NOTE-954: Powers, Clark & McFarland — General Feedback Theory, Part I

Contribution

The founding paper of perceptual control theory, in two parts; this is the first, the model without its psychological application. It defines a control unit (Feedback, Comparator and Output Functions plus an Environment Function), stacks such units so that a higher order’s output is a lower order’s reference, and adds three things the 1973 Science paper (NOTE-963) leaves out: a recording function at every unit that supplies references as replays of past perceptions (memory), an “imagination connection” by which those replays reach the higher order’s perception without passing through the world, and an inherited “negentropy” or N-system that reorganizes the network, input functions included, at a rate set by intrinsic error. There are no data.

Key insight

Every goal is a remembered perception, and a goal sent down can be perceived on the way. “the reference-signals which control a given feedback unit are examples of its own past sensory signals, and one could now express the task of the control system as being that of reproducing in present-time experience some previously-experienced perceptual field” (p. 18). Let the higher system perceive the reference it sends instead of the feedback it gets, and “the ‘match’ is automatically ensured” (p. 20): that is imagination, memory, planning and dreaming. How much of each perception comes from the world and how much from the replay is set by a “mixing control” whose seat the authors leave open. Separately, what changes the perceiving apparatus itself is not this loop but the N-system, an inherited controller of bodily variables whose output is random reorganization.

Assumptions

• Analogue, magnitude-only signals. “we are concerned only with information flow, and not with the means by which the information is transmitted” (p. 5).
• Stable functions between reorganizations. A function is “a stable relationship, which does not alter its form over reasonable periods of time” (p. 4). The learned hierarchy is “a model of those human systems which produce learned behavior, after learning has taken place” (p. 12). Change of form is the N-system’s alone.
• External loops first. “We will be primarily concerned with externally connected feedback loops” (p. 6), and the summary calls the hierarchy “composed of elementary feedback control systems of the external-loop type” (p. 21). The imagination connection is the one internal loop added, and is drawn dotted because “its introduction must be qualified” (p. 19).
• Stability by fiat. “by leaving the details of the functions unspecified, we have by definition a stable system” (p. 9).
• Quasi-static equilibrium. Only steady-state relations; transients are neglected on a time scale chosen per system, from 0.1 s to “even days” (p. 9).
• Outputs only at the first order. “all its output boundary functions belong to first-order control systems” (p. 10); “Only first-order systems act directly on the (non-CNS) environment” (p. 22).
• Genetically fixed top references. The N-system’s references “must be genetically determined, not determined by experience” (p. 14).

Key results

There are no theorems and no data; these are the model’s stated properties.

• The control unit (pp. 6–8). f = F(v_i), o = O(e) = O(r − f), v_i = E(o). With an unresisting environment the system settles with f = r and makes f “track” a slowly changing r; under disturbance a small residual error holds the output (p. 8).
• Internal loops are invisible from outside (p. 6). “only the external type is unequivocally perceivable as a feedback loop by an external observer. The behavior of any system with internal feedback could be simulated exactly by another system with no internal loops, so such internal loops cannot be firmly identified by external observations.”
• The hierarchy (pp. 10–12). First-order systems are the spinal loops. Output signals of higher orders are identified with lower references, because tying outputs together sends feedback systems “into violent conflict” (p. 11). “the output of a second-order system is not a muscular force, but a goal toward which first-order systems automatically adjust their input-signals” (p. 11). A system of any one order “perceives an environment made up of the feedback-signals of the systems in the next lower order” (p. 12).
• What the system knows (pp. 11–12). “it is of no concern at all to the feedback system what actual effects are produced in the environment”; the systems “cannot even know what is going on ‘out there.’ They perform the sole function of bringing their feedback-signals, the only reality they can perceive, to some reference-level, the only goal they know.”
• The limit of the learned hierarchy (p. 12). It “cannot do a thing about an environment which changes its properties … We still lack something to account for non-rote learning, for that requires altering the structure of the system, not merely its information content.”
• The N-system (pp. 12–16). Its output, “the processes which alter organization in uncommitted neurones” (p. 13), does four things: (1) uncommitted neurones “become tentatively organized to process a number of feedback signals from the highest existing order”; (2) others become tentative output organizations generating references for the next lower order; (3) at a variable rate; (4) an organization that occurs “often enough” persists, where “‘Often enough’ means one or more times” (p. 13, note 1). The input side is perceptual: “The continuing reorganization occurring in the new input function does not have such externally-observable results, but is subjectively recognized as a kind of trial-and-error effort to perceive new patterns … The ‘hypotheses’ here should be thought of as tentative definitions of new variables, which may or may not prove to repeat themselves in experience, depending on the organization of lower-order perceptual functions and the properties and nature of the environment” (p. 14). Its inputs are “intrinsic signals … measures of a set of physiological states” (p. 14). “the rate of learning is approximately proportional to the intrinsic error-signal, and this is a fundamental property of the human organism” (p. 15). Reorganization stops not because anything “tells” it to, but because “this particular organization produces behavior which results in a lessening of the intrinsic error” (pp. 15–16). “The output action of the N-system is conceived of as essentially random” (p. 21).
• Memory (pp. 16–18). Imagining is defined as “the ability to perceive sensory events generated internally rather than generated by present-time interactions at the input boundary of the whole system” (p. 16). A recording function R at each unit records its feedback signal and, when stimulated from outside the unit, replays “a facsimile of the signal that was recorded … To all intents, it is a sensory signal, but one arising from a past event rather than a present one” (p. 17). Higher outputs now stimulate recordings rather than set references directly (p. 18). “Rote learning could occur in the form of new recordings and hence an enlarged repertoire of reference-signals” (p. 18). Forgetting is undecided: “There is no present way to tell whether forgetting is due to fading of the recordings or to failure of the recovery apparatus” (p. 17).
• Why the replay must go up, not sideways (pp. 18–19). Perception is of feedback signals only, so the model so far “can reproduce a past experience without being able to perceive that experience” (p. 18). The replay cannot be fed back into the same order’s F, since F would process it twice (the y = x² example: the result represents x⁴, p. 19). It bears the same relation to lower signals as present feedback does, so “if the reference-signal were to enter a Feedback Function of the next higher order, it would always be interpreted properly” (p. 19). Hence the imagination connection.
• What it does (pp. 19–20). The higher system “would find its feedback signal at the required reference-level solely on the basis of the imagination-signals from lower order, even though the lower-order signals might be quite far from the reference-levels in the lower-order systems” (p. 19); then “a condition like dreaming or fantasy would occur, in which every goal set for the lower-order systems appeared to be immediately satisfied-in imagination, of course … if the reference-signal substitutes for the feedback-signal, the ‘match’ is automatically ensured” (p. 20). “The imagination-signal makes it possible for our system to perceive reproductions of past perceptual signals (that is, to remember as well as record), to plan an action ‘mentally’ without actually performing it, to hallucinate, and as mentioned, to dream” (p. 20).
• The mixing control (p. 20). “Obviously, the hierarchy could not perform very reliably in a real and sometimes dangerous environment if its actions were completely ‘short-circuited’ by the imagination connections. Somehow this configuration must contribute more information to the perceptual field at some times, less at others. Under conditions of sensory deprivation, it apparently provides a great deal of information, while under conditions of, e.g., immediate danger (barring pathology) it contributes little.” “There appears to be a kind of mixing control, which can be adjusted to full imagination (as when asleep) to full present-time perception. This might be a property of the Feedback Functions, corresponding to a shift in perceptual attention, or of the manner in which Output Functions stimulate lower-order recordings. We are open to suggestions.”
• The normal mix (p. 20). “The normal condition is probably one in which most information is present-time perceptual information, and small errors are filled in by the imagination connection-this would be a pro-survival property, in that it would allow the feedback systems to be very exact in their control-actions, while not tying them up over trivial discrepancies. The phenomenon of ‘filling in’ small discrepancies is well-known under the label ‘closure.’”
• The test of the significant variable (pp. 22–24). An observer finds another system’s controlled variables by disturbing candidate abstractions and seeing which are held constant; introspection supplies candidate classes (“sequence” is the example), to be checked by the test.

Claims

id	claim	strength	support
C1	Behaviour is organized as a hierarchy of negative-feedback systems in which each order acts only by setting lower references and perceives only lower feedback signals	moderate	model construction, pp. 10–12; anatomical hints (spinal loops, branching proprioceptive fibres)
C2	References are replays of recorded past perceptions, so a goal is a remembered perceptual state	weak	postulated, pp. 17–18; “Current experiments in brain stimulation tend strongly to support this view” (p. 17), uncited
C3	An imagination connection from a lower reference into the higher Feedback Function gives memory, mental planning, hallucination and dreaming	weak	functional argument from the y = x² example, pp. 18–20
C4	A mixing control sets the share of imagination in each perception, high under sensory deprivation and in sleep, low under danger	weak	one paragraph, p. 20; common experience; mechanism left open
C5	Non-rote learning is random reorganization by an inherited system whose rate is proportional to intrinsic error, forming new input as well as output functions	weak to moderate	pp. 12–16; credited in part to Hebb and McCulloch; no data
C6	Internal feedback loops cannot be firmly identified by external observation	strong as a modelling point	p. 6, by the simulation argument

Concepts

• Percept, variable, function, system. A percept is “the basic unit of experience”; a variable combines an unvarying class of percepts (identity) and a varying one (magnitude); a function is a stable relation imposed by some physical device; a system is “a collection of functions (not, as is often proposed, a collection of variables)” (pp. 2–4).
• Feedback-signal f, reference-signal r, error-signal e. “signal” is reserved for variables inside the system (p. 7).
• Order. First-order systems are the boundary loops (spinal reflexes); an nth-order system perceives (n−1)th-order feedback signals and outputs (n−1)th-order references (pp. 10–12).
• Recording function R. Records a unit’s feedback signal and replays it on stimulation; the replay serves as the unit’s reference (pp. 16–18).
• Imagination connection. A branch from a unit’s reference signal into the Feedback Function of the higher system that set it (p. 19).
• Mixing control. Whatever sets the proportion of imagination to present-time perception (p. 20).
• N-system, intrinsic signals, intrinsic state. The inherited reorganizing controller; its inputs, “measures of a set of physiological states”; and the state in which all its references are met (p. 14).
• Test of the significant variable. Disturb a candidate variable and see whether the system keeps it constant (pp. 22–23).

Connections

Table 1 names twelve sources. Ashby’s Design for a Brain (with “defects in 2/3 and 2/4” noted), Wiener’s Cybernetics and the 1948 Teleological Mechanisms symposium supply the control concepts; Hebb’s cell assembly and phase sequence are called “primitive feedback concepts”; Lorente de Nó’s cortical diagram in Fulton (1949) is read as showing “upgoing feedback signals …, outgoing output signals, and imagination connections”; Shannon and Weaver and analogue-computing texts supply the signal language; a 1954 Air Force frequency-response report is “A good example of what we are not trying to accomplish.” “Uncommitted neurones” is McCulloch’s term (p. 13). The 1973 Science paper (LIT-1180, read in NOTE-963) restates the hierarchy and the reorganizing top level and drops the recording function, the imagination connection and the mixing control. Part II (LIT-1197, NOTE-959) names the orders and works out reorganization, consciousness and conflict.

Bearing on the record

• CLAIM-341 (thesis).
  • The Rivals bullet’s quotations are accurate. “plan an action ‘mentally’ without actually performing it”, “match”, “automatically ensured”, “could not perform very reliably” and “completely ‘short-circuited’” are all on p. 20 (the last two in one sentence).
  • The imagination loop does not reshape the observer. It replays recordings into an unchanged Feedback Function, and rote learning only enlarges “the repertoire of reference-signals” (p. 18). So the claim is right to call it the synchronic, self-satisfying form. The paper adds that this form is not only for dreaming: in “the normal condition”, “small errors are filled in by the imagination connection”, which the authors identify with closure (p. 20). In this model the self-confirming loop runs all the time, at a small share.
  • But the theory does reshape the observer, and the claim’s contrast is with the wrong paper. The claim says “Powers’s sensors are assumed constant”, quoting the 1973 paper. In 1960 the functions are stable only “over reasonable periods of time” (p. 4), and the N-system’s first act is to organize new input functions, “tentative definitions of new variables”, experienced as “a kind of trial-and-error effort to perceive new patterns” and as “tentative formulation of hypotheses” (p. 14). That is the claim’s diachronic shape: a change to what the observer can perceive, felt as hypothesis-making. The difference lies in what drives the change and what keeps it, not in whether perception changes.
    • What drives it is error in inherited “intrinsic signals … measures of a set of physiological states” (p. 14), and its output is “essentially random” (p. 21). No judgement enters.
    • What keeps it is behaviour: an organization persists when it “produces behavior which results in a lessening of the intrinsic error” (pp. 15–16), in “the lower-order systems and the environment”. So in Part I the selection of a new observer runs through action and the world. Part II qualifies this: a new organization can be vetoed by “a moment spent imagining” (NOTE-959). The claim’s loop, judgement reshaping the observer, sits between the paper’s two mechanisms. The imagination loop has judgement-like content but changes nothing. Reorganization changes the observer, but it is driven from the body and kept by behaviour (my observation).
  • Only the lowest order acts on the world (“Only first-order systems act directly on the (non-CNS) environment”, p. 22), and each higher order “does not act directly on the external world, but on the only environment with which it is in immediate contact, the set of next-lower-order systems” (p. 22). This is a stronger statement of CLAIM-337’s “the lower system is the higher one’s proximal environment” than the 1973 paper gives, where higher systems sense quantities in the world. Here they perceive only lower signals.
  • supports: CLAIM-341 on the LIT is doubtful. The paper’s hierarchy is “of the external-loop type” (p. 21); its one internal loop is hedged for exactly the reason CLAIM-339 gives; and its reshaping of the observer is selected through behaviour. It is a rival that contains the claim’s ingredients, not support for it. The LIT’s relation was left as filed, for the owner to decide.
• CLAIM-339 (counter). The paper states its worry in its own terms: a hierarchy “completely ‘short-circuited’ by the imagination connections” could not “perform very reliably in a real and sometimes dangerous environment” (p. 20). Its remedy is not action as such but a mixing control that keeps present-time perception dominant. In locked-in syndrome present-time perception is intact while first-order output is gone. On this model every higher goal that closes through movement then stays in error in present-time perception, and the only place it can be satisfied is imagination (my observation; the paper does not discuss paralysis). Part II names a full switch to imagination as a defence against conflict (NOTE-959).
• CASE-107.
  • Sensory deprivation. The paper says one sentence: under it the imagination connection “apparently provides a great deal of information” (p. 20). No source and no data are given. Locked-in syndrome is not sensory deprivation; it is deprivation of output with input spared, a case the paper does not consider.
  • The asymmetry. The CASE says lucidity in the completely locked-in state cannot be shown without a channel that is itself an action. The paper makes the general point in 1960: internal loops “cannot be firmly identified by external observations”, since a system with internal feedback “could be simulated exactly by another system with no internal loops” (p. 6).
• QUESTION-121.
  • Candidate 2, the body. The N-system is a scoring channel the learned hierarchy does not set: its references “must be genetically determined, not determined by experience” (p. 14), and its inputs are physiological. This is the 1973 paper’s top level, stated earlier and in more detail. The same caution applies: its scores select organizations through behaviour (pp. 15–16).
  • The mixing control is where an anchor would have to sit. What keeps imagination from confirming itself is whatever sets the share of present-time perception. The authors do not know what it is, offering attention in the Feedback Functions or the way outputs stimulate recordings, and add “We are open to suggestions” (p. 20). The paper has no answer to the question, and locates where it lies.
• Checks of LIT-1188. The summary is correct against pp. 19–20. “Why this is here” is correct in what it quotes, and should add that the 1960 theory reshapes perceptual input functions through reorganization, so the contrast with “constant sensors” holds for the 1973 paper only. Crossref lists the third author as “Farland”; the reprint gives “McFarland”.
• For the anthology. No instruction for machine-learning practice.

Limitations

• No data. The empirical remarks (brain stimulation, sensory deprivation, closure) are uncited asides.
• Stability, the forms of the functions and the mixing control are left unspecified, the first by definition.
• The N-system’s output is “defined simply in terms of what it must do” (p. 13); its specificity is left open (Part II, p. 35).
• How a higher output selects which recording to replay is left open: it “might be a function of R, or it might result from some property of higher-order Output Functions” (p. 18).
• Read from an OCR extraction of a reset reprint; figures not legible in the extraction; journal pagination not checked.

Open questions

• What the mixing control is, and whether anything other than intrinsic error or danger sets it. That is the place in this model where QUESTION-121’s answer would go.
• Whether reorganization of input functions can be triggered by error in the learned hierarchy rather than only by intrinsic error. Part II allows “mean error signal in the hierarchy” as an intrinsic variable (p. 35), which would make a failed judgement a cause of reorganization (NOTE-959).
• Whether, in output deprivation with input spared, the model predicts a shift of the mix toward imagination, and so the self-confirming regime CLAIM-339 fears.