximation or variational mean field methods face their own severe limitations. These approaches make simplifying assumptions—such as Gaussian probability distributions or independence between variables—that fundamentally alter the computational problem being solved. While such simplified problems may be tractable, they no longer involve the structured representations that Bayesian cognitive modelers argue are essential for explaining human cognition. A theory that achieves tractability by assuming away representational structure has abandoned the very explanatory target it claimed to address.

The implications are stark: predictive processing cannot appeal to approximation as a general solution to intractability. If neural implementations of predictive processing are to be tractable, they must satisfy severe structural constraints on the generative models they encode. The burden shifts to specifying what these constraints are and demonstrating that biological neural networks actually satisfy them.

The Constraint Requirements for Tractability

Kwisthout and van Rooij’s fixed-parameter tractability analysis reveals what constraints would be sufficient to render predictive processing computations tractable. A computation is fixed-parameter tractable if it can be computed in time f (k₁, k₂, …, kₘ) × n^a, where k₁, k₂, …, kₘ are parameters of the input, n is the input size, a is a constant, and f is some function of the parameters. Such algorithms can be efficient for large inputs provided the parameters remain small.

The analysis identifies several parameters that must be constrained for tractability. The treewidth of the Bayesian network—a graph-theoretic measure of how locally connected the network structure is—must be small. The number of values each variable can take must be small. The size of hypothesis and prediction spaces must be small. Alternatively, for MAX variants (computing most probable assignments rather than full distributions), the most probable hypothesis must have very high probability, meaning near-deterministic inference with minimal uncertainty.

Concretely, prediction and hypothesis updating are computable in fixed-parameter tractable time O(c^|Pred| × c^t × n) for prediction and O(c^|Hyp| × c^t × n) for hypothesis updating, where c is the maximum number of values per variable, t is treewidth, and n is network size. For these algorithms to be efficient, c, |Pred|, |Hyp|, and t must all be small. As a rough heuristic, parameters in the range 2-10 might be considered small, while values like 100-10,000 would be large. The exponential dependence on these parameters means that even moderate increases quickly lead to computational explosion.

These constraints are extraordinarily severe. Low treewidth requires highly local connectivity patterns where variables interact only with small neighborhoods. Small cardinality restricts representational richness—variables can encode only a handful of possibilities. Small hypothesis and prediction spaces limit the number of competing interpretations the system can consider. These restrictions are fundamentally incompatible with the rich, structured, hierarchical representations that both Bayesian cognitive models and predictive processing theorists claim are necessary for explaining human cognition.

The Structured Representation Dilemma

This creates a devastating dilemma for predictive processing. The framework’s appeal partly rests on its claimed ability to implement the sophisticated Bayesian models that cognitive scientists have developed to explain reasoning, learning, perception, and other cognitive capacities. These models typically involve structured representations encoding complex relational information—hierarchical taxonomies, compositional structure, causal relationships, and abstract schemas. Such representations are precisely what give Bayesian cognitive models their explanatory power, allowing them to capture how humans generalize from limited data, perform analogical reasoning, and understand novel situations.

However, structured representations necessarily involve high-dimensional hypothesis spaces, complex dependencies between variables (high treewidth), and large cardinalities to encode rich information. These are exactly the properties that render inference intractable. A Bayesian network encoding realistic knowledge about, say, visual scene understanding, social cognition, or language comprehension will inevitably have the complexity that leads to intractability.

Proponents might respond by invoking the simplified representational assumptions that make some approximation methods tractable—Gaussian distributions, independence assumptions, or other restrictions. But accepting these simplifications abandons the structured representations that made Bayesian approaches explanatorily powerful. Gaussian assumptions work for simple continuous variables but cannot capture the discrete, compositional structure of concepts, the hierarchical organization of knowledge, or the complex dependencies that characterize real-world causal models. Independence assumptions eliminate the very relational structure that structured representations are meant to encode.

The dilemma is this: either accept rich structured representations and face intractability, or adopt simplified representations that are tractable but explanatorily impoverished. Predictive processing cannot have it both ways: it cannot claim to implement the sophisticated Bayesian models of cognition, while also maintaining computational tractability. The mathematical proofs establish that these goals are incompatible for unconstrained networks.

Implications for Neural Plausibility

The intractability results have profound implications for claims about neural plausibility. The computational complexity analysis by Pecevski et al. (2011) on spiking neural network implementations of Bayesian inference reveals that the number of neurons required scales exponentially with network treewidth—specifically, proportional to c^t. For networks with the structural complexity required for cognitive modelling, this implies astronomical neural resource requirements far exceeding what biological brains contain.

Moreover, as we noted above, no neural mechanisms have been clearly identified for representing probability distributions or implementing the computational operations required for Bayesian inference. Probabilistic population codes, often invoked as candidate mechanisms, require precise tuning of neural variability and correlation structures that may not exist in biological populations. The theory requires neurons or neural populations to encode probability distributions, update these distributions through Bayesian conditioning, marginalize over intermediate variables, and compute prediction errors between distributions—all without clear evidence for how neural circuits could accomplish these operations.

The fixed-parameter tractability analysis suggests specific empirical predictions that could test whether biological networks satisfy the constraints necessary for tractable inference. Is cortical connectivity sufficiently local to yield low treewidth? Do neural representations encode only small numbers of discrete possibilities? Do brain regions consider only small numbers of competing hypotheses simultaneously? Are neural representations highly certain, effectively deterministic?

Current neuroscientific evidence suggests the opposite. Cortical networks exhibit rich, distributed connectivity patterns rather than purely local organization. Neural representations appear to encode higher-dimensional information spaces. Brain activity shows considerable variability and uncertainty rather than near-deterministic selection of single hypotheses. These observations suggest that biological neural networks may not satisfy the severe constraints required for tractable predictive processing.

From Universal Theory to Domain-Specific Tool

The intractability results force a fundamental reassessment of predictive processing’s scope and status. The framework has been promoted as “a unified brain theory” (Friston, 2010) explaining all cortical processing—from basic sensory perception to high-level cognition, consciousness, and psychopathology. Clark characterized it as potentially “the future of cognitive science,” offering a unified computational principle underlying diverse cognitive phenomena (Clark, 2013).

However, the mathematical proofs demonstrate that this universal ambition is impossible for unconstrained networks with structured representations. At most, predictive processing might apply to narrowly constrained domains where the required conditions hold—perhaps some aspects of low-level sensory processing involving local computations over small state spaces with minimal uncertainty. Even here, alternative explanations not invoking Bayesian inference might be equally or more plausible.

What must be excluded from the framework’s scope includes precisely those cognitive capacities that Bayesian models were developed to explain: planning and reasoning over complex state spaces, learning rich generative models from limited data, language comprehension and production involving compositional structure, analogical reasoning requiring relational representations, and creative problem-solving considering multiple competing hypotheses. These capacities require the representational richness and computational flexibility that lead inexorably to intractability.

The scope limitation is not just a minor adjustment but instead a fundamental reconceptualization. Instead of a unified theory of cortical computation, predictive processing becomes at most a domain-specific framework applicable where its severe constraints happen to be satisfied. The burden shifts entirely to framework proponents in order to specify precisely which cognitive domains satisfy these constraints and to provide empirical evidence that neural implementations in those domains actually exhibit the required properties.

Conceptual Problems Revealed

The intractability critique reveals deeper conceptual problems with predictive processing’s theoretical structure. The tractability claim was not peripheral, but rather central to the framework’s appeal. Much of the enthusiasm for predictive processing stemmed from its promise finally to provide a computationally feasible story about how brains implement the sophisticated Bayesian inference that cognitive models postulate. Without this promise, the framework loses much of its theoretical motivation.

Moreover, a troubling circularity emerges. Predictive processing claims to explain how brains implement Bayesian inference, positioning itself as bridging computational-level theories in cognitive science with neural implementation. However, the implementation requires constraints so severe that they preclude the very cognitive capacities that Bayesian models were developed to explain. The framework thus undermines its own explanatory target—it cannot explain how brains implement the computations it purports to explain.

Additionally, serious measurement problems arise. The computational-level parameters that determine tractability—treewidth, variable cardinality, hypothesis space size—do not directly correspond to measurable neural properties. How would neuroscientists test whether cortical networks have treewidth less than 5? How would they measure the effective size of hypothesis spaces encoded by neural populations? The gap between abstract computational parameters and concrete neural measurements remains vast, rendering the theory’s empirical testability questionable.

Evaluating Possible Responses

Defenders of predictive processing theories might offer several responses to the intractability critique, but each faces serious difficulties.

The first possible response might be that brains use fundamentally different algorithms than those analyzed by Kwisthout and van Rooij—algorithms that avoid the intractability problems while still implementing something recognizable as predictive processing. However, this response effectively abandons the framework’s explanatory claims. If the actual neural algorithms differ fundamentally from the computational transformations that define predictive processing, then predictive processing does not actually explain neural implementation. The response amounts to saying “brains do something else,” which concedes the critique, while also offering no alternative account.

A second possible response might invoke evolutionary adaptation, suggesting that natural selection has discovered constraints and network structures that render inference tractable. This is certainly possible, but represents an additional empirical claim requiring demonstration rather than assumption. More problematically, the required constraints may be incompatible with known cognitive capacities. If tractability requires severely restricted representations, then evolutionary selection for tractable inference would constrain cognitive abilities in ways that seem inconsistent with observed human cognition. The burden of proof lies with framework proponents to show both that the required constraints exist in biological networks and that they are compatible with cognitive capacities.

And a third possible response appeals to environmental structure, suggesting that the statistical regularities in natural environments might reduce effective computational complexity. Real-world causal structures might have special properties—sparsity, modularity, hierarchical organization—that make inference tractable despite worst-case intractability. This is an interesting possibility deserving investigation, but remains speculative without concrete evidence. Moreover, computational complexity theory establishes that intractable problems remain intractable for typical cases, not just worst cases. Appeals to environmental structure require demonstrating that natural environments fall into the atypical cases where inference becomes tractable—a strong empirical claim yet to be substantiated.

A Framework in Crisis

The computational intractability analysis reveals predictive processing to be a framework that’s fundamentally in crisis. Its central computational claims—that it provides tractable implementation of Bayesian inference, that prediction error minimization enables efficient inference, that hierarchical structure resolves computational problems—are demonstrably false for networks with the structured representations required for cognitive modelling. The standard defense invoking approximation fails, as approximate inference is itself intractable without severe constraints.

What remains viable is dramatically limited. As has been said above, at most, predictive processing might serve as a heuristic or metaphor for understanding certain neural phenomena in narrowly constrained domains. It might describe some aspects of neural processing where the required constraints happen to be satisfied. But it cannot sustain claims to be a unified theory of cortical computation, a general implementation mechanism for Bayesian cognitive models, or a comprehensive account of perception, action, learning, and consciousness.

The path forward requires intellectual honesty about these limitations. Proponents must abandon universalist rhetoric about unified brain theories and grand explanatory scope. They must specify precisely which cognitive domains and neural systems satisfy the constraints necessary for tractable inference. They must develop testable empirical predictions about how neural implementations encode these constraints. Most importantly, they must accept theoretical pluralism—acknowledging that different brain systems likely use radically different computational strategies rather than all implementing variants of predictive processing.

The computational complexity objection does not prove that brains cannot perform sophisticated inference or that Bayesian models of cognition are wrong. It proves that predictive processing, as currently formulated, cannot be the general mechanism by which brains implement such inference. The search for neural implementations of probabilistic reasoning must look elsewhere, perhaps to hybrid architectures combining multiple computational strategies, domain-specific mechanisms exploiting particular environmental regularities, or entirely different approaches to understanding neural computation. The sooner the field acknowledges predictive processing’s fundamental theoretical limitations, the sooner it can pursue more promising alternative frameworks for understanding how brains generate intelligent behavior.

REFERENCES

(Adams et al., 2013). Adams, R.A. et al. “The Computational Anatomy of Psychosis.” Frontiers in Psychiatry 4: 47.

(Alais and Burr, 2004). Alais, D., and Burr, D. “The Ventriloquist Effect Results from Near-Optimal Bimodal Integration.” Current Biology 14, 3: 257-262.

(Anderson, 2014). Anderson, M.L. After Phrenology: Neural Reuse and the Interactive Brain. MIT Press.

(Arora and Barak, 2009). Arora, S. and Barak, B. Computational Complexity: A Modern Approach. Cambridge: Cambridge Univ. Press.

(Barrett and Kurzban, 2006). Barrett, H. C. and Kurzban, R. “Modularity in Cognition: Framing the Debate.” Psychological Review 113, 3: 628-647.

(Barrett et al., 2004). Barrett, L.F. et al. “Arousal Focus and Interoceptive Sensitivity.” In L. F. Barrett al. (eds.), Emotion and Consciousness. New York: Guilford Press. Pp.: 217-244.

(Bastos et. al, 2012). Bastos, A.M. et. al. “Canonical Microcircuits for Predictive Coding.” Neuron 76, 4: 695-711.

(Beck, et al. 2012). Beck, J.M. et al. “Not Noisy, Just Wrong: The Role of Suboptimal Inference in Behavioral Variability.” Neuron 74, 1: 30-39.

(Bowers and Davis, 2012). Bowers, J.S., and Davis, C.J. “Bayesian Just-So Stories in Psychology and Neuroscience.” Psychological Bulletin 138, 3: 389-414.

(Bruineberg, et al., 2018). Bruineberg, J. et al. “The Anticipating Brain is Not a Scientist: The Free-Energy Principle from an Ecological-Enactive Perspective.” Synthese 195, 6: 2417-2444.

(Bubic et al., 2010). Bubic, A. et al. “Prediction, Cognition and the Brain.” Frontiers in Human Neuroscience 4: 25.

(Carandini, 2012). Carandini, M. “From Circuits to Behavior: A Bridge too Far?” Nature Neuroscience 15, 4: 507-509.

(Chalmers, 1996). Chalmers, D.J. The Conscious Mind. Oxford: Oxford Univ. Press.

(Chemero, 2009). Chemero, A. Radical Embodied Cognitive Science. Cambridge MA: MIT Press.

(Clark, 2013). Clark, A. “Whatever Next? Predictive Brains, Situated Agents, and the Future of Cognitive Science.” Behavioral and Brain Sciences 36, 3: 181-204.

(Clark, 2016). Clark, A. Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Oxford: Oxford Univ. Press.

(Clark et al., 2018). Clark, J.E. et al. “What is Mood? A Computational Perspective.” Psychological Medicine 48, 14: 2277-2284.

(Corlett et al., 2009). Corlett, P.R. et al. “From Drugs to Deprivation: A Bayesian Framework for Understanding Models of Psychosis.” Psychopharmacology 206, 4: 515-530.

(Dagum and Luby, 1993). Dagum, P., and Luby, M. “Approximating Probabilistic Inference in Bayesian Belief Networks is NP-hard.” Artificial Intelligence 60, 1: 141-153.

(den Ouden et al., 2012). den Ouden, H.E. et al. “How Prediction Errors Shape Perception, Attention, and Motivation” Frontiers in Psychology 3, 548.

(Eberhardt and Danks, 2001). Eberhardt, F., and Danks, D. “Confirmation in the Cognitive Sciences: The Problematic Case of Bayesian Models.” Minds and Machines 21, 3: 389-410.

(Edwards et al., 2012). Edwards, M.J. et al. “A Bayesian Account of ‘Hysteria’.” Brain. 135, 11: 3495-3512.

(Egner et al., 2010). Egner, T. et al. “Expectation and Surprise Determine Neural Population Responses in the Ventral Visual Stream.” Journal of Neuroscience 30, 49: 16601-16608.

(Ernest and Banks, 2002). Ernst, M.O. and Banks, M.S. “Humans Integrate Visual and Haptic Information in a Statistically Optimal Fashion.” Nature 415, 6870: 429-433.

(Feldman and Friston, 2010). Feldman, H., and Friston, K.J. “Attention, Uncertainty, and Free-Energy.” Frontiers in Human Neuroscience 4: 215.

(Felleman and Van Essen, 1991). Felleman, D.J. and Van Essen, D.C. “Distributed Hierarchical Processing in the Primate Cerebral Cortex.” Cerebral Cortex 1, 1: 1-47.

(Fletcher and Frith, 2009). Fletcher, P.C. and Frith, C.D. “Perceiving is Believing: A Bayesian Approach to Explaining the Positive Symptoms of Schizophrenia.” Nature Reviews Neuroscience 10, 1: 48-58.

(Friston, 2005). Friston, K. “A Theory of Cortical Responses.” Philosophical Transactions of the Royal Society B. 360, 1456: 815-836.

(Friston, 2010). Friston, K. “The Free-Energy Principle: A Unified Brain Theory?” Nature Reviews Neuroscience 11, 2: 127-138.

(Friston et al., 2009). Friston, K. et al. “Reinforcement Learning or Active Inference?” PLoS ONE 4, 7: e6421.

(Friston et al., 2012). Friston, K. et al. “Free-Energy Minimization and the Dark-Room Problem.” Frontiers in Psychology 3: 130.

(Friston et al., 2017). Friston, K. et al. “Active inference: A Process Theory.” Neural Computation 29, 1: 1-49.

(Gallagher and Allen, 2016). Gallagher, S., and Allen, M. “Active Inference, Enactivism and the Hermeneutics of Social Cognition.” Synthese 195, 6: 2627-2648.

(Garey and Johnson, 1979). Garey, M., and Johnson, D. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co.

(Garrido et al., 2009). Garrido, M.I. et al. “The Mismatch Negativity: A Review of Underlying Mechanisms.” Clinical Neurophysiology 120, 3: 453-463.

(Geisler et al., 2001). Geisler, W.S. et al. “Edge Co-Occurrence in Natural Images Predicts Contour Grouping Performance.” Vision Research 41, 6: 711-724.

(Gibson, 1979). Gibson, J.J. The Ecological Approach to Visual Perception. Boston MA: Houghton Mifflin.

(Gigerenzer and Gaissmaier, 2011). Gigerenzer, G., and Gaissmaier, W. “Heuristic Decision Making.” Annual Review of Psychology 62: 451-482.

(Gładziejewski, 2016). Gładziejewski, P. “Predictive Coding and Representationalism.” Synthese 193, 2: 559-582.

(Godfrey-Smith, 1996). Godfrey-Smith, P. Complexity and the Function of Mind in Nature. Cambridge: Cambridge Univ. Press.

(Gopnik and Wellman, 2012). Gopnik, A., and Wellman, H. M. “Reconstructing Constructivism: Causal Models, Bayesian Learning Mechanisms, and the Theory Theory.” Psychological Bulletin 138, 6: 1085-1108.

(Gregory, 1980). Gregory, R. L. “Perceptions as Hypotheses.” Philosophical Transactions of the Royal Society B. 290, 1038: 181-197.

(Griffiths et al., 2010). Griffiths, T. et al. “Probabilistic Models of Cognition: Exploring Representations and Inductive Biases.” Trends in Cognitive Sciences 14, 8: 357-364.

(Grotheer and Kovács, 2016). Grotheer, M., and Kovács, G. “Can Predictive Coding Account for Repetition Suppression?” Cortex 80: 113-124.

(Heilbron and Chait, 2018). Heilbron, M., and Chait, M. “Great Expectations: Is There Evidence for Predictive Coding in Auditory Cortex?” Neuroscience 389: 54-73.

(Hesselmann et al., 2010). Hesselmann, G. et al. “Predictive Coding or Evidence Accumulation? False Inference and Neuronal Fluctuations.” PLoS ONE 5, 3: e9926.

(Hohwy, 2012). Hohwy, J. “Attention and Conscious Perception in the Hypothesis Testing Brain.” Frontiers in Psychology 3: 96.

(Hohwy, 2013). Hohwy, J. The Predictive Mind. Oxford: Oxford Univ. Press.

(Hohwy et al., 2008). Hohwy, J. et al. “Predictive Coding Explains Binocular Rivalry: An Epistemological Review.” Cognition 108, 3: 687-701.

(Ioannidis, 2005). Ioannidis, J.P. “Why Most Published Research Findings are False.” PLoS Medicine 2, 8: e124.

(Jones and Love, 2011). Jones, M., and Love, B.C. “Bayesian Fundamentalism or Enlightenment? On the Explanatory Status and Theoretical Contributions of Bayesian Models of Cognition.” Behavioral and Brain Sciences 34, 4: 169-188.

(Kahneman, 2011). Kahneman, D. Thinking, Fast and Slow. New York: Farrar, Straus and Giroux.

(Kapur, 2003). Kapur, S. “Psychosis as a State of Aberrant Salience: A Framework Linking Biology, Phenomenology, and Pharmacology in Schizophrenia.” American Journal of Psychiatry 160, 1: 13-23.

(Keller and Mrsic-Flogel, 2018). Keller, G.B., and Mrsic-Flogel, T.D. “Predictive Processing: A Canonical Cortical Computation.” Neuron 100, 2: 424-435.

(Klein, 2018). Klein, C. “What do Predictive Coders Want?” Synthese 195, 6: 2541-2557.

(Knill and Pouget, 2004). Knill, D.C., and Pouget, A. “The Bayesian Brain: The Role of Uncertainty in Neural Coding and Computation.” Trends in Neurosciences 27, 2: 712-719.

(Knill and Richards, Eds, 1996). Knill, D.C. and Richards, W. (eds.) Perception as Bayesian Inference. Cambridge: Cambridge University Press.

(Kok et al., 2012). Kok, P. et al. “Less is More: Expectation Sharpens Representations in the Primary Visual Cortex.” Neuron 75, 2: 265-270.

(Kwisthout and van Rooij, 2020). Kwisthout, J., and van Rooij, I. “Computational Resource Demands of a Predictive Bayesian Brain.” Computational Brain and Behavior 3: 174-188.

(Kwisthout et al., 2011). Kwisthout, J. et al. “Bayesian Intractability is Not an Ailment Approximation Can Cure.” Cognitive Science 35, 5: 779-784.

(Landy et al., 2011). Landy, M.S. et al. “Ideal-Observer Models of Cue Integration.” In J. Trommershäuser, K. Kording, and M. S. Landy (eds.), Sensory Cue Integration. Oxford: Oxford Univ. Press: 5-29.

(Lee and Mumford, 2003). Lee, T.S., and Mumford, D. “Hierarchical Bayesian Inference in the Visual Cortex.” Journal of the Optical Society of America A 20, 7: 1434-1448.

(Ma et al., 2006). Ma, W.J. et al. “Bayesian Inference with Probabilistic Population Codes.” Nature Neuroscience 9, 11: 1432-1438.

(Mamassian andGoutcher, 2001). Mamassian, P. and Goutcher, R. “Prior Knowledge on the Illumination Position.” Cognition 81, 1: B1-B9.

(Marcus and Davis, 2013). Marcus, G.F., and Davis, E. “How Robust are Probabilistic Models of Higher-Level Cognition?” Psychological Science 24, 12: 2351-2360.

(Marr, 2010). Marr, D. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: W.H. Freeman.

(Medical Xpress, 2024). Netherlands Institute for Neuroscience. “How the Brain Plans Ahead to Predict the World.” Medical Xpress. 30 October. Available online at URL = <https://medicalxpress.com/news/2024-10-brain-world.html>.

(Merleau-Ponty, 1945/2012). Merleau-Ponty, M. Phenomenology of Perception. Trans, D. Landes. London: Routledge.

(Moran, et al., 2013). Moran, R.J. “Free Energy, Precision and Learning: The Role of Cholinergic Neuromodulation.” Journal of Neuroscience 33, 19: 8227-8236.

(Mumford, 1992). Mumford, D. “On the Computational Architecture of the Neocortex. II. The Role of Cortico-Cortical Loops.” Biological Cybernetics 66, 3, 241-251.

(Niv, 2009). Niv, Y. “Reinforcement Learning in the Brain.” Journal of Mathematical Psychology 53, 3: 139-154.

(Noë, 2006). Noë, A. Action in Perception. Cambridge MA: MIT Press.

(O’Regan and Noë, 2001). O’Regan, J. K., and Noë, A. “A Sensorimotor Account of Vision and Visual Consciousness.” Behavioral and Brain Sciences 24, 5: 939-973.

(Orbán, G. et al., 2016). Orbán, G. et al. “Neural Variability and Sampling-Based Probabilistic Representations in the Visual Cortex.” Neuron 92, 2: 530-543.

(Paulus and Stein, 2006). Paulus, M.P., and Stein, M.B. “An Insular View of Anxiety.” Biological Psychiatry 60, 4: 383-387.

(Pecevski et al., 2011). Pecevski, D. et al. “Probabilistic Inference in General Graphical Models Through Sampling in Stochastic Networks of Spiking Neurons.” PLoS Computational Biology 7, 12: e1002211.

(Pellicano and Burr, 2012). Pellicano, E., and Burr, D. “When the World Becomes ‘Too Real’: A Bayesian Explanation of Autistic Perception.” Trends in Cognitive Sciences 16, 10: 504-510.

(Rahnev and Denison, 2018). Rahnev, D., and Denison, R.N. “Suboptimality in Perceptual Decision Making.” Behavioral and Brain Sciences 41: e223.

(Rao and Ballard, 1999). Rao, R.P. and Ballard, D.H. “Predictive Coding in the Visual Cortex: A Functional Interpretation of Some Extra-Classical Receptive-Field Effects.” Nature Neuroscience 2, 1: 79-87.

(Ratcliffe, 2008). Ratcliffe, M. “Touch and Situatedness.” International Journal of Philosophical Studies 16, 3: 299-322.

(Rescorla, 2016). Rescorla, M. “Bayesian Perceptual Psychology.” In M. Matthen (ed.), The Oxford Handbook of Philosophy of Perception. Oxford: Oxford Univ. Press. Pp. 694-716.

(Sanborn, and Chater, 2016). Sanborn, A.N., and Chater, N. “Bayesian Brains Without Probabilities.” Trends in Cognitive Sciences 20, 12: 883-893.

(Seth, 2021). Seth, A.K. Being You: A New Science of Consciousness. Boston MA: Dutton.

(Summerfield et al., 2008). “Neural Repetition Suppression Reflects Fulfilled Perceptual Expectations.” Nature Neuroscience 11, 9: 1004-1006.

(Sutton and Barto, 2018). Sutton, R.S., and Barto, A.G. Reinforcement Learning: An Introduction. 2^nd edn., Cambridge MA: MIT Press.

(Téglás et al., 2011). Téglás, E. “Pure Reasoning in 12-Month-Old Infants as Probabilistic Inference.” Science 332, 6033: 1054-1059.

(Tenenbaum, 2011). Tenenbaum, J.B. “How to Grow a Mind: Statistics, Structure, and Abstraction.” Science 331: 1279-1285.

(Todd and Gigerenzer, 2012). Todd, P.M., and Gigerenzer, G. Ecological Rationality: Intelligence in the World. Oxford: Oxford Univ. Press.

(Van de Cruys et al., 2014). Van de Cruys, S. et al. “Precise Minds in Uncertain Worlds: Predictive Coding in Autism.” Psychological Review 121, 4: 649-675.

(van Rooij, 2008). van Rooij, I. “The Tractable Cognition Thesis.” Cognitive Science 32: 939-984.

(van Rooji et al., 2019). van Rooij, I. Cognition and Intractability: A Guide to Classical and Parameterized Complexity Analysis. Cambridge: Cambridge Univ. Press.

(Varela et al., 1991). Varela, F.J. et al. The Embodied Mind: Cognitive Science and Human Experience. Cambridge MA: MIT Press.

(Walsh et al., 2020). Walsh, K.S. et al. “Evaluating the Neurophysiological Evidence for Predictive Processing as a Model of Perception.” Annals of the New York Academy of Sciences 1464, 1: 242-268.

(Weiss, et al., 2002). Weiss, Y. “Motion Illusions as Optimal Percepts.” Nature Neuroscience 5, 6: 598-604.

(Williams, 2018). Williams, D. “Predictive Processing and the Representation Wars.” Minds and Machines 28, 1: 141-172.

(Winkler et al., 1996). Winkler, I. “Adaptive Modeling of the Unattended Acoustic Environment Reflected in the Mismatch Negativity Event-Related Potential.” Brain Research 742, 1-2: 239-252. (Yuille and Kersten, 2006). Yuille, A., and Kersten, D. “Vision as Bayesian Inference: Analysis by Synthesis?” Trends in Cognitive Sciences 10, 7: 301-308.

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