Design, Cups, and Blankets. A Free-Energy-Principle-Based Approach to Product Design

Luca M. Possati

arxiv: 2604.22902 · v2 · submitted 2026-04-24 · 📊 stat.ME · stat.ML

Design, Cups, and Blankets. A Free-Energy-Principle-Based Approach to Product Design

Luca M. Possati This is my paper

Pith reviewed 2026-05-08 10:59 UTC · model grok-4.3

classification 📊 stat.ME stat.ML

keywords product designobject type inferencesurface boundarydesign theoryrequirement-steered inferencefunctional modes

0 comments

The pith

Object type in product design emerges as an inference from physical data and functional requirements rather than a preset choice.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Classical design starts by deciding an object will be a cup and then optimizes its shape and materials. This paper instead treats the decision of what type the object is as something to be inferred from measurements of its surfaces and what it must accomplish. It models the object's surface as a boundary that captures all interactions with the outside world. Different ways this boundary is organized point to different object types. The paper introduces a way to compute this inference and shows why standard design approaches cannot even formulate the question.

Core claim

Object type is not a presupposition but an inference, something that can be determined from physical data and functional requirements jointly. Different structures of the surface boundary correspond to different object types; different parameterizations of the same structure correspond to different functional modes of the same type. The approach makes requirement-steered interface type inference computationally tractable by extending an existing detection method with constraints, reframing design as inference rather than optimization.

What carries the argument

The minimal boundary of a product's surface through which all causal exchange between the object and environment must pass; its structure determines the object type while its parameters determine functional modes.

If this is right

Design can pose and solve the problem of inferring object type from data and requirements.
Different structures of the surface boundary indicate different types of objects.
Parameter changes within one boundary structure correspond to variations in how the same type functions.
The inference is made tractable by extending an existing detection algorithm with constraints from requirements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This opens the possibility of design tools that propose object categories automatically based on specs.
Similar boundary models might apply to other domains where categories are inferred from interaction data.
Empirical tests could involve feeding real product measurements into the algorithm and checking alignment with intended types.

Load-bearing premise

That the surface of an inanimate product can be treated as a boundary whose structure, derived from physical data and requirements, directly reveals the object's type.

What would settle it

Running the constrained detection method on a collection of physical object descriptions, such as various cup-like items, and verifying whether it consistently infers the correct type matching human classification or produces mismatches that cannot be resolved.

Figures

Figures reproduced from arXiv: 2604.22902 by Luca M. Possati.

**Figure 1.** Figure 1: Markov blanket structure. Left: abstract dependency graph illustrating the threeway partition {S, B, Z}. Green nodes (blanket B) mediate all causal influence between the red environment S and the blue internal states Z. Dashed red arcs indicate the forbidden direct connections between S and Z, enforced by zeroing the corresponding blocks of the dynamics matrix A. Right: discretized cup cross-section as a … view at source ↗

**Figure 2.** Figure 2: A Markov blanket topology and two phenomena it supports. A fixed blanket topology B (left) is compatible with a family F(B) of generative models (right). The three models shown illustrate two distinct phenomena, not a single family. Tea and Travel Mug share the same topology (|B|=6, |Z|=13) and belong to the same family F (1): they differ only in spectral radius ρ(Abb) and Lagrange fingerprint λ ∗ — this i… view at source ↗

**Figure 3.** Figure 3: The design loop. The forward loop (solid arrows) runs from the designer’s generative model through the product’s Markov blanket B to the user’s generative model: the designer encodes a functional mode Θ∗ ∈ F(B) into the surface; the user reconstructs it from the contact distribution pcup(yb). The design gap DKL(˜puser∥pcup) measures the residual mismatch. The inverse loop (dashed arrows) runs in the opposi… view at source ↗

**Figure 4.** Figure 4: The complete and constitutive design loop. The blanket topology B determines the family F(B) of generative models, which constitutes the designer’s epistemic space — the set of user–object relationships the designer can represent. This space shapes the admissible requirements {Rk} and user prior p˜user, which select a functional mode Θ∗ ∈ F(B) and thus a contact distribution pcup(yb | Θ∗ ). The contact dis… view at source ↗

**Figure 5.** Figure 5: P1 — Intra-family navigation on double-wall data ( view at source ↗

**Figure 6.** Figure 6: P2 — Family transition under a continuous requirement scan (18 values of view at source ↗

**Figure 7.** Figure 7: P3 — Ontological disambiguation on spatially flat data ( view at source ↗

**Figure 8.** Figure 8: Closed design loop (3 users × 3 cup styles × 3 iterations). A: Minimum design gap mins G(u, s) as a function of iteration for each user profile. The cold-sensitive user shows monotone reduction; the slight increase for standard and heat-tolerant users reflects prior-variance contraction in the simplified inverse-loop update. B: Full gap matrix G(u, s) at iteration 0. C: Gap matrix at iteration 2; the opti… view at source ↗

**Figure 9.** Figure 9: The object as a relational equilibrium. Cup (left) and user (right) are both physical systems with Markov blankets, each governed by its own linear dynamics x(t) = A x(t− 1) + η. The blanket parameters (Abb, Cb,λ ∗ ) of the cup and (Ahh, Ch, ν ∗ ) of the user determine two Gaussian stationary distributions pcup and puser over the contact observables. By the Markov blanket property, the two interiors are co… view at source ↗

read the original abstract

Classical design theory treats the type of an object as a given: the designer decides in advance that this will be a cup, then optimizes its parameters. This paper argues that object type is not a presupposition but an inference, something that can be determined from physical data and functional requirements jointly. We call this problem requirement-steered interface type inference and show that it is inexpressible within existing design frameworks. This paper makes two contributions that are jointly necessary and individually incomplete. The first is the problem itself, which classical design cannot pose because it presupposes the very thing our problem seeks to determine. The second is C-DMBD, a constrained extension of the Dynamic Markov Blanket Detection algorithm, which makes requirement-steered inference computationally tractable. Drawing on the free-energy principle and active inference, established frameworks in theoretical neuroscience and Bayesian mechanics, we model a product's surface as a Markov blanket: the minimal boundary through which all causal exchange between object and environment must pass. Different blanket structures correspond to different object types; different parameterizations of the same structure correspond to different functional modes of the same type. This paper is a proof of concept and a theoretical proposal. It reframes design as inference rather than optimization, and as a relation between generative models rather than a specification of parameters.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper names a new design problem around inferring object types from data and requirements via Markov blankets but offers no derivations, examples, or mappings to support the claim.

read the letter

The core move is to treat object type as something inferred rather than presupposed, by modeling a product's surface as a Markov blanket and using a constrained version of Dynamic Markov Blanket Detection to incorporate functional requirements. That framing is new in the design literature and correctly identifies that classical optimization approaches start after the type decision has already been made. The paper does a clean job of stating why the problem cannot be posed inside existing frameworks and of linking it to active inference ideas without overclaiming immediate applications. The limitation is that none of the mechanics are shown. There is no derivation of how raw geometry or material data gets partitioned into internal and external states, no example of how a requirement alters the free-energy functional, and no demonstration that distinct blanket structures actually produce distinct types rather than just different parameter settings inside one type. C-DMBD is introduced by name only, with no objective function, no constraint formulation, and no comparison to the base DMBD algorithm. The transfer from neuroscience blankets to physical product surfaces is asserted rather than justified with a concrete mapping. This is a conceptual proposal aimed at readers who already work with free-energy or active-inference models and want to see them tried in engineering contexts. It is not yet ready for readers who need reproducible methods or falsifiable predictions. A serious editor should send it to review so the authors can supply the missing derivations and a worked example; the idea is coherent enough on its own terms to merit that step even though the current version is thin on evidence.

Referee Report

3 major / 2 minor

Summary. The paper claims that classical design theory presupposes object type (e.g., 'this will be a cup') and optimizes parameters within that type, whereas the authors argue that type itself should be inferred jointly from physical data and functional requirements. They introduce 'requirement-steered interface type inference' as a new problem that cannot be posed in existing frameworks, and propose C-DMBD (a constrained extension of Dynamic Markov Blanket Detection) that draws on the free-energy principle to model a product's surface as a Markov blanket. Different minimal blanket structures are said to correspond to distinct object types, while parameterizations within a structure correspond to functional modes; the work is presented as a theoretical proof-of-concept reframing design as inference over generative models rather than parameter optimization.

Significance. If the central mapping from physical data and requirements to Markov blanket structures can be made rigorous and shown to yield falsifiable type distinctions, the paper would offer a novel interdisciplinary bridge between Bayesian mechanics/active inference and design theory, potentially allowing design problems to be posed without presupposing categorical object identity. The explicit credit given to the free-energy principle for treating blankets as the locus of causal exchange is a strength, but the absence of any derivation, worked example, or validation data limits immediate impact.

major comments (3)

[Abstract / C-DMBD description] Abstract and the section introducing C-DMBD: the claim that 'C-DMBD makes requirement-steered inference computationally tractable' is asserted without any derivation, pseudocode, or small-scale example showing how the added constraints (functional requirements) modify the DMBD objective function to produce distinct blanket structures rather than merely reparameterizing a fixed structure.
[Modeling the product surface as Markov blanket] The modeling step that treats the product surface as a Markov blanket: no explicit mapping is supplied from raw physical quantities (geometry, material properties, boundary conditions) to the partition into internal states, external states, and blanket states. Without this partition rule, it is unclear how the free-energy functional is constructed from data rather than presupposing a typed generative model.
[Introduction / comparison with classical design] The assertion that classical design frameworks 'cannot pose' the type-inference problem: the manuscript does not demonstrate that standard model-selection or multi-model optimization techniques (e.g., Bayesian model averaging over candidate object classes) are formally incapable of treating type as an inference variable; a concrete counter-example or impossibility proof is required to support the 'inexpressible' claim.

minor comments (2)

[Conceptual framework] The distinction between 'different blanket structures' (types) and 'different parameterizations of the same structure' (modes) is conceptually central but left informal; a brief notational convention or diagram would clarify whether structure is defined by the topology of the blanket or by the support of the generative model.
[Throughout] The paper is labeled a 'proof of concept' yet contains no illustrative computation or synthetic data example; adding even a minimal numerical illustration of blanket detection on a simple geometric object would strengthen readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate the revisions we will make to improve clarity and rigor while preserving the paper's theoretical, proof-of-concept character.

read point-by-point responses

Referee: [Abstract / C-DMBD description] Abstract and the section introducing C-DMBD: the claim that 'C-DMBD makes requirement-steered inference computationally tractable' is asserted without any derivation, pseudocode, or small-scale example showing how the added constraints (functional requirements) modify the DMBD objective function to produce distinct blanket structures rather than merely reparameterizing a fixed structure.

Authors: We accept that the current presentation of C-DMBD is primarily conceptual and does not include explicit pseudocode or a worked numerical example. The tractability argument rests on the observation that functional requirements enter the free-energy objective as additional soft constraints that bias the search toward minimal blanket structures satisfying those requirements, rather than optimizing parameters inside a fixed structure. In the revised manuscript we will add a dedicated subsection with pseudocode for the constrained DMBD step and a small-scale synthetic example (e.g., a 2-D geometric object with two alternative requirement sets) illustrating how the same data yield different blanket partitions. revision: yes
Referee: [Modeling the product surface as Markov blanket] The modeling step that treats the product surface as a Markov blanket: no explicit mapping is supplied from raw physical quantities (geometry, material properties, boundary conditions) to the partition into internal states, external states, and blanket states. Without this partition rule, it is unclear how the free-energy functional is constructed from data rather than presupposing a typed generative model.

Authors: The referee correctly identifies that the manuscript invokes the standard Markov-blanket partition from the free-energy principle without spelling out the data-to-partition procedure for product geometry. We will insert a new subsection that defines an operational mapping: surface voxels or mesh elements are classified as blanket states when they mediate all causal influence between the object's interior (internal states) and the environment (external states), using boundary-condition information to identify the interface. This construction remains data-driven and does not presuppose object type; the type emerges from the inferred blanket structure. revision: yes
Referee: [Introduction / comparison with classical design] The assertion that classical design frameworks 'cannot pose' the type-inference problem: the manuscript does not demonstrate that standard model-selection or multi-model optimization techniques (e.g., Bayesian model averaging over candidate object classes) are formally incapable of treating type as an inference variable; a concrete counter-example or impossibility proof is required to support the 'inexpressible' claim.

Authors: We agree that a stronger comparative argument is needed. Bayesian model averaging and related techniques still require the modeler to enumerate a finite set of candidate classes in advance; each class corresponds to a presupposed object type. Our requirement-steered inference, by contrast, lets the blanket structure itself be discovered without such an a-priori enumeration, with functional requirements acting as the steering signal. In revision we will add a concise subsection that contrasts the two approaches on a shared design scenario, showing that any BMA formulation must still commit to the candidate types before inference begins, whereas C-DMBD does not. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper proposes reframing object type as an inference problem using Markov blankets drawn from the free-energy principle, then introduces C-DMBD as a constrained extension of an existing DMBD algorithm to make requirement-steered inference tractable. No equations, fitted parameters, or self-citations are exhibited that reduce the central claim (types as distinct blanket structures) to its own inputs by construction. The modeling choice is presented as an explicit analogy and proof-of-concept proposal rather than a derived result whose outputs are forced by prior fits or definitional loops within the paper itself. The distinction between blanket structures and parameterizations is definitional within the new framework but does not create a self-referential prediction that collapses to the input data or assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The proposal rests on transferring the free-energy principle and Markov blanket formalism from neuroscience to product design without demonstrated equivalence or independent validation in the design domain.

axioms (2)

domain assumption The free-energy principle and active inference frameworks from theoretical neuroscience apply directly to modeling product surfaces as Markov blankets for type inference.
Invoked in the abstract when the paper states it draws on FEP to model the product's surface as a Markov blanket.
domain assumption Classical design theory presupposes object type and therefore cannot express requirement-steered type inference.
Stated explicitly as the reason the new problem is inexpressible within existing frameworks.

invented entities (2)

requirement-steered interface type inference no independent evidence
purpose: To define the problem of inferring object type from data and requirements rather than presupposing it.
Newly named problem that the paper claims cannot be posed in prior design theory.
C-DMBD algorithm no independent evidence
purpose: Constrained extension of Dynamic Markov Blanket Detection to make type inference computationally tractable under design requirements.
Newly introduced algorithm name with no implementation or pseudocode supplied.

pith-pipeline@v0.9.0 · 5528 in / 1634 out tokens · 31826 ms · 2026-05-08T10:59:20.274402+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 14 canonical work pages

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Papalambros, P. Y., & Wilde, D. J. (2017).Principles of Optimal Design: Modeling and Computation. 3rd ed. Cambridge University Press

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L., Arora, M., & Allison, J

Luan, S., Thurston, D. L., Arora, M., & Allison, J. T. (2017).Developing and Comparing Alternative Design Optimization Formulations for a Vibration Absorber Example. InProceed- ings of the ASME 2017 International Design Engineering Technical Conferences and Com- 30 puters and Information in Engineering Conference (IDETC/CIE 2017). DETC2017-68337. doi:10.1...

work page doi:10.1115/detc2017-68337 2017

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& Ramstead, M.J.D

Beck, A. & Ramstead, M.J.D. (2025).Dynamic Markov Blanket Detection for Macroscopic Physics Discovery. arXiv:2502.21217

work page arXiv 2025

[4] [4]

(2019).A free energy principle for a particular physics

Friston, K. (2019).A free energy principle for a particular physics. arXiv:1906.10184

work page arXiv 2019

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(1988).Probabilistic Reasoning in Intelligent Systems

Pearl, J. (1988).Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann

1988

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Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm.Journal of the Royal Statistical Society B, 39(1), 1–38

1977

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(2013).Life as we know it.Journal of the Royal Society Interface, 10(86), 20130475

Friston, K. (2013).Life as we know it.Journal of the Royal Society Interface, 10(86), 20130475. doi:10.1098/rsif.2013.0475

work page doi:10.1098/rsif.2013.0475 2013

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10 Under review as a conference paper at ICLR 2026 Jun Gao, Yongqi Li, Ziqiang Cao, and Wenjie Li

Friston, K. (2010).The free-energy principle: A unified brain theory? Nature Reviews Neu- roscience, 11, 127–138. doi:10.1038/nrn2787

work page doi:10.1038/nrn2787 2010

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Friston, K., and Frith, C. (2015). A Duet for one.Consciousness and Cognition, 36:390–405. doi:10.1016/j.concog.2014.12.003

work page doi:10.1016/j.concog.2014.12.003 2015

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Parr, T., Pezzulo, G., & Friston, K. J. (2022).Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. The MIT Press

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Friston, K., Da Costa, L., Sakthivadivel, D. A. R., Heins, C., Pavliotis, G. A., Ramstead, M. J. D., & Parr, T. (2023).Path integrals, particular kinds, and strange things.Physics of Life Reviews, 47, 35–62. doi:10.1016/j.plrev.2023.08.016

work page doi:10.1016/j.plrev.2023.08.016 2023

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Sakthivadivel, D. A. R. (2022).Weak Markov Blankets in High-Dimensional, Sparsely-Coupled Random Dynamical Systems. arXiv preprint arXiv:2207.07620. doi:10.48550/arXiv.2207.07620

work page doi:10.48550/arxiv.2207.07620 2022

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Sakthivadivel, D. A. R. (2022).A Worked Example of the Bayesian Mechanics of Classical Objects. arXiv preprint arXiv:2206.12996. doi:10.48550/arXiv.2206.12996

work page doi:10.48550/arxiv.2206.12996 2022

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Ramstead, M. J. D., Sakthivadivel, D. A. R., Heins, C., Koudahl, M., Millidge, B., Da Costa, L., Klein, B., & Friston, K. J. (2023).On Bayesian mechanics: a physics of and by beliefs.Interface Focus, 13(3), 20220029. doi:10.1098/rsfs.2022.0029

work page doi:10.1098/rsfs.2022.0029 2023

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(2026).Active Inference for Physical AI Agents – An Engineering Perspective

de Vries, B. (2026).Active Inference for Physical AI Agents – An Engineering Perspective. arXiv preprint arXiv:2603.20927. doi:10.48550/arXiv.2603.20927

work page doi:10.48550/arxiv.2603.20927 2026

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(2016).Surfing Uncertainty: Prediction, Action, and the Embodied Mind

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

2016

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Namjoshi, S. V. (2026).Fundamentals of Active Inference: Principles, Algorithms, and Applications of the Free Energy Principle for Engineers. Cambridge, MA: The MIT Press

2026

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(2007).Engineering Design: A Sys- tematic Approach

Pahl, G., Beitz, W., Feldhusen, J., and Grote, K.-H. (2007).Engineering Design: A Sys- tematic Approach. 3rd edn. London: Springer. doi:10.1007/978-1-84628-319-2. 31

work page doi:10.1007/978-1-84628-319-2 2007

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Antonsson, E. K. and Cagan, J. (eds.) (2001).Formal Engineering Design Synthesis. Cam- bridge: Cambridge University Press. doi:10.1017/CBO9780511529627

work page doi:10.1017/cbo9780511529627 2001

[20] [20]

C., Taylor, R

Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z. (2013).The Finite Element Method: Its Basis and Fundamentals. 7th edn. Oxford: Butterworth-Heinemann. doi:10.1016/C2009-0- 24909-9

work page doi:10.1016/c2009-0- 2013

[21] [21]

& Sigmund, O

Bendsøe, M.P. & Sigmund, O. (2003).Topology Optimization: Theory, Methods, and Appli- cations. Springer

2003

[22] [22]

& Wright, S.J

Nocedal, J. & Wright, S.J. (2006).Numerical Optimization(2nd ed.). Springer

2006

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& Haslegrave, C.M

Pheasant, S. & Haslegrave, C.M. (2006).Bodyspace: Anthropometry, Ergonomics and the Design of Work(3rd ed.). Taylor & Francis. 32

2006