Building a brain with SYCL and modern C++

Smithe, Toby St. Clere; Potter, Ralph

doi:10.1145/3204919.3204928

Cited by 3 publications

(6 citation statements)

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“…In real-world systems, however, even such quasi-bisimulation is too strong. In the setting of computational neuroscience, it is proposed [10,11] that certain neural circuits implement approximate Bayesian inference by optimizing certain statistical games [12]. A statistical game consists of a Bayesian lens-a pair of a 'forwards' stochastic channel A Ñ PB and a 'backwards' inversion PA ˆB Ñ PA-equipped with a loss function to evaluate the systems predictive performance.…”

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

“…Embodied predictive systems such as brains then realize these games as dynamical systems. Here we sketch this functorial semantics, using a category of 'hierarchical bidirectional Stat-systems', following [12,13].…”

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

“…We noted above that the category HiBi resembles a category of lenses, but it does not sufficiently resemble the category of Bayesian lenses: notice that the backwards maps of the latter have codomains of the form PA ˆT Ñ PS rather than A ˆT Ñ S. For this reason, HiBi makes for an inadequate semantic category for predictive processing. However, all is not lost, for we can define a modification of HiBi by analogy to the definition of Bayesian lenses as Grothendieck lenses for the indexed category Stat of state-dependent maps [13].…”

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

“…We are now in a position to sketch the 'Laplace doctrine' of dynamical semantics for approximate inference. We first recall the notion of D-Bayesian inference game [12]: Definition 5.3 (Bayesian inference). Let D : K ℓpPqpI, Xq ˆK ℓpPqp1, Xq Ñ R be a measure of divergence between states on X.…”

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

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Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing

Smithe

2023

Electron. Proc. Theor. Comput. Sci.

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We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such as ordinary differential equations, open Markov processes, and random dynamical systems. We then extend Spivak's operad Org to this setting, and construct associated monoidal categories whose morphisms represent hierarchical open systems; when their interfaces are simple, these categories supply canonical comonoid structures. We exemplify these constructions using the 'Laplace doctrine', which provides dynamical semantics for active inference, and indicate some connections to Bayesian inversion and coalgebraic logic.

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Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

Section: The Laplace Doctrine Of Predictive Processingmentioning

confidence: 99%

See 2 more Smart Citations

Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing

Smithe

2023

Electron. Proc. Theor. Comput. Sci.

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“…To analyse the game G , that is, to extract its Nash equilibria, we then close the game by specifying an initial state x ∈ X and a payoff function u : Y → R, and then apply ε G to the composite x G u. Since open games have been introduced, similar models have been proposed for learners [6] and Bayesian reasoners [22,2], so that a general framework has been proposed in [3] to gather all these examples of 'cybernetic systems'. 1 Despite having inspired this framework, open games remain quite singular when compared to their siblings.…”

Section: Motivationmentioning

confidence: 99%

Diegetic Representation of Feedback in Open Games

Matteo

2023

Electron. Proc. Theor. Comput. Sci.

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We improve the framework of open games with agency [4] by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as equilibrium predicates. This new approach overlaps almost completely with the way gradient-based learners [6] are specified and trained. Indeed, we show feedback propagation in games can be seen as a form of backpropagation, with a crucial difference explaining the distinctive character of the phenomenology of non-cooperative games. We outline a functorial construction of arena of games, show players form a subsystem over it, and prove that their 'fixpoint behaviours' are Nash equilibria.

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A category theory perspective on the Language of Thought: LoT is universal

Phillips

2024

Front. Psychol.

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The Language of Thought (LoT) hypothesis proposes that some collections of mental states and processes are symbol systems to explain language-like systematic properties of thought. Recent proponents of this hypothesis point to additional LoT-like properties in non-linguistic domains to claim that LoT remains the “best game in town” in terms of explanatory coverage. Nonetheless, LoT assumes but does not explain why/how symbolic representations connect to other (non-symbolic) formats. The perspective presented here is supposed to bridge this gap as a duality in a category theoretical sense: (perceptual) data are projected onto a base (conceptual) space in one direction, and in the opposite direction, these data are referenced by that space. Accordingly, perception is dual to conception. These constructions follow from a universal mapping principle affording an explanation for why/how symbolic and non-symbolic formats are connected: as the “best” possible transformation between the two forms— so the slogan, LoT is universal. This view also sheds some light on the apparent pervasiveness of logic-like capacities across age-groups and species, and these constructions constitute special types of categories called toposes (topoi), and every topos has an interpretation in first-order logic.

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Building a brain with SYCL and modern C++

Cited by 3 publications

References 0 publications

Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing

Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing

Diegetic Representation of Feedback in Open Games

A category theory perspective on the Language of Thought: LoT is universal

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