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The Value of Information in Multi-Scale Feedback Systems

T0 review · 3 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper sets out to establish that the value of an information flow in a Multi-Scale Feedback System can be measured as the difference it makes to a goal-scored state value, and supplies concrete formulas and four case studies.

desk verdict A useful vocabulary for information value in multi-scale feedback systems, but the flow-attribution claim is not supported by the temporal-difference equations. read the letter →

arxiv 2505.11509 v1 pith:KBXCESZZ submitted 2025-05-02 cs.MA cs.SYeess.SYnlin.AO

Louisa Jane Di Felice , Ada Diaconescu , Payam Zahadat , Patricia Mellodge This is my paper · ORCID
classification cs.MAcs.SYeess.SYnlin.AO
keywords adaptationsyntacticinformationsemanticpragmaticcomplexitymulti-scalefeedbacksystemsvalueofcomplexadaptive
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to show that information in a complex adaptive system has a measurable value, not just a measurable size, and that this value can be computed by comparing the system's state before and after a feedback cycle. The authors define Multi-Scale Feedback Systems as collections of agents that abstract local information upward and receive control information downward, then propose three families of measures: syntactic (how much information is carried and at what resource cost), semantic (how much the flow changes an agent's knowledge and how close that knowledge is to truth or to optimal knowledge), and pragmatic (how much the flow changes action and how close that action brings the system to its goal). The contribution is a general recipe plus worked examples from four models: a robotic collective, a collective decision-making task, a task-distribution hierarchy, and a set of coupled oscillators. If the recipe works, an analyst can rank feedback architectures by how effectively they use information, which matters for designing self-adaptive systems and for understanding how information drives adaptation in natural ones.

What carries the argument

The load-bearing object is the feedback cycle of a Multi-Scale Feedback System, treated as the unit of comparison: state information is abstracted from micro-scale to macro-scale, processed, and reified downward as control information, and the analyst evaluates the system at $t-\theta$ and at $t$. The measure that carries the argument is the analyst-assigned state-value function $SV$, defined for knowledge states and action states with respect to a ground truth, an optimal knowledge state, or a goal; the paper's three value formulas are all differences of $SV$ across the cycle. The descriptive deltas and efficiency ratios do auxiliary work: deltas isolate the magnitude of change, and efficiencies divide values by $C_{\mathrm{syn}}$ to connect information value to the physical resources it costs.

What would settle it

Take one recorded simulation of the robotic collective and compute $V_{\mathrm{pr,gl}}$ for the same information flow under two different state-value functions: one that scores the robot distribution by absolute error from the desired counts and one that scores it by object-weighted error. If the two state-value functions reverse the ranking of the main and ground-truth strategies, the pragmatic measure is an artifact of the analyst's choice rather than a property of the information flow, and the paper's central claim that these measures quantify the value of information flows would not be well-defined.

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Extended reading notes

Core claim

The central claim is that the value of an information flow in a Multi-Scale Feedback System is the difference it makes to a scalar state-value function $SV$ that scores how close the system's knowledge or action state is to a reference state. The paper defines the semantic truth value as $V^{t-\theta\to t}_{\mathrm{sm,th}} = SV^{t}_{\mathrm{th}} - SV^{t-\theta}_{\mathrm{th}}$, the semantic goal value as $V^{t-\theta\to t}_{\mathrm{sm,gl}} = SV^{t}_{\mathrm{opt}} - SV^{t-\theta}_{\mathrm{opt}}$, and the pragmatic goal value as $V^{t-\theta\to t}_{\mathrm{pr,gl}} = SV^{t}_{\mathrm{gl}} - SV^{t-\theta}_{\mathrm{gl}}$, where $t-\theta$ is the previous comparison time and $I_{t-\theta\to t}$ is the information that flowed in between. Descriptive deltas $\Delta_{\mathrm{sm}}$ and $\Delta_{\mathrm{pr}}$ measure the magnitude of change in knowledge and action regardless of goal, and efficiencies divide each value by the syntactic content $C_{\mathrm{syn}}$. Across the four case studies, the measures separate accurate-but-slow knowledge from fast-but-inaccurate knowledge, show when extra hierarchy costs efficiency, and track how delays change the value of otherwise identical information.

Load-bearing premise

The load-bearing premise is that the analyst can assign a scalar state-value function $SV$ to every knowledge and action state that correctly reflects how valuable that state is with respect to the system's goal; if that assignment is arbitrary or contested, every semantic and pragmatic number the paper reports is arbitrary.

Editorial extensions

If this is right

  • Feedback strategies can be compared by resource efficiency rather than by message size: the short-memory robotic collective matches or beats the long-memory one over long cycles at a fraction of the syntactic cost.
  • Semantic and pragmatic measures can disagree, and the disagreement is informative: in collective decision-making, a strategy that keeps the environment alive does so through fast oscillation rather than accurate perception, so survival and knowledge accuracy separate.
  • Delays become a tunable quantity: the four models show that delaying feedback can either compensate for inaccurate adaptation or cause overshoot, so designers can adjust cycle length rather than only improving sensing.
  • Accuracy is not always an asset: the ground-truth robotics strategy underperforms estimation strategies, implying that the value of information depends on how quickly the system can act on it, not only on how correct it is.
  • The same information flow can have different values at different scales, so ranking a strategy requires stating the scale and the goal first.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The before/after comparison is not inherently multi-scale: any feedback loop can be read as a two-scale system, so the same value measures could rank single-loop controllers, a testable extension the paper does not pursue.
  • Sweeping the sensing horizon in the robotic collective would map where precision begins to hurt, turning the paper's observed trade-off between accuracy and delay into a quantitative design curve.
  • If the state-value function $SV$ were tied to survival probability, the measures would connect to viability-based semantic information and could be applied to biological systems whose goals are not supplied by an engineer.
  • Because $SV$ is a free choice, two analysts with different goals will necessarily disagree about whether the same flow is valuable; the framework thus makes the choice of goal an explicit empirical variable rather than a hidden one.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 7 minor

Summary. The paper proposes a conceptual framework for measuring syntactic, semantic, and pragmatic information in Multi-Scale Feedback Systems (MSFS). It defines three value-oriented measures—semantic truth value Vsm,th, semantic goal value Vsm,gl, and pragmatic goal value Vpr,gl—as changes in analyst-assigned state-value functions over an interval [t−θ,t], together with descriptive deltas and efficiency ratios. The framework is illustrated through four case studies: a robotic collective, collective decision-making, task distribution, and hierarchical oscillators, where different strategies, parameter settings, or hierarchy depths are compared. The central claim is that these measures allow analysts to quantify the value of information flows in any complex adaptive system with identifiable goals and to reason about feedback architectures. The paper is not presented as a theorem-based result; it is a proposal with worked examples and a general recipe for measurement.

Significance. If the proposed measures were well-founded, the paper would provide a useful vocabulary and a practical recipe for quantifying information value in engineered and natural adaptive systems. The four case studies span different feedback structures and include explicit equations, which is a strength, as is the paper's transparency about the observer-dependence of value. However, as written, the value measures do not isolate the contribution of the information flow: they are temporal differences of scalar state-value functions rather than comparisons with and without the flow, and the scalar functions are assigned rather than derived. The reported numbers are therefore best described as descriptive traces of state-value change, not as values of the information flow I_{t−θ→t}. This is a fixable problem, but it is load-bearing for the paper's central claim.

major comments (3)
  1. [§3.2, Eqs. (1)–(3)] The text states that value is measured by comparing how the system performs towards a goal state with and without information (Gould, 1974), but the operational equations compute only temporal differences: Vsm,th = SVth(t) − SVth(t−θ), Vsm,gl = SVopt(t) − SVopt(t−θ), and Vpr,gl = SVgl(t) − SVgl(t−θ). No baseline removes or holds fixed the rest of the system, so a positive Vpr,gl can be produced by initialization, system dynamics, delays, or a different feedback cycle, and is not attributable to the flow I_{t−θ→t}. The case-study comparisons (e.g., main vs. ground truth vs. random in §4.2.1, consensus vs. randomCN in §4.3.2) change algorithms, memory, timing, and information content simultaneously, so they are not controlled ablations of a single flow. Since the efficiency ratios inherit this attribution problem, the central claim that the measures quantify the value of information flows is not currently supported. A controlled with/without comparison or an explicit causal model of the flow is needed.
  2. [§4.3.4.1.3, Eq. (24); §4.4.4.2, Eqs. (36)–(43)] The scalar state-value functions are assigned rather than derived, and the paper provides no construction principle or sensitivity analysis for them. In the collective decision-making case, Eq. (24) defines Δgl = 1 − 2|0.5 − WA|, but the system collapses at WA = 0.10 and WA = 0.90, where this expression equals 0.2 rather than 0; the goal-value function therefore does not assign the terminal states the minimum value implied by the stated goal. In the task-distribution case, SVgl is set to {0, 0.25, 0.5, 0.75, 1} directly, and the numerical values of Vpr,gl (e.g., BB ≈ 0.72 at m = 10, RS converging to 0.33) are consequences of these arbitrary assignments. Unless the framework specifies how SV is obtained from a utility or loss function, or shows that conclusions are robust across reasonable SV choices, the reported semantic and pragmatic values are not generalizable measures.
  3. [§4.5.3.1.1, Eqs. (50)–(51)] The syntactic measure changes meaning across the case studies: memory units in the robotic collective, Shannon entropy in collective decision-making and task distribution, and a JS-divergence dissimilarity in the hierarchical oscillator case. In Eq. (50), Csynm,i = 1 − D_JS(fm,i||U)/log(2) assigns the maximum value to the uniform distribution and measures distance from uniformity, not message size, resource use, or information transmitted through the feedback cycle. Consequently, the claim that the 3-scale system contains more information than the 2-scale system (Csyn = 6.6459 vs. 4.7917) relies on summing dissimilarity-to-uniform scores and is not commensurable with the syntactic measures used elsewhere. The paper should either justify a common interpretation of Csyn across cases or restrict efficiency comparisons to within-case claims.
minor comments (7)
  1. [Figure 2 caption] The caption reads 'Green arrows show abstracted flows of state information, green arrows flows of control information'; the second color should presumably be different (e.g., blue), and the legend should be clarified.
  2. [References] Several references preserve LaTeX/encoding artifacts, such as 'V on Uexk¨ull' and 'Weizs¨acker'; please correct these to the actual author names.
  3. [Table 1] The semantic-information block of Table 1 contains the column header 't2)t2', which appears to be a typo for 't2→t3'; please check all headers.
  4. [§4.4.4.2, Eq. (37)] The piecewise definition of Vsm,th uses 'SVkn' with inconsistent subscripts and an 'NA' condition without defining the full notation; in particular, the clause 'SVkn(...)==NA ∨ SVkn(...)==NA' should be written with explicit expressions for both time arguments and a clear definition of NA.
  5. [§4.4.4.2, Eq. (38)] The efficiency normalization uses an arbitrary scaling factor coef = 10 with no justification; please state how coef is chosen and how it affects comparisons between strategies.
  6. [§4.2.2.2 and §4.3.3] Several performance claims (e.g., that the short-memory strategy outperforms the long-memory strategy for the full sub-model, or that parameter-region differences are due to noise) are qualitative readings of pooled figures without error bars, confidence intervals, or statistical tests; adding quantitative support would strengthen the case-study conclusions.
  7. [Throughout] No data or code repository is provided for the simulation results; for a paper whose main evidence is computational case studies, a reproducibility statement or availability link should be added.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the proposed measures are explicitly defined, observer-relative constructions; self-citations are non-load-bearing.

full rationale

The paper does not present a first-principles derivation or an empirical prediction that could reduce to its own inputs. Section 3.2 defines the semantic and pragmatic measures by equations (1)-(3) as temporal differences of analyst-assigned state-value functions; these are stipulated definitions, not derived quantities. The context-dependence of the state-value assignment is acknowledged ('While the measurement of values is necessarily context-dependent'), and the task-distribution case explicitly states 'We assign state values SVgl... {0, 0.25, 0.5, 0.75, 1}' rather than fitting them to data. Consequently, Vpr,gl is the expected improvement under a chosen value function, which is a normative input, not a hidden fitted parameter. The discrepancy between the Gould-inspired with/without definition of value and the operational before/after comparisons is a causal-attribution and validity limitation, not a circular reduction: the equations are the definitions, so no derived result is being passed off as an independent measurement. Self-citations (MSFS prior work and the hierarchical oscillator model) provide concepts and models but are not invoked as a uniqueness theorem or to forbid alternatives, and the case-study simulations are externally checkable. Minor self-citation is present, but none of it is load-bearing in a circular sense.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central contributions are definitions applied to four models. Every value number is downstream of hand-set state values or coarse-graining choices, and the hierarchical oscillator case rests on a nonstandard identification of syntactic information with similarity to uniform. These choices are disclosed in the text, but they mean the reported quantities are illustrative rather than externally validated.

free parameters (5)
  • State-value assignment SVgl (task distribution) = SVgl(S0) = {0, 0.25, 0.5, 0.75, 1}
    Assigned linearly by hand in Section 4.4.4.2; Vpr,gl and all pragmatic values inherit this arbitrary scale, so the reported 0.15, 0.72, and 0.94 values are direct consequences.
  • HO coupling parameters Fm, tau_m, W = not reported in main text
    Section 4.5.2 states they are 'set to values known to result in synchronized oscillation' but does not give the values; without them the oscillator results cannot be reproduced.
  • Sensing horizon M (robotic collective) = M = 100 and M = 10
    Chosen to compare memory configurations; Csyn = 6M + 38 memory units, so the syntactic comparison is proportional to this hand-set resource model.
  • Task switching probability pch (task distribution) = 0.15
    Fixed by hand in Section 4.4.2 for both Blackboard and Random-switch strategies; it shapes the stochastic matrix and all computed goal-reaching probabilities.
  • CD scan parameters N and R = N and R in [1, 30]
    Varied over a grid rather than fitted; averaged results depend on the chosen 40 simulations per combination and the cap of 5000 steps.
assumptions (6)
  • ad hoc to paper Value of an information flow can be represented as the change in a scalar state-value function SV assigned to each state (Eqs. 1-3).
    Load-bearing premise for all semantic and pragmatic measures; no argument is given that scalar SV captures multidimensional goals.
  • ad hoc to paper Syntactic information content in the hierarchical oscillator case is measured by 1 - D_JS(f||U)/log2, summed over oscillators.
    Eqs. 48-51 identify a uniformity index with information content; uniform distributions get maximal Csyn, the opposite of Shannon entropy, and no units or resource interpretation are supplied.
  • ad hoc to paper Agent opinions are independent when computing scale-level entropy in the collective decision-making case.
    Eq. 17 sets H(S1) = N * H(Oi), ignoring correlations among agents; this affects all Csyn,cycle comparisons.
  • ad hoc to paper Collective states in the task distribution case may be lumped by the number z of workers performing task k1 for entropy purposes.
    Eq. 27 collapses 0001, 0010, 0100, and 1000 into one state; the reported information loss percentages depend on this coarse-graining.
  • domain assumption An observer and a goal can always be identified for a CAS, making value measures well-defined.
    Section 5 states goals can be determined at different scales, but the framework requires that such a goal exists and is observable.
  • standard math Background information-theoretic definitions (Shannon, KL, JS, Kolmogorov complexity) and the Kim et al. oscillator ODE model are accepted.
    Used throughout Sections 2 and 4.5 without proof.
invented entities (1)
  • Scalar semantic and pragmatic information values (Vsm,th, Vpr,gl, and delta measures)
    purpose: To quantify knowledge and action effects of information flows in feedback cycles
    These are new composite definitions, but they are not anchored to external observable handles; their values are produced by user-assigned state values and model simulations, so they cannot be falsified outside the models.

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Pith. "Pith review of The Value of Information in Multi-Scale Feedback Systems." pith.science (2026). https://pith.science/paper/KBXCESZZ

@misc{pith2026250511509,
  author       = {Pith},
  title        = {Pith review of: The Value of Information in Multi-Scale Feedback Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBXCESZZ}},
  note         = {Machine review of arXiv:2505.11509}
}
read the original abstract

Complex adaptive systems (CAS) can be described as systems of information flows dynamically interacting across scales in order to adapt and survive. CAS often consist of many components that work towards a shared goal, and interact across different informational scales through feedback loops, leading to their adaptation. In this context, understanding how information is transmitted among system components and across scales becomes crucial for understanding the behavior of CAS. Shannon entropy, a measure of syntactic information, is often used to quantify the size and rarity of messages transmitted between objects and observers, but it does not measure the value that information has for each specific observer. For this, semantic and pragmatic information have been conceptualized as describing the influence on an observer's knowledge and actions. Building on this distinction, we describe the architecture of multi-scale information flows in CAS through the concept of Multi-Scale Feedback Systems, and propose a series of syntactic, semantic and pragmatic information measures to quantify the value of information flows. While the measurement of values is necessarily context-dependent, we provide general guidelines on how to calculate semantic and pragmatic measures, and concrete examples of their calculation through four case studies: a robotic collective model, a collective decision-making model, a task distribution model, and a hierarchical oscillator model. Our results contribute to an informational theory of complexity, aiming to better understand the role played by information in the behavior of Multi-Scale Feedback Systems.

Figures

Figures reproduced from arXiv: 2505.11509 by the authors.

Figure 1
Figure 1. a. MSFS across three scales, with a single feedback cycle Figure 1b. Syntactic, semantic, and pragmatic information measure domains [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. a. Robotic collective Micro-scale S0 Grid of information sources Meso-scale S1 Agents’ individual opinions Oi Macro-scale S2 Collective opinion Ocoll … … … … … … Micro-scale S0 Individual oscillators Meso-scale S1 Pairwise averages of oscillators Macro-scale S2 Average of the pairwise averages Micro-scale S0 workers: individual tasks & errors Meso-scale S1 mid-managers: sum of tasks & errors Macro-scale S2 top manag… view at source ↗
Figure 3
Figure 3. a. ∆ (t−1)→t sm Figure 3b. ∆t th,counts Figure 3c. ∆t th,full Figure 3d. ∆t th,partial [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: a. V t−1→t sm,th,counts Figure 4b. V t−1→t sm,th,full Figure 4c. V t−1→t sm,th,partial Figure 4d. E t−1→t th,counts Figure 4e. E t−1→t th,full Figure 4f. E t−1→t th,partial [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Pragmatic delta (eq. 13) of the various strategies. Figure 6a. V t−10→t pr,gl Figure 6b. V t−100→t pr,gl Figure 6c. V t−500→t pr,gl Figure 6d. E t−10→t pr,gl Figure 6e. E t−100→t pr,gl Figure 6f. E t−500→t pr,gl [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: a. V t−10→t pr,gl Figure 6b. V t−100→t pr,gl Figure 6c. V t−500→t pr,gl Figure 6d. E t−10→t pr,gl Figure 6e. E t−100→t pr,gl Figure 6f. E t−500→t pr,gl [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: a. consensus strategy, N=R=5 Figure 7b. consensus strategy, N=R=10 Figure 7c. consensus strategy, N=R=25 Figure 7d. randomCN strategy, N=R=5 Figure 7e. randomCN strategy, N=R=10 Figure 7f. randomCN strategy, N=R=25 Figure 7g. randomTOT strategy, N=R=10 Figure 7h. rando…
Figure 8
Figure 8. Figure 8: a. Average simulation length (tavg) as a function of N for all strategies Figure 8b. Average simulation length (tavg) as a function of R for all strategies Figure 8c. Average delta of truth (∆th,avg) as a function of N for all strategies Figure 8d. Average delta of tru…
Figure 9
Figure 9. Figure 9: a. Semantic delta ∆sm of the consensus strategy Figure 9b. Semantic delta ∆sm of the randomCN strategy Figure 9c. Pragmatic delta ∆pr of the consensus strategy Figure 9d. Pragmatic delta ∆pr of the randomCN strategy Figure 9e. Semantic truth value Vsm,th for the consen…
Figure 10
Figure 10. Figure 10: a. t0 Figure 10b. t1 Figure 10c. t2 Figure 10d. t3 Figure 10e. t4 Figure 10f. t5 [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: a. Probabilities to reach the goal Figure 11b. Pragmatic goal values with correct info Figure 11c. Efficiency of the pragmatic goal value Figure 11d. Pragmatic goal values with error info [PITH_FULL_IMAGE:figures/full_fig_p030_11.png]
Figure 12
Figure 12. Figure 12: The hierarchical oscillator system with three scales. Each oscillator is an (X, Y ) pair and communication across scales is by means of X concentration values. information received by oscillator i in Sm is the X concentration of its parent oscillator in Sm+1, which im…
Figure 13
Figure 13. Figure 13: Calculated values for syntactic information. The left side of the figure depicts the 3-scale system while the right side depicts the 2-scale system. The efficiency is calculated by dividing the pragmatic goal value by Csyn. Epr,gl(t) = Vpr,gl(t) Csyn (59) 4.5.3.2 Resu…
Figure 14
Figure 14. Figure 14: a. X concentrations Figure 14b. Semantic delta Figure 14c. Semantic truth value Figure 14d. Semantic truth value efficiency Figure 14e. Pragmatic delta Figure 14f. Pragmatic goal value [PITH_FULL_IMAGE:figures/full_fig_p036_14.png]

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.