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Learning Is Emergence, Not Control: A Physicist's Reframing

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2026-07-08 17:59 UTC pith:6YKBZRSN

load-bearing objection A well-organized perspective on active-to-smart matter; the central learning-vs-control distinction is underdefended at the boundary with adaptive control. the 2 major comments →

arxiv 2607.06051 v1 pith:6YKBZRSN submitted 2026-07-07 cond-mat.soft

From Active to Odd to Smart Matter

Olivier Dauchot This is my paper
classification cond-mat.soft
keywords matteractivecollectivemechanicalalongemergencelearningresponse
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This perspective argues that the field of active matter is undergoing a conceptual trajectory from spontaneous collective dynamics (active liquids and solids with odd elasticity) toward task-driven, adaptive materials (smart matter). The central claim is that learning should not be understood as an alternative to emergence or as a form of external control, but as a new kind of emergence in which the rules governing collective behavior themselves become dynamical variables shaped by experience. The paper distinguishes learning from design, programming, control, and feedback by identifying a sharp boundary: in all the latter, rules are fixed in advance, while learning requires the system to modify its own internal rules based on accumulated performance. The author organizes learning matter along three axes: physical versus logical (whether adaptation lives in material parameters or abstract policies), supervised versus reinforcement versus unsupervised (the mode of learning), and individual versus social (the locus of learning). The unifying thread is that activity breaks detailed balance while learning breaks time-translation invariance of the equations of motion, and both are enabled by internal degrees of freedom. The paper proposes that statistical physics is the natural framework for coarse-graining learning dynamics, identifying universality classes, and finding organizing principles for this new class of non-equilibrium materials.

Core claim

The paper's central conceptual contribution is the reframing of learning as an emergent organization of rules rather than of states. In traditional active matter, fixed microscopic rules produce emergent collective states. In programmable matter, rules are externally imposed to achieve function. In learning matter, the rules themselves become dynamical variables that evolve through interaction with the environment. This distinction is what the author argues makes learning qualitatively different from control or feedback: feedback stabilizes or regulates but does not explore alternative strategies or optimize performance, whereas learning transforms feedback from a regulatory mechanism into a

What carries the argument

The paper builds its argument on two intertwined axes: the gas-liquid-solid progression of condensed matter states, and the shift from spontaneous collective dynamics to task-driven functionality. The key conceptual machinery is the distinction between fixed rules (design, programming, control, feedback) and dynamical rules (learning), organized along three independent dimensions: substrate (physical vs logical), mode (supervised, unsupervised, reinforcement), and locus (individual vs social). The physical framing uses two symmetry-breaking operations: activity breaks detailed balance, learning breaks time-translation invariance of the equations of motion.

Load-bearing premise

The paper assumes that the distinction between learning and feedback is sharp enough to constitute a genuine paradigm shift rather than a difference of degree. It defines feedback as operating with fixed rules and learning as modifying rules, but acknowledges the boundary is not rigid. If learning turns out to be feedback on slower timescales, the proposed conceptual shift from control to emergence may be one of degree rather than kind.

What would settle it

If it can be shown that every system the paper classifies as 'learning matter' can be equivalently described as a feedback-controlled system with slowly-varying parameters, then the claimed qualitative distinction between learning and feedback collapses, and the proposed paradigm shift reduces to a relabeling.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If learning is genuinely a form of emergence, then statistical physics tools developed for phase transitions and universality should apply to learning dynamics in materials, potentially yielding universality classes of learning matter that are independent of microscopic implementation.
  • The distinction between physical and logical learning suggests that materials whose constitutive parameters evolve through use could be described by modified field theories where the constitutive relations themselves carry history dependence, opening a new domain for non-equilibrium statistical mechanics.
  • The social learning axis raises the question of whether collective learning in active materials could exhibit phase transitions between individual and collective optimization regimes, analogous to synchronization or consensus transitions.
  • If the boundary between feedback and learning is as the paper describes, then many systems currently labeled as 'controlled' or 'programmable' active matter may already be operating in a learning regime without being recognized as such, suggesting a reclassification may be warranted.
  • The framing of learning as breaking time-translation invariance connects it to other forms of aging and history-dependent dynamics in glassy and jammed systems, suggesting a unified description may be possible.

Where Pith is reading between the lines

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

  • The paper's argument that learning is qualitatively distinct from feedback hinges on the claim that feedback laws are fixed while learning modifies rules. But in many physical systems, feedback laws themselves contain parameters that drift on slow timescales (e.g., homeostatic plasticity in biological systems), which could place them on a continuum with learning rather than in a separate category.
  • If learning matter breaks time-translation invariance of the equations of motion, this connects it formally to aging phenomena in glassy systems, suggesting that tools from glass physics (effective temperature, aging exponents, fluctuation-dissipation violations) might be portable to characterize learning dynamics in active materials.
  • The paper does not address whether there exist fundamental thermodynamic costs or bounds on learning in physical systems. If learning requires modifying internal rules based on experience, this implies information erasure and Landauer-type costs that could constrain the efficiency of physical learning, a connection the framework invites but does not develop.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 10 minor

Summary. This Perspective by Dauchot proposes a unifying conceptual trajectory from active to odd to smart matter, organized along two axes: the gas–liquid–solid progression of condensed matter and a paradigm shift from spontaneous collective dynamics to task-driven functionality. The manuscript reviews active liquids (§II), active solids and odd elasticity (§III), programmable active matter (§IV), and learning matter (§V), before synthesizing these into an outlook (§VI) arguing that learning constitutes a new form of emergence rather than an extension of control. The paper's central load-bearing claim is that learning is qualitatively distinct from design, programming, control, and feedback because it involves autonomous modification of internal rules based on past performance, and that this distinction opens a genuinely new frontier for statistical physics.

Significance. The manuscript provides a useful conceptual map for a rapidly growing and fragmented field. The distinctions drawn in §IV among design, programming, control, feedback, and learning are clearly articulated and serve as a practical vocabulary guide for physicists entering this space. The three-axis taxonomy of learning matter introduced in §V (physical vs. logical, supervised vs. unsupervised vs. reinforcement, individual vs. social) is a genuine organizational contribution that could help structure future research. The framing of learning as 'an emergent organization not only of states, but of rules' (§VI) is thought-provoking and connects naturally to the statistical physics expertise of the target readership. The paper is honest about the current state of the field, including the notable admission that odd elasticity has not yet been experimentally reported in active solids (§III).

major comments (2)
  1. §IV, paragraph on 'Control and Feedback' and 'Why the distinction matters': The central claim that learning is qualitatively distinct from control and feedback rests on the assertion that feedback 'stabilizes or regulates, but it neither explores alternative strategies nor optimizes performance.' This criterion, however, is satisfied by adaptive and model-predictive control, which update controller parameters online based on observed performance, explore alternative strategies via perturbation, and optimize against a cost function. The manuscript does not engage with this intermediate category. The distinction the paper needs to be sharp is sharpest at the boundary between adaptive feedback control and learning, and it is precisely there that the paper is silent. Without addressing this, the claim that learning constitutes a paradigm shift rather than a continuation of control theory (el
  2. §V, final paragraph ('Why learning matter is conceptually new'): The characterization that 'learning breaks the time translational invariance of the equations of motion' is offered as a distinguishing physical feature of learning matter. However, time-translation invariance is broken by any system with adaptive gains, aging, memory, or slow parameter drift — including the adaptive control systems discussed above. This property does not uniquely pick out learning. The author should either refine this criterion to distinguish learning from generic history-dependent dynamics, or acknowledge that breaking time-translation invariance is necessary but not sufficient for learning.
minor comments (10)
  1. Abstract: 'more recentparadigm shift' — missing space between 'recent' and 'paradigm'.
  2. §I, first paragraph: double period after '[1–5]..' — remove the extra period.
  3. §IV, subsection 'Design: from structure to function': 'This line of practise is obviously not specific to active matter' — 'practise' should be 'practice' in this context (noun rather than verb).
  4. §IV, subsection 'Control and Feedback': 'an external, or internal, entity, often called the controller, which directly guides the operation of the system during operation' — the word 'operation' appears twice in close proximity; consider rephrasing.
  5. §V, subsection 'Physical versus logical learning': 'The prototypic example is that of self driving cars [45]' — 'self driving' should be hyphenated as 'self-driving'.
  6. §VI, final paragraph: 'Are there and what are the underlying organizing principle of learning matter?' — grammatical issue; should read 'Are there underlying organizing principles of learning matter, and what are they?' or similar.
  7. Figure 4 caption: 'thesubstrate', 'themode', 'thelocus' — missing spaces in these phrases.
  8. §III, paragraph 3: 'Odd elasticity at the macroscale has not been reported yet in such active solids.' This is an important and honest caveat. Consider strengthening by noting whether current experimental efforts are underway or what the key obstacles are.
  9. §V, subsection 'Supervised, unsupervised, and reinforcement learning': 'the application of reinforcement learning in robotics has become a research field in its own [47]' — 'in its own' should be 'in its own right'.
  10. The reference list includes Ref. [23] (Shimoyama et al., 1996) which is cited in §III but does not appear to be discussed in the text beyond the citation; a brief contextualizing mention would help the reader.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful and constructive reading of our Perspective. The two major comments both target the same conceptual boundary — between adaptive control and learning — and both are well taken. We agree that the manuscript as written draws the distinction too sharply in §IV and overstates the physical signature of learning in §V. We will revise both passages.

read point-by-point responses

  1. Referee: §IV, 'Control and Feedback' and 'Why the distinction matters': The claim that learning is qualitatively distinct from control and feedback rests on the assertion that feedback 'stabilizes or regulates, but it neither explores alternative strategies nor optimizes performance.' This criterion is satisfied by adaptive and model-predictive control, which update controller parameters online, explore alternative strategies, and optimize against a cost function. The manuscript does not engage with this intermediate category.

    Authors: The referee is correct. Our characterization of feedback in §IV is too narrow: it describes classical fixed-gain feedback but ignores the entire spectrum of adaptive, model-predictive, and optimal control, which do update parameters online, do explore (at least locally), and do optimize against a cost function. By omitting this intermediate category, we created a false dichotomy between fixed feedback laws and learning, which weakens rather than strengthens our argument. We will revise the 'Control and Feedback' paragraph and the 'Why the distinction matters' paragraph to explicitly acknowledge adaptive and model-predictive control as an intermediate regime. We will then refine our distinction as follows: adaptive control typically operates within a pre-specified class of controller structures and a pre-defined cost function; the controller adapts its parameters but not its architecture or representation. Learning, as we intend it in the context of learning matter, additionally allows the modification of the rules or representations themselves — including the possibility of discovering behaviors or strategies not anticipated by the designer. We acknowledge that this boundary is genuinely fuzzy, especially for reinforcement learning with restricted policy classes, and we will say so explicitly rather than claiming a sharp qualitative boundary. We believe this revision actually strengthens the Perspective by making the distinction more defensible. revision: yes

  2. Referee: §V, final paragraph: The characterization that 'learning breaks the time translational invariance of the equations of motion' does not uniquely pick out learning — any system with adaptive gains, aging, memory, or slow parameter drift also breaks TTI. The author should either refine this criterion or acknowledge that breaking TTI is necessary but not sufficient.

    Authors: The referee is right that breaking time-translation invariance is not specific to learning. Aging glasses, systems with slow parameter drift, adaptive gain controllers, and any history-dependent dynamics all break TTI. Presenting this as a distinguishing feature of learning matter was an overstatement. We will revise the passage in §V to acknowledge that breaking TTI is necessary but not sufficient for learning, and that it is shared with many other history-dependent non-equilibrium systems. We will then clarify what we believe is the more specific physical signature of learning matter: not merely that the equations of motion become history-dependent, but that the modification of the rules is driven by an evaluative signal (reward, error, or selection pressure) and accumulates in a way that improves future performance. This is closer to what distinguishes learning from generic aging or drift, though we acknowledge that even this criterion has borderline cases (e.g., variational structures that minimize dissipation). We will frame the physical signature of learning matter as a conjunction — history-dependent rules plus performance-driven accumulation — rather than TTI breaking alone. revision: yes

Circularity Check

0 steps flagged

No circularity: this is a perspective paper with no derivation chain, no fitted-parameter-as-prediction, and no load-bearing self-citation.

full rationale

This paper is a perspective/review that proposes a conceptual trajectory from active to odd to smart matter. It contains no quantitative derivation chain, no equations whose outputs are tested against inputs, and no fitted parameters presented as predictions. The central claim — that 'learning is not an alternative to emergence, but a new form of it' (§VI) — is a conceptual assertion, not a derived result that could be circular. The author's self-citations (Refs [19, 24, 26, 51]) are used as illustrative examples of experimental or theoretical phenomena (self-alignment, collective actuation, social learning in robot swarms), not as load-bearing premises from which the paper's conclusions are algebraically derived. No step in the paper reduces to its own inputs by construction. The absence of a formal derivation chain means there is nothing to exhibit as circular. This is the expected honest non-finding for a perspective paper of this type.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 1 invented entities

The paper introduces no free parameters (no fitting, no data). The axioms are conceptual assertions about the relationship between learning, feedback, and emergence — none are formally derived. 'Smart matter' is the main invented entity, serving as an organizing category. It lacks independent falsifiable predictions that would distinguish it from existing concepts of adaptive or programmable materials.

axioms (4)
  • domain assumption Active matter phases are governed by dynamical symmetries and non-equilibrium currents rather than free-energy landscapes
    Stated in §II as established background from active field theory literature [1,2,6,8,13]. Used to motivate the progression from active to smart matter.
  • domain assumption Self-alignment in active solids naturally gives rise to nonreciprocal couplings among internal degrees of freedom
    Stated in §III as the conceptual bridge between the microscopic and symmetry-based approaches to active solids. This convergence is asserted but not formally derived in the paper.
  • ad hoc to paper Learning is qualitatively distinct from feedback because it involves exploration and optimization, not just regulation
    Stated in §IV: 'Feedback stabilizes or regulates, but it neither explores alternative strategies nor optimizes performance.' This distinction is load-bearing for the entire 'smart matter' framing but is asserted, not derived.
  • ad hoc to paper Learning breaks time-translation invariance of the equations of motion
    Stated in §V: 'Activity typically breaks detailed balance; learning breaks the time translational invariance of the equations of motion.' This is a conceptual claim used to position learning matter within statistical physics, but no formal demonstration is given.
invented entities (1)
  • Smart matter no independent evidence
    purpose: Umbrella term for materials whose collective behavior and mechanical response are adapted, optimized, and learned toward functional goals rather than fixed by design
    Introduced as a new category in §I. The paper provides examples of constituent phenomena (physical learning networks, RL in robotics, social learning in swarms) but 'smart matter' as a unified class of matter is a framing device, not an independently verified entity with falsifiable predictions.

pith-pipeline@v1.1.0-glm · 13897 in / 2452 out tokens · 355670 ms · 2026-07-08T17:59:19.820078+00:00 · methodology

0 comments
read the original abstract

The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. Simultaneously, innovative developments in swarm robotics , programmable metamaterials , and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. This Perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas--liquid--solid progression of condensed matter, and the more recentparadigm shift from spontaneous collective dynamics to task-driven functionality. We try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics.

Figures

Figures reproduced from arXiv: 2607.06051 by Olivier Dauchot.

Figure 1
Figure 1. Figure 1: FIG. 1. Conceptual map from active to smart matter. The horizontal axis follows the gas–liquid–solid progression, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Active Solids : nonreciprocity as a design principle (Left) (a): Self alignment, the non reciprocal coupling [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Programmable active matter: when design [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Learning matter organized along three axes: (a) the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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Reference graph

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