When Reality Outpaces Cognition: A New Scaling Principle for Reliable Intelligence

# When Reality Outpaces Cognition:A New Scaling Principle for Reliable Intelligence
Source: [https://arxiv.org/html/2610.20764](https://arxiv.org/html/2610.20764)
Talha Bin RiazTREND Project\|\|Funded by the Advanced Research \+ Invention Agency \(ARIA\)Affiliation:University of Stirling Correspondence:ahsan\.adeel1@stir\.ac\.uk

![Refer to caption](https://arxiv.org/html/2610.20764v1/MRD.png)Figure 2:Operational challenge of when reality outpaces cognition\.The agent is trained at the baseline Speed of Reality \(SR,0=1S\_\{R,0\}=1\), but tested at50×50\\timesthe baseline \(SR=50S\_\{R\}=50\) while computational resources remain fixed\. From State 1, it must infer the action appropriate for the future State 50 while States 2–50 remain unobserved\. The challenge is whether the agent has learned sufficiently generalisable task\-relevant world dynamics to infer a reliable action across this observation–reality gap\.Abstract: This paper challenges the understanding capabilities of existing AI paradigms and emerging world models by asking a fundamental question: How quickly can reality change before an intelligent system can no longer reliably perceive, reason, and act? We formulate this as a theory\- and model\-agnostic challenge in which systems must infer reliable actions for increasingly distant future states across a growing observation–reality gap\. We operationalize this challenge through the effective Speed of Coherent Cognition \(SCeffS\_\{C\}^\{\\mathrm\{eff\}\}\), defined as the highest tested Speed of Reality \(SRS\_\{R\}\) through which a system continuously satisfies a predefined behavioural reliability criterion from baseline\. As a proof of concept, reinforcement\-learning agents are trained at the baselineSRS\_\{R\}and evaluated, without retraining, asSRS\_\{R\}is increased by up to50×50\\timeswhile computational resources remain fixed\. We compare Transformer and gated\-MLP baselines withC​o4Co^\{4\}, an architecture inspired by cellular mechanisms implicated in conscious processing and awake thought\. Across the tested scenarios,C​o4Co^\{4\}achieves substantially higherSCeffS\_\{C\}^\{\\mathrm\{eff\}\}than the baselines, motivatingSCeffS\_\{C\}^\{\\mathrm\{eff\}\}as a new benchmark and the scaling of coherent cognition as a principle for reliable AI\.

## 1Introduction

IncreasingSRS\_\{R\}does not merely evaluate the processing speed of an intelligent system, but rather its ability to infer the consequences of actions and maintain reliable behaviour in rapidly changing situations that have not yet been directly observed\. One might ask why an AI system should not simply be trained at theSRS\_\{R\}expected during deployment\. However, for future autonomous AI systems, particularly in mission\- or safety\-critical settings, it may not be possible to guarantee that training exhaustively captures the maximum rate of relevant change, ambiguity, uncertainty, or abrupt environmental dynamics that may be encountered during deployment\. Such systems must perceive, reason, and act reliably as environmental dynamics depart from those experienced during training\. Understanding where and how this reliability degrades is therefore important for establishing safe operating limits and developing AI systems that remain dependable under unforeseen deployment conditions\[[1](https://arxiv.org/html/2610.20764#bib.bib20)\]\. The proposed challenge is domain\-general in formulation and may extend to settings in which physical, informational, multi\-agent, or adversarial dynamics outpace a system’s capacity to maintain coherent understanding and reliable behaviour, with implications for the development and evaluation of safe and reliable AI\. The relationship between the proposed challenge and neighbouring work on temporal out\-of\-distribution \(OOD\) generalisation, frame skipping/action repetition, observation latency, delayed control, partial observability, dynamics shifts, and world models is discussed in Appendix A\[[2](https://arxiv.org/html/2610.20764#bib.bib2),[3](https://arxiv.org/html/2610.20764#bib.bib4),[4](https://arxiv.org/html/2610.20764#bib.bib3),[5](https://arxiv.org/html/2610.20764#bib.bib5),[6](https://arxiv.org/html/2610.20764#bib.bib6),[7](https://arxiv.org/html/2610.20764#bib.bib7),[8](https://arxiv.org/html/2610.20764#bib.bib8),[9](https://arxiv.org/html/2610.20764#bib.bib9),[10](https://arxiv.org/html/2610.20764#bib.bib10),[11](https://arxiv.org/html/2610.20764#bib.bib11),[12](https://arxiv.org/html/2610.20764#bib.bib14),[13](https://arxiv.org/html/2610.20764#bib.bib29),[14](https://arxiv.org/html/2610.20764#bib.bib12),[15](https://arxiv.org/html/2610.20764#bib.bib13)\]\.

## 2FormalizingSRS\_\{R\}andSCeffS\_\{C\}^\{\\mathrm\{eff\}\}

We begin with an illustrative example of reality outpacing cognition\. Imagine running through a dense forest \(Figures 1 and 2\)\. From the observable environment detected by biological and extended sensors, internally generated predictions guide attention moment\-by\-moment toward contextually valid and relevant signals, such as trees, branches, and rocks, in order to support reliable action\. As bodily motion increases, the local observable environment changes more rapidly relative to the observer\. The speed of this change determines how fast the cognitive system must update and use its internal representation of the environment to maintain coherent understanding and make reliable and useful probabilistic judgments\. At ordinary speeds, the runner observes the environment evolving through successive situations\. For example, an approaching obstacle may be observed asfar→closer→close→very close\\text\{far\}\\rightarrow\\text\{closer\}\\rightarrow\\text\{close\}\\rightarrow\\text\{very close\}allowing the runner to continuously update action as the situation evolves\.

Now imagine that the speed of this observable reality increases beyond the rate at which the cognitive system can maintain and use such coherent representations\. As the runner continues, the forest rushes past faster and faster\. In the extreme case, for example atSR=50S\_\{R\}=50, the runner observes the forest at State 1 and must infer the action appropriate for the future State 50 while States 2–50 remain unobserved\. For example, an approaching obstacle may be observed asfar→very close\\text\{far\}\\rightarrow\\text\{very close\}, without the intermediate states being observed\. Rather than observing and updating action across the successive states experienced at ordinary speeds, the runner must bridge an increasing observation–reality gap\. As more unobserved environmental changes occur, uncertainty about the future ground\-truth state increases\. Trees, branches, and rocks become increasingly difficult to distinguish in time, while previously adequate interpretations may become outdated before they can reliably guide action\. Increasing visual blur \(Figure 1, left\) is a metaphor for the growing ambiguity caused by unobserved environmental change, not literal sensory blur\.

Eventually, environmental dynamics exceed the system’s capacity to integrate available evidence, maintain a coherent and useful representation of its surroundings, and infer an appropriate action for the relevant future state before that state is observed\. The resulting mismatch increases the likelihood of misjudgment and harmful action, such as colliding with a tree or stumbling over a rock\. We refer to this regime asmind\-\-reality111A conceptual label for the relationship between the rate of environmental change and a system’s capacity for coherent cognition, without implying any particular account of machine mentality\.overload\. Conceptually,

where,

- •SRS\_\{R\}denotes theSpeed of Reality, characterizing the rate of task\-relevant environmental change relative to the system’s observation–action cycle\. IncreasingSRS\_\{R\}therefore increases the amount of environmental evolution occurring across this cycle, enlarging the gap between the currently observed state and the future state for which an action must remain appropriate\.
- •SCS\_\{C\}denotes theSpeed of Coherent Cognition, defined as the rate at which the system can distinguish valid and relevant information from invalid or irrelevant information, and selectively utilize the former to maintain reliable perception, reasoning, and action\.

Importantly, increasingSRS\_\{R\}during testing systematically increases the task\-relevant environmental change occurring between observation and required action, thereby progressively enlarging the observation–reality gap\. However, the broader challenge is not restricted to temporal acceleration and can be generalised to other forms of increasing environmental ambiguity, uncertainty, and complexity that challenge a system’s ability to distinguish valid and relevant information from invalid or irrelevant information and maintain reliable behaviour\. Thus,SRS\_\{R\}provides one operational instantiation of a more general challenge: determining the limits of coherent cognition under increasingly demanding environmental conditions\.

The relationship betweenSRS\_\{R\}andSCS\_\{C\}can then be expressed through the dimensionless mind–reality ratio:

γ=SCSR\\gamma=\\frac\{S\_\{C\}\}\{S\_\{R\}\}\(2\)such that

γ≥1\\displaystyle\\gamma\\geq 1Mind–reality synchrony\(3\)γ<1\\displaystyle\\gamma<1Mind–reality overload\(4\)Here,SCS\_\{C\}denotes a theoretical capacity, distinct from the empirically estimated quantitySCeffS\_\{C\}^\{\\mathrm\{eff\}\}introduced below\.

The challenge is not whether a system can process familiar observations faster, but whether its learned task\-relevant world dynamics can support reliable action over temporal horizons that increasingly extend beyond those encountered during training\.

Letℛ⁡\(SR\)\\mathcal\{R\}\(S\_\{R\}\)denote a task\-specific behavioural reliability measure at a givenSRS\_\{R\}, and letτ\\taudenote a predefined minimum reliability threshold\. Reliable behaviour is maintained when:

ℛ⁡\(SR\)≥τ\\mathcal\{R\}\(S\_\{R\}\)\\geq\\tau\(5\)
Let the finite set ofSRS\_\{R\}values evaluated experimentally be

𝒮test=\{s1,s2,…,sn\},s1=SR,0<s2<⋯<sn\\mathcal\{S\}\_\{\\mathrm\{test\}\}=\\\{s\_\{1\},s\_\{2\},\\ldots,s\_\{n\}\\\},\\qquad s\_\{1\}=S\_\{R,0\}<s\_\{2\}<\\cdots<s\_\{n\}\(6\)
wheresks\_\{k\}denotes thekkth tested value ofSRS\_\{R\}, ordered from the training baseline\. We define the experimentally estimatedSCeffS\_\{C\}^\{\\mathrm\{eff\}\}as

SCeff=max⁡\{sk∈𝒮test\|ℛ⁡\(si\)≥τ​∀i≤k\}S\_\{C\}^\{\\mathrm\{eff\}\}=\\max\\left\\\{s\_\{k\}\\in\\mathcal\{S\}\_\{\\mathrm\{test\}\}\\;\\middle\|\\;\\mathcal\{R\}\(s\_\{i\}\)\\geq\\tau\\;\\;\\forall\\,i\\leq k\\right\\\}\(7\)
SCeffS\_\{C\}^\{\\mathrm\{eff\}\}is the highest testedSRS\_\{R\}through which the predefined reliability criterion is continuously satisfied from the training baseline\. It therefore represents an empirical behavioural boundary rather than a direct measure of cognitive speed\. Comparisons ofSCeffS\_\{C\}^\{\\mathrm\{eff\}\}should be made under matched experimental conditions\.

SCeffS\_\{C\}^\{\\mathrm\{eff\}\}is not an exhaustive measure of understanding, but characterizes the dynamic reliability boundary at which this capacity begins to break down\. Conceptually, the condition for coherent cognition can be expressed as

ScalingSCS\_\{C\}therefore means extending the range of environmental dynamics over which this condition can be maintained\. It is not merely a matter of processing observations faster, but of effectively using available information and computational resources to maintain task\-relevant representations and select reliable actions as environmental dynamics accelerate\. This motivates the new scaling principle:

> ScaleSCS\_\{C\}, not merely FLOPs, parameters, and data\.

## 3OperationalisingSCeffS\_\{C\}^\{\\mathrm\{eff\}\}

For reinforcement\-learning \(RL\) tasks, Co4\(Figure 1, right\)\[[16](https://arxiv.org/html/2610.20764#bib.bib22),[17](https://arxiv.org/html/2610.20764#bib.bib28)\]is compared with the Transformer\-based architecture proposed in\[[18](https://arxiv.org/html/2610.20764#bib.bib27)\]and a gated MLP \(gMLP\)\[[19](https://arxiv.org/html/2610.20764#bib.bib25)\]\. We additionally compare Co4variants in which the form of apical modulation\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[20](https://arxiv.org/html/2610.20764#bib.bib26),[21](https://arxiv.org/html/2610.20764#bib.bib24)\], including apical amplification \(AA\) and apical driven \+ awake \(ADA\) are systematically altered\. The architectures are evaluated under matched experimental conditions, including the same environments and computational constraints, with architecture\-specific configurations reported below\. As a proof of concept, we evaluate the proposed test in two environments: car racing\[[18](https://arxiv.org/html/2610.20764#bib.bib27),[22](https://arxiv.org/html/2610.20764#bib.bib18)\]and complex vision\-guided quadrupedal locomotion\[[23](https://arxiv.org/html/2610.20764#bib.bib19)\]\.

### 3\.1TheC​o4Co^\{4\}Computational Principle

C​o4Co^\{4\}evaluates incoming evidence against local and global contextual predictions and contextual adequacy via modulatory \(MOD\) functions\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[20](https://arxiv.org/html/2610.20764#bib.bib26)\]before substantially influencing downstream processing\. Evidence that is both valid and relevant is amplified \(effectively assigned greater precision\[[24](https://arxiv.org/html/2610.20764#bib.bib23)\]\), whereas poorly supported evidence is attenuated, implementing the principle ofverification before propagation\.

In the proof\-of\-concept experiments considered here,C​o4Co^\{4\}implements this principle through triadic modulation loops amongQQ\-,KK\-, andVV\-two\-point neurons \(TPNs\)\[[17](https://arxiv.org/html/2610.20764#bib.bib28)\], which modulate information according to contextual support before attentional competition\. ForQQ\-TPNs, each token provides a primary evidence stream \(RR\), while local and global contextual inputs \(CC\) are provided by theKKandVVprojections, respectively\. The same principle applies toKK\- andVV\-TPNs\. Adequacy represents task\-dependent prediction or feedback\. Further details are provided in\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[25](https://arxiv.org/html/2610.20764#bib.bib21)\]\.

### 3\.2Vision\-Guided Quadrupedal Locomotion

We evaluate vision\-guided quadrupedal locomotion under two task conditions of increasing complexity: easy and complex\. Here, “easy” and “complex” refer to scenarios in which objects are farther from and closer to the agent, respectively\. All systems are trained only at the baseline Speed of Reality,SR,0=1S\_\{R,0\}=1, and subsequently evaluated without retraining asSRS\_\{R\}is increased while computational resources remain fixed\. Because the two conditions differ in task difficulty and reward scale, reliability thresholds are predefined separately for each condition\.

#### 3\.2\.1Easy Locomotion Task

In the easier vision\-guided locomotion environment, where obstacles are more widely separated, all architectures learn effective policies under the baseline training condition \(SR=1S\_\{R\}=1\), although with different learning curves and asymptotic rewards \(Figure 3\)\. The Transformer andC​o4Co^\{4\}architectures each consist of two layers and four attention heads, whereas the gMLP architecture consists of two layers\. The Transformer achieves a baseline performance comparable to theC​o4Co^\{4\}variants, whereas the gMLP converges to a lower reward\. This environment therefore provides a useful setting for testing whether policies that perform successfully under the training condition differ in their ability to maintain reliable behaviour asSRS\_\{R\}increases\.

![Refer to caption](https://arxiv.org/html/2610.20764v1/rewards_plot_randomshape_smoothened.png)Figure 3:Training performance in the easy vision\-guided quadrupedal locomotion environment\.Running average reward over training epochs for the Transformer, gMLP, and twoC​o4Co^\{4\}variants atSR,0=1S\_\{R,0\}=1\. In the easy environment, obstacles are more widely separated, allowing all architectures to learn the locomotion task, although with different learning trajectories and final performance levels\.![Refer to caption](https://arxiv.org/html/2610.20764v1/reward_graph_randomshape_4_whiskers.png)Figure 4:ScalingSCeffS\_\{C\}^\{\\mathrm\{eff\}\}in the easy vision\-guided quadrupedal locomotion task\.Reward is shown asSRS\_\{R\}increases from the training baselineSR,0=1S\_\{R,0\}=1toSR=50S\_\{R\}=50without retraining\. The dashed line denotes the predefined reliability thresholdτ=500\\tau=500\.Table 1:Performance in the easy vision\-guided quadrupedal locomotion task asSRS\_\{R\}increases\. Values are mean±\\pmstandard deviation\.Figure 4 and Table 1 show the resulting reward asSRS\_\{R\}increases without retraining\. The Transformer satisfies the reliability criterion throughSR=2S\_\{R\}=2and first falls below the threshold atSR=3S\_\{R\}=3, yieldingSC,Transformereff=2S\_\{C,\\mathrm\{Transformer\}\}^\{\\mathrm\{eff\}\}=2\. Co4\-ADA maintains mean reward above the reliability threshold throughSR=10S\_\{R\}=10and falls below the threshold atSR=20S\_\{R\}=20, yieldingSC,Co4​\-ADAeff=10S\_\{C,\\mathrm\{Co\}^\{4\}\\text\{\-ADA\}\}^\{\\mathrm\{eff\}\}=10\. Co4\-AA remains above the reliability threshold throughSR=20S\_\{R\}=20and falls below the threshold atSR=30S\_\{R\}=30, yieldingSC,Co4​\-AAeff=20S\_\{C,\\mathrm\{Co\}^\{4\}\\text\{\-AA\}\}^\{\\mathrm\{eff\}\}=20\. The corresponding transitions are therefore localized betweenSR=10S\_\{R\}=10andSR=20S\_\{R\}=20for Co4\-ADA, and betweenSR=20S\_\{R\}=20andSR=30S\_\{R\}=30for Co4\-AA\. The standard gMLP does not satisfy the predefined reliability criterion at the training baseline,SR,0=1S\_\{R,0\}=1, and therefore does not satisfy the baseline eligibility requirement for estimatingSCeffS\_\{C\}^\{\\mathrm\{eff\}\}under this test; itsSCeffS\_\{C\}^\{\\mathrm\{eff\}\}is left undefined\.

Representative attention visualizations provide a qualitative view of how the architectures process task\-relevant visual information\. Figure 5 shows comparatively diffuse attention for the Transformer baseline and more selective attention for Co4with contextual modulation\. When the obstacle is distant, Co4concentrates attention on the immediately relevant traversable region and shifts attention toward the obstacle as it becomes locally relevant\. The corresponding sequence\-level attention map is also substantially sparser\. These examples are consistent with the hypothesis that contextual modulation restricts the propagation of currently irrelevant and invalid information before attentional competition\.

![Refer to caption](https://arxiv.org/html/2610.20764v1/attenntion_map_viz.png)Figure 5:Representative attention patterns in vision\-guided quadrupedal locomotion\.The Transformer exhibits comparatively diffuse attention \(top\): when the obstacle is distant, attention extends substantially over background regions, while proximity to the obstacle produces broadly distributed attention across the visual input\. In contrast, Co4\(middle\) exhibits more selective attention, concentrating on the immediately relevant traversable region while the obstacle is distant and shifting toward the obstacle as it becomes locally relevant\. This difference is also reflected in the sequence\-level attention maps \(bottom\), where Co4produces a substantially sparser pattern\.![Refer to caption](https://arxiv.org/html/2610.20764v1/rewards_plot_allThinWide_smoothenedn.png)Figure 6:Training performance in the complex vision\-guided quadrupedal locomotion environment\.Running average reward during training for the Transformer and gMLP baselines and Co4variants implementing different forms of apical modulation\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[20](https://arxiv.org/html/2610.20764#bib.bib26)\]\. Performance differs substantially across modulation conditions\. Disabling the Co4modulation equations provides a control for assessing the functional contribution of contextual modulation\.![Refer to caption](https://arxiv.org/html/2610.20764v1/gMLP.png)Figure 7:ScalingSCeffS\_\{C\}^\{\\mathrm\{eff\}\}in the complex vision\-guided quadrupedal locomotion task\.Reward is shown asSRS\_\{R\}increases from the training baselineSR,0=1S\_\{R,0\}=1toSR=50S\_\{R\}=50without retraining\. The dashed line denotes the predefined reliability thresholdτ=300\\tau=300\. Although the three\-layer gMLP performed comparably to the two\-layerC​o4Co^\{4\}during training, it showed substantially weaker generalisation asSRS\_\{R\}increased\. Further architectural optimization, including increasing the number of layers, is beyond the scope of the present general challenge\.
#### 3\.2\.2Complex Locomotion Task

Figure 6 shows training performance in the complex vision\-guided quadrupedal locomotion environment atSR,0=1S\_\{R,0\}=1\. The Transformer andC​o4Co^\{4\}architectures each consist of two layers and four attention heads, whereas the gMLP architecture is evaluated with both two\-layer and three\-layer configurations\. The Co4\-AA and Co4\-ADA achieve the highest running\-average rewards over training, whereas the Transformer, gated\-MLP, and severalC​o4Co^\{4\}ablations and alternative modulation schemes converge to lower reward levels\. In particular, disabling the Co4modulation equations\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[20](https://arxiv.org/html/2610.20764#bib.bib26)\]removes much of the performance advantage observed for the better\-performing Co4variants\. These results support the functional importance of contextual modulation for learned task performance\.

Importantly, performance atSR=1S\_\{R\}=1alone does not establish how well an agent has captured the dynamics required to remain reliable when its access to current reality is reduced\. The subsequentSRS\_\{R\}test therefore evaluates how far each trained system can be taken beyond its baseline observation condition, without retraining, before its behavioural reliability criterion is no longer satisfied\.

Table 2:Performance in the complex vision\-guided quadrupedal locomotion environment asSRS\_\{R\}increases\. Values are mean±\\pmstandard deviation\.![Refer to caption](https://arxiv.org/html/2610.20764v1/carracing_learning_curve.png)Figure 8:Learning curves for the car\-racing task\.![Refer to caption](https://arxiv.org/html/2610.20764v1/reward_graph_withWhiskers_carracing.png)Figure 9:Scaling the Speed of Coherent Cognition in the car\-racing task\.Mean reward for the Transformer baseline and Co4asSRS\_\{R\}increases from11to77, without retraining and with computational resources held fixed\. The dashed line indicates the predefined reliability threshold,τ=300\\tau=300\. The Transformer remains reliable throughSR=2S\_\{R\}=2and Co4throughSR=4S\_\{R\}=4, yieldingSCeff=2S\_\{C\}^\{\\mathrm\{eff\}\}=2andSCeff=4S\_\{C\}^\{\\mathrm\{eff\}\}=4, respectively\.Figure 7 and Table 2 show the resulting reward asSRS\_\{R\}increases without retraining\. The Transformer baseline maintains reliable behaviour throughSR=2S\_\{R\}=2and first falls below the reliability threshold atSR=3S\_\{R\}=3, yieldingSC,Transformereff=2S\_\{C,\\mathrm\{Transformer\}\}^\{\\mathrm\{eff\}\}=2\. Co4remains reliable throughSR=20S\_\{R\}=20and first falls below threshold at the next tested operating point,SR=30S\_\{R\}=30, yieldingSC,Co4eff=20S\_\{C,\\mathrm\{Co\}^\{4\}\}^\{\\mathrm\{eff\}\}=20\. Under this predefined criterion and the tested operating points, Co4therefore extends the observed continuously reliable range ofSRS\_\{R\}by a factor of ten relative to the Transformer baseline under the tested operating points\.

### 3\.3Car Racing

The car\-racing models are also trained only atSR,0=1S\_\{R,0\}=1\. For this experiment, reliable behaviour is defined by the predefined reward thresholdτ=300\\tau=300\. The Transformer andC​o4Co^\{4\}architectures each consist of two layers and four attention heads\. Figure 8 depicts the learning curves of the two models\. TheC​o4Co^\{4\}–AA model reaches its peak reward after approximately 100 iterations, whereas the Transformer requires nearly 500 iterations to achieve a comparable reward level\. This indicates substantially faster convergence for theC​o4Co^\{4\}–AA\.

Table 3:Performance in the car racing task asSRS\_\{R\}increases\. Values are mean±\\pmstandard deviationFigure 9 and Table 3 show the resulting reward asSRS\_\{R\}increases without retraining\. The Transformer baseline satisfies the reliability criterion throughSR=2S\_\{R\}=2and first falls below threshold atSR=3S\_\{R\}=3, yieldingSC,Transformereff=2S\_\{C,\\mathrm\{Transformer\}\}^\{\\mathrm\{eff\}\}=2\. Co4remains reliable throughSR=4S\_\{R\}=4and first falls below threshold atSR=5S\_\{R\}=5, yieldingSC,Co4eff=4S\_\{C,\\mathrm\{Co\}^\{4\}\}^\{\\mathrm\{eff\}\}=4\. Co4therefore extends the observed continuously reliable range ofSRS\_\{R\}by a factor of two relative to the Transformer baseline under the tested operating points\.

## 4Conclusion and Future Directions

An important next step is to apply this challenge to state\-of\-the\-art AI and emerging world models\[[22](https://arxiv.org/html/2610.20764#bib.bib18),[26](https://arxiv.org/html/2610.20764#bib.bib15),[27](https://arxiv.org/html/2610.20764#bib.bib17),[28](https://arxiv.org/html/2610.20764#bib.bib16)\], as well as computational frameworks such as Active Inference\[[24](https://arxiv.org/html/2610.20764#bib.bib23)\]\. We hypothesise that the superior reliability demonstrated byC​o4Co^\{4\}may arise from an enhanced capacity for grounded imagination\[[21](https://arxiv.org/html/2610.20764#bib.bib24),[29](https://arxiv.org/html/2610.20764#bib.bib1),[17](https://arxiv.org/html/2610.20764#bib.bib28),[16](https://arxiv.org/html/2610.20764#bib.bib22)\]\. While the present proof of concept demonstrates behavioural advantages consistent with this hypothesis, the underlying mechanisms of grounded imagination will be investigated explicitly in future work involving scaled world models\. Overall, for reliable AI, the scaling principle is simple:scaleSCS\_\{C\}, not merely FLOPs, parameters, and data\.

## 5Impact

Improving the epistemic reliability of increasingly capable AI systems is essential for their safe deployment\[[1](https://arxiv.org/html/2610.20764#bib.bib20)\]\. By challenging existing AI paradigms and introducing a new principle for scaling AI, this work offers a potential biologically inspired foundation for scaling justified trust in AI systems, with broader benefits for society\[[25](https://arxiv.org/html/2610.20764#bib.bib21)\]\.

## 6Acknowledgments

We acknowledge funding from the Advanced Research \+ Invention Agency \(ARIA\) through the Nature Computes Better Opportunity Seeds programme\. We thank Professor Bill Phillips, Professor Leslie Smith, and Professor Bruce Graham from the University of Stirling; Dr James Kay from the School of Mathematics, University of Glasgow; Dr Lucy S\. Petro from the School of Psychology and Neuroscience, University of Glasgow; Professor Johan Frederik Storm, Professor of Neurophysiology at the University of Oslo, and Professor Hadi Larijani from Glasgow Caledonian University\. We also acknowledge ChatGPT for assistance with proofreading and coding support\.

## Appendix ARelated Work

Prior work\[[2](https://arxiv.org/html/2610.20764#bib.bib2),[3](https://arxiv.org/html/2610.20764#bib.bib4),[4](https://arxiv.org/html/2610.20764#bib.bib3),[5](https://arxiv.org/html/2610.20764#bib.bib5),[6](https://arxiv.org/html/2610.20764#bib.bib6),[7](https://arxiv.org/html/2610.20764#bib.bib7),[8](https://arxiv.org/html/2610.20764#bib.bib8),[9](https://arxiv.org/html/2610.20764#bib.bib9),[10](https://arxiv.org/html/2610.20764#bib.bib10),[11](https://arxiv.org/html/2610.20764#bib.bib11),[12](https://arxiv.org/html/2610.20764#bib.bib14),[13](https://arxiv.org/html/2610.20764#bib.bib29),[14](https://arxiv.org/html/2610.20764#bib.bib12),[15](https://arxiv.org/html/2610.20764#bib.bib13)\]has studied several neighbouring aspects of temporal robustness in reinforcement learning, including observation and action delays, temporal abstraction and adaptive action duration, robustness to changes in control frequency and temporal discretization, and generalisation under environment or dynamics shifts\. These directions address important forms of temporal and distributional variation, but differ from the evaluation considered here\. In the proposed challenge, agents are trained exclusively at a baseline Speed of Reality,SR,0=1S\_\{R,0\}=1, and evaluated without retraining or adaptation asSRS\_\{R\}is systematically increased while computational resources remain fixed\. Thus, increasingSRS\_\{R\}progressively enlarges the observation–reality gap beyond that experienced during training\. The intervention is therefore not simply frame skipping, a change in sensory appearance or physical parameters, or training an agent to compensate for a known delay or altered control frequency\. Instead, it tests whether task\-relevant dynamics learned at the baseline support reliable action across increasingly distant temporal relationships that were not encountered during training\. The resultingSRS\_\{R\}sweep provides a model\-agnostic stress test of zero\-shot temporal generalisation under increasingly rapid task\-relevant environmental change, complementing existing delay, control\-frequency, robustness, and OOD evaluation paradigms\.

## Appendix BExperimental details

For quadrupedal locomotion, a single image is used to compute each output\. Covering more than 50% of the track is considered reliable behaviour\. The robot is rewarded according to multiple objectives, ranging from keeping its body above the ground \(i\.e\., remaining upright\) to maintaining high velocities along thexx,yy, andzzaxes, and is penalised for contact with obstacles\. The mean and standard deviation are computed over 10 runs\. The simulation setup remains the same as that presented in\[[23](https://arxiv.org/html/2610.20764#bib.bib19)\]\.

For car racing, each training input consists of the current image frame together with the previous three frames\. Each episode contains a maximum of 1000 frames while the car remains on the track\. The car receives a reward for visiting each new track tile during training and is penalised for other behaviours\. Reliable behaviour is defined as achieving at least 50% of the task, with the corresponding reward score used to define the reliability threshold\. The mean and standard deviation are computed over 10 runs\. The simulation setup remains the same as that presented in\[[18](https://arxiv.org/html/2610.20764#bib.bib27),[22](https://arxiv.org/html/2610.20764#bib.bib18)\]\.

### B\.1Architectural and Computational Comparison

C​o4Co^\{4\}and the Transformer baseline are matched in parameter count\. Unlike conventional full attention,C​o4Co^\{4\}employs contextual modulation to distinguish valid and relevant from invalid or irrelevantQQ\-KK\-VVtoken representations before downstream processing\. Once contextual verification has been performed, the downstream readout can be selected according to architectural and computational requirements, including attention, pruning, gating, or MLP\-based processing\.

In the present proof\-of\-concept implementation, attention is restricted to the top\-kkcontextually relevant tokens, yielding an attention\-related computational complexity ofO⁡\(N\+k2\)O\(N\+k^\{2\}\), whereNNis the number of input tokens,k≪Nk\\ll N, andk≤Nk\\leq\\sqrt\{N\}\. Thus, the implementation combines contextual verification with computationally selective attention, achieving substantially improved behavioural reliability with matched parameter counts and reduced computational FLOPs relative to the Transformer baseline\. Further details are provided in\[[17](https://arxiv.org/html/2610.20764#bib.bib28),[16](https://arxiv.org/html/2610.20764#bib.bib22)\]\.

## References

- \[1\]D\. Dalrymple, J\. Skalse, Y\. Bengio, S\. Russell, M\. Tegmark, S\. Seshia, S\. Omohundro, C\. Szegedy, B\. Goldhaber, N\. Ammann,et al\.\(2024\)Towards guaranteed safe ai: a framework for ensuring robust and reliable ai systems\.arXiv preprint arXiv:2405\.06624\.Cited by:[§1](https://arxiv.org/html/2610.20764#S1.p1.1),[§5](https://arxiv.org/html/2610.20764#S5.p1.1)\.
- \[2\]S\. Sharma, A\. Srinivas, and B\. Ravindran\(2017\)Learning to repeat: fine grained action repetition for deep reinforcement learning\.arXiv preprint arXiv:1702\.06054\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[3\]A\. Biedenkapp, R\. Rajan, F\. Hutter, and M\. Lindauer\(2021\)Temporl: learning when to act\.InInternational Conference on Machine Learning,pp\. 914–924\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[4\]C\. Tallec, L\. Blier, and Y\. Ollivier\(2019\)Making deep q\-learning methods robust to time discretization\.InInternational Conference on Machine Learning,pp\. 6096–6104\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[5\]S\. Ramstedt and C\. Pal\(2019\)Real\-time reinforcement learning\.Advances in neural information processing systems32\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[6\]S\. Ramstedt, Y\. Bouteiller, G\. Beltrame, C\. Pal, and J\. Binas\(2020\)Reinforcement learning with random delays\.arXiv preprint arXiv:2010\.02966\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[7\]I\. Anokhin, R\. Rishav, M\. Riemer, S\. Chung, I\. Rish, and S\. Ebrahimi Kahou\(2025\)Handling delay in real\-time reinforcement learning\.InInternational Conference on Learning Representations,Vol\.2025,pp\. 47812–47835\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[8\]C\. Tessler, Y\. Efroni, and S\. Mannor\(2019\)Action robust reinforcement learning and applications in continuous control\.InInternational Conference on Machine Learning,pp\. 6215–6224\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[9\]Z\. Zhang, Z\. Li, B\. Rahmati, R\. H\. Yang, Y\. Ma, A\. Rasouli, S\. Pakdamansavoji, Y\. Wu, L\. Zhang, T\. Cao,et al\.\(2026\)Do world action models generalize better than vlas? a robustness study\.arXiv preprint arXiv:2603\.22078\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[10\]S\. Li, Y\. Wu, X\. Cui, H\. Dong, F\. Fang, and S\. Russell\(2019\)Robust multi\-agent reinforcement learning via minimax deep deterministic policy gradient\.InProceedings of the AAAI conference on artificial intelligence,Vol\.33,pp\. 4213–4220\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[11\]S\. Padakandla\(2021\)A survey of reinforcement learning algorithms for dynamically varying environments\.ACM Computing Surveys \(CSUR\)54\(6\),pp\. 1–25\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[12\]R\. Kirk, A\. Zhang, E\. Grefenstette, and T\. Rocktäschel\(2023\)A survey of zero\-shot generalisation in deep reinforcement learning\.Journal of Artificial Intelligence Research76,pp\. 201–264\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[13\]T\. Xiao, E\. Jang, D\. Kalashnikov, S\. Levine, J\. Ibarz, K\. Hausman, and A\. Herzog\(2020\)Thinking while moving: deep reinforcement learning with concurrent control\.arXiv preprint arXiv:2004\.06089\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[14\]H\. Zhang, H\. Chen, C\. Xiao, B\. Li, M\. Liu, D\. Boning, and C\. Hsieh\(2020\)Robust deep reinforcement learning against adversarial perturbations on state observations\.Advances in neural information processing systems33,pp\. 21024–21037\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[15\]J\. Tobin, R\. Fong, A\. Ray, J\. Schneider, W\. Zaremba, and P\. Abbeel\(2017\)Domain randomization for transferring deep neural networks from simulation to the real world\.In2017 IEEE/RSJ international conference on intelligent robots and systems \(IROS\),pp\. 23–30\.Cited by:[Appendix A](https://arxiv.org/html/2610.20764#A1.p1.1),[§1](https://arxiv.org/html/2610.20764#S1.p1.1)\.
- \[16\]A\. Adeel\(2025\)Beyond attention: toward machines with intrinsic higher mental states\.arXiv preprint arXiv:2505\.06257\.Cited by:[§B\.1](https://arxiv.org/html/2610.20764#A2.SS1.p2.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1),[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[17\]A\. Adeel and M\. Bilal\(2026\)Scalable machines with intrinsic higher mental\-state dynamics\.arXiv preprint arXiv:2603\.13453\.Cited by:[§B\.1](https://arxiv.org/html/2610.20764#A2.SS1.p2.1),[Figure 6](https://arxiv.org/html/2610.20764#S3.F6),[Figure 6](https://arxiv.org/html/2610.20764#S3.F6.7.1),[§3\.1](https://arxiv.org/html/2610.20764#S3.SS1.p1.1),[§3\.1](https://arxiv.org/html/2610.20764#S3.SS1.p2.1),[§3\.2\.2](https://arxiv.org/html/2610.20764#S3.SS2.SSS2.p1.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1),[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[18\]Y\. Tang and D\. Ha\(2021\)The sensory neuron as a transformer: permutation\-invariant neural networks for reinforcement learning\.Advances in Neural Information Processing Systems34,pp\. 22574–22587\.Cited by:[Appendix B](https://arxiv.org/html/2610.20764#A2.p2.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1)\.
- \[19\]H\. Liu, Z\. Dai, D\. So, and Q\. V\. Le\(2021\)Pay attention to mlps\.Advances in neural information processing systems34,pp\. 9204–9215\.Cited by:[§3](https://arxiv.org/html/2610.20764#S3.p1.1)\.
- \[20\]B\. P\. Graham, J\. W\. Kay, and W\. A\. Phillips\(2025\)Context\-sensitive processing in a model neocortical pyramidal cell with two sites of input integration\.Neural Computation37\(4\),pp\. 588–634\.Cited by:[Figure 6](https://arxiv.org/html/2610.20764#S3.F6),[Figure 6](https://arxiv.org/html/2610.20764#S3.F6.7.1),[§3\.1](https://arxiv.org/html/2610.20764#S3.SS1.p1.1),[§3\.2\.2](https://arxiv.org/html/2610.20764#S3.SS2.SSS2.p1.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1)\.
- \[21\]W\. A\. Phillips, T\. Bachmann, W\. Spratling, L\. Muckli, L\. Petro, and T\. Zolnik\(2024\)Cellular psychology: relating cognition to context\-sensitive pyramidal cells\.Trends in Cognitive Sciences\.Cited by:[§3](https://arxiv.org/html/2610.20764#S3.p1.1),[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[22\]D\. Ha and J\. Schmidhuber\(2018\)World models\.arXiv preprint arXiv:1803\.101222\(3\),pp\. 440\.Cited by:[Appendix B](https://arxiv.org/html/2610.20764#A2.p2.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1),[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[23\]R\. Yang, M\. Zhang, N\. Hansen, H\. Xu, and X\. Wang\(2021\)Learning vision\-guided quadrupedal locomotion end\-to\-end with cross\-modal transformers\.arXiv preprint arXiv:2107\.03996\.Cited by:[Appendix B](https://arxiv.org/html/2610.20764#A2.p1.1),[§3](https://arxiv.org/html/2610.20764#S3.p1.1)\.
- \[24\]K\. Friston\(2010\)The free\-energy principle: a unified brain theory?\.Nature reviews neuroscience11\(2\),pp\. 127–138\.Cited by:[§3\.1](https://arxiv.org/html/2610.20764#S3.SS1.p1.1),[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[25\]A\. Adeel\(2026\)A cellular doctrine of morality: intrinsic active precision and the mind\-reality overload dilemma\.arXiv preprint arXiv:2605\.01376\.Cited by:[§3\.1](https://arxiv.org/html/2610.20764#S3.SS1.p2.1),[§5](https://arxiv.org/html/2610.20764#S5.p1.1)\.
- \[26\]J\. Ding, Y\. Zhang, Y\. Shang, Y\. Zhang, Z\. Zong, J\. Feng, Y\. Yuan, H\. Su, N\. Li, N\. Sukiennik,et al\.\(2025\)Understanding world or predicting future? a comprehensive survey of world models\.ACM Computing Surveys58\(3\),pp\. 1–38\.Cited by:[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[27\]Y\. LeCunet al\.\(2022\)A path towards autonomous machine intelligence version 0\.9\. 2, 2022\-06\-27\.Open Review62\(1\),pp\. 1–62\.Cited by:[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[28\]L\. Maes, Q\. L\. Lidec, D\. Scieur, Y\. LeCun, and R\. Balestriero\(2026\)Leworldmodel: stable end\-to\-end joint\-embedding predictive architecture from pixels\.arXiv preprint arXiv:2603\.19312\.Cited by:[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.
- \[29\]B\. P\. Graham and J\. W\. Kay\(2026\)Inhibitory and neuromodulatory control of two\-pathway signal integration in a model neocortical pyramidal cell\.Current Research in Neurobiology,pp\. 100166\.Cited by:[§4](https://arxiv.org/html/2610.20764#S4.p1.1)\.