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Matter that learns what matters

Natalia G. Berloff

arXiv:2610.34428v1cond-mat.dis-nncs.ETnlin.AOphysics.optics

TL;DR

The paper asks whether a material’s action outcomes can train a persistent physical state that governs which sources it reads and how strongly they affect stored answers. It models this with optical link records and derives conditions for functional readout. Admission and use traces formed valid records selectively, while the readout bounds show why persistence alone does not ensure a useful record.

Abstract

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Can a material learn what deserves its attention? We show that it can in a model optical network, in which action outcomes train a persistent record in each link. The record biases whether a source is consulted and sets how strongly it changes a stored answer, so useful sources gain attention and influence without being identified in advance. The network's experience thus shapes the information available for its future learning. Resonant readouts make this learning fragile: reinforcement can carry a record past resonance, where it persists but its influence weakens. We derive bounds within which relevant signals guide the answer, irrelevant signals are rejected and stored answers remain open to revision. These bounds guide a learning rule that limits reinforcement as records form; in simulations, it acquires useful records and keeps them functional. When relevance changes, an obsolete record can block its own replacement. A local state that strengthens negative writing after unsuccessful actions releases obsolete records and completes the learning sequence more often. How a memory is read should decide how it is written.

One population stores the record and sets both readouts

Each link’s population stores a persistent relevance record that shifts both cavity and reader resonances. The record therefore shapes source selection and the strength of its influence on the stored answer, but can persist beyond the range where both readouts work.

One population stores the record and sets both readouts

  • The population x stores a bistable record: outcome pulses can push it across xU into the stable formed state xH, which the holding drive sustains.The cavity probe response biases source selection, while the reader gain sets how strongly a selected source moves the answer memory.Source: Figure 1 · p. 3, One population stores the record and… · p. 4
  • The crossbar places a cavity and reader at each source–memory crossing, with one population xjk controlling each link.The probe produces source-sensing signals, and a selected source reaches both memories but changes them with strengths set by their records.Source: Figure 1 · p. 3
  • At w = 1, the formed-state cavity response is 5.83 times the unformed-state response; reader-gain ratios are 9 at w = 1 and about 23 at w = 0.6.The sensing peak is at x = 3, while reader gain peaks at xH; beyond both peaks, a record can remain formed but lose readout strength.Source: One population stores the record and… · pp. 4–5

Action outcomes establish endogenous information control

Action outcomes update persistent link records through local traces, allowing reading activity to guide which sources are selected and how much they change answers. Admission and use traces formed valid records selectively, and transplanted populations transferred both source preference and memory influence.

Action outcomes establish endogenous information control

  • The writer weights a common outcome signal by each link’s eligibility trace and a population factor H(x); its outcome term is positive for correct answers and negative for errors at baseline.The trace can be driven by cavity light, reader intensity, or the reader’s effect on answer motion; the latter two are active only while the link’s need is acting.Source: Action outcomes establish endogenous… · p. 5
  • As valid records formed in one admission network, unassisted valid-source selection rose from 0.40 to 0.88 for need E.The figure follows record formation and source choice during acquisition.Source: Action outcomes establish endogenous… · p. 5, Figure 2 · p. 6
  • In all eight pairs of the first admission transplant test, both source preference and memory influence followed the transplanted records rather than the recipient’s training.The newly preferred source’s sensing signal exceeded its strongest competitor by 2.35 to 4.0 times, and the valid source moved memory by 2.00 in every pair versus at most 0.019 for others; equalized records removed selectivity.Source: Action outcomes establish endogenous… · p. 5, Figure 2 · p. 6
  • Admission and use each formed both valid records in 23 of 24 networks, with no persistent false records among 96 non-valid links; co-presence formed both in 13 and left 34 false records.The trace-rule comparison is summarized across networks in Figure 3.Source: Action outcomes establish endogenous… · pp. 5–6, Figure 3 · p. 7
  • Admission and use traces improved performance: disconnecting readers reduced correct actions by 13–14 percentage points, and both rules formed the newly valid record after reassignment.When an unrelated source was read alongside each valid source, only use met the joint criteria for valid-record formation and limiting false records.Source: Action outcomes establish endogenous… · p. 6, Figure 3 · p. 7

Storage stability is not functional stability

A persistent record is not necessarily a useful one: continued positive writing can carry it beyond the peaks of the readouts. Reliable operation therefore requires records to satisfy sensing, protection, and revision conditions together.

Storage stability is not functional stability

  • With reference reader width w = 1, learned records form, persist, and improve actions when read, yet settle near x = 4, beyond both readouts’ peaks.Positive writing continues after formation, while bistable restoring flow, set by slow reservoir decay, is too weak to hold the record near xH.Source: Storage stability is not functional… · pp. 7–8
  • The paper defines a functional record set by three conditions: valid-source selection probability at least 0.9, protection from answer reversal by non-valid readings, and revision by a valid source within one reading.Together these define the functional window.Source: Storage stability is not functional… · p. 8
  • At w = 1, two unformed non-valid readers can jointly reverse an answer, although either reader alone is harmless.The standard protocol presents at most one non-valid reading at a time, but the protection criterion also covers two simultaneous non-valid readings.Source: Storage stability is not functional… · p. 8
  • For protection and revision, the sufficient common reader-width range is 0.4551 ≤ w < 0.7101; at w = 0.6, fixed valid records in [3.30, 3.70] satisfy all three requirements.These are sufficient conditions; the bounds do not rule out narrower readers.Source: Storage stability is not functional… · p. 8

Success can push a record out of its functional window

With the original writer, valid records could form yet remain outside the functional sensing window. In selected replays, stronger outcome pulses pushed valid records farther from resonance and weakened source selection.

Success can push a record out of its functional window

  • At w = 0.6 and Λ = 5, most valid records remained below the sensing interval at the acquisition deadline, while several exceeded it.Continuations from learned states lost sensing mostly through the interval’s upper end.Source: Success can push a record out of its… · p. 8
  • 0.849–0.895: full-pulse replays lowered valid-source settled-field selection probability, while pulse-off replays kept it above 0.9.The replayed valid record remained formed in every case.Source: Success can push a record out of its… · p. 8
  • In all four selected events, the full pulse moved a valid record already beyond both readout peaks farther from resonance.Competing records differed by at most 0.017 between full-pulse and pulse-off replays; the events were chosen after inspection.Source: Success can push a record out of its… · p. 8

A self-limiting writer keeps learned records useful

A writer shaped by record population acquired functional records in six networks, but replacement remained difficult. Bounds on readout motivate limiting positive reinforcement before records lose useful influence.

A self-limiting writer keeps learned records useful

  • No constant gain met both requirements, so the writer weakens positive updates as the record forms and sets a capacity ceiling at x_c = 3.60.The population-dependent absorption and capacity factors shape positive writing; the negative gain matches the original writer at Λ− = 5.Source: A self-limiting writer keeps learned… · pp. 8, 9, 11
  • The bounds certify a functional window for w from 0.4551 to below 0.7101 when valid records lie in [3.30, 3.60].The bounds require protection against two opposing unformed readers and valid revision within one reading.Source: Figure 4 · p. 9
  • 6/6 networks acquired functional records, operated to reassignment, and preserved the unchanged need; the shaped writer acquired records versus 0/6 without its absorption line or capacity and 1/6 with the original writer.The comparison of the shaped writer with versions lacking the line or capacity had Fisher’s exact P = 0.002.Source: Figure 5 · p. 10, A self-limiting writer keeps learned… · p. 11
  • Adding the capacity reduced total excursion time above x = 3.60 by about fortyfold versus the absorption line alone in six histories.It also eliminated excursions above 3.70 in those histories.Source: Figure 5 · p. 10, A self-limiting writer keeps learned… · p. 11
  • Only two of six networks completed replacement by cycle 2000, and the other four failed at least one replacement-related criterion.The full sequence also required operation after the change and no persistent false record.Source: Figure 5 · p. 10, A self-limiting writer keeps learned… · p. 11

An obsolete record can block its own replacement

An obsolete source can remain preferred after its record falls below the sensing threshold, restricting opportunities for its replacement. Resetting that record restored replacement in two tested networks.

An obsolete record can block its own replacement

  • In N5 and N6, the obsolete source remained the most probable choice at every decision between its first crossing below xU and the replacement deadline.Its mean selection probability was 0.88 and 0.92, versus 0.065 and 0.04 for the new source.Source: An obsolete record can block its own… · p. 11
  • Crossing below xU does not erase a record’s advantage, and passive filling plus bistable restoring flow can recover obsolete populations.Noise contributed to recovery in N6.Source: An obsolete record can block its own… · p. 11
  • Resetting only the obsolete population to xL restored stronger new-source sensing and enabled both N5 and N6 to pass replacement tests.The unchanged need continued to pass its sensing tests; the reset changed both readouts, so their effects were not separated.Source: An obsolete record can block its own… · p. 11

A local response to adverse outcomes completes the learning sequence

A local state that tracks trace-weighted adverse outcomes strengthens negative writing on repeatedly unsuccessful links. In new simulations, the extension completed the full learning sequence more often than the self-limiting writer.

A local response to adverse outcomes completes the learning sequence

  • The signed, decaying susceptibility rises after adverse outcomes and falls after favourable ones, with updates weighted by each link’s eligibility trace.Only its positive part strengthens negative writing; positive writing remains unchanged.Source: A local response to adverse outcomes… · p. 12
  • In six development networks, susceptibility became positive on obsolete links after reassignment and stayed at or below zero on formed valid links during tested operation.A parameter was tuned using saved histories of N5 and N6.Source: A local response to adverse outcomes… · p. 12
  • 47 of 60 networks completed the full sequence with adverse-outcome susceptibility, versus 35 with the self-limiting writer.The paired improvement was 20 percentage points (Holm-adjusted P = 0.0037).Source: A local response to adverse outcomes… · p. 12
  • The extension’s advantage over a uniformly stronger negative branch was not statistically significant, leaving the role of history dependence unresolved.The adjusted P value was 0.070.Source: A local response to adverse outcomes… · p. 12

Implications for physical learning

The model shows that action outcomes can train persistent records that govern both which sources a material consults and how strongly they affect its memory. Because resonant readouts couple memory writing to reading, records can persist while losing function, so useful learning requires bounded writing and room for revision.

Implications for physical learning

  • Action outcomes train local records that let the network learn source relevance without supplied validity labels or target records.The shared reservoir population controls two resonant readouts: one biases source selection and the other sets influence on the answer memory.Source: Implications for physical learning · p. 12
  • A record can remain formed yet lose influence when reinforcement carries it beyond resonance, motivating sufficient bounds for selection, protection, and revision.The bounds identify a common range for these three functions.Source: Implications for physical learning · p. 12
  • An obsolete record can keep its source favoured and restrict readings of the evidence needed to replace it.Local sensitivity to adverse outcomes is one proposed way to release obsolete preferences; how much benefit comes from history dependence rather than added negative writing remains unresolved.Source: Implications for physical learning · p. 12
  • The resonance constraint can apply beyond optics when a persistent state shifts a resonance read at a fixed frequency.The mechanism also requires local traces, outcome-dependent writing, and a shared state controlling both readouts.Source: Implications for physical learning · p. 12
  • A candidate polariton link needs two optical modes sharing an exciton reservoir, while full-network implementation mechanisms and scaling under noise remain open.The passage specifies physical mechanisms for selection, outcome-gated writing, traces, capacity limitation, and susceptibility as outstanding needs.Source: Implications for physical learning · p. 13
  • Keeping learned information control useful means writing each memory with its readout in mind and keeping obsolete preferences open to revision.The paper frames this as the practical consequence of experience shaping both decisions and later evidence.Source: Implications for physical learning · p. 13

Methods

The model uses a driven cavity and slow reservoir to create a persistent link state, while optical readers couple sources to answer memories. Its network dynamics combine these links with a phase-bistable memory and driven reading and writing elements.

Methods

  • A driven cavity fills a slow reservoir whose population shifts the cavity resonance and changes subsequent absorption.The full field–reservoir equations specify field decay, reservoir decay, drive detuning, resonance shift per excitation, and capture rate.Source: Field–reservoir element and network · p. 13
  • When the field relaxes much faster than the reservoir, it can be eliminated, yielding a reduced model with low- and high-record states.The reduction uses x = g_R n/κ and δ = Δ/κ.Source: Field–reservoir element and network · p. 13
  • Network simulations retain cavity and reader fields, with each link carrying a reservoir population and each need an answer memory.Without reader or correction drives, the memory has stable states z_j = ±1 and follows the normal form of a degenerate optical parametric oscillator above threshold.Source: Field–reservoir element and network · p. 13
  • A binary gate controls link probing, while assisted reading tunes the acting need’s selected reader to resonance; the candidate physical implementation has additional constraints.The polariton proposal requires one reservoir coordinate to tune both modes with specified relative detunings and small direct self-interaction shifts throughout holding, probing, and writing.Source: Field–reservoir element and network · pp. 13–14

Selection, parameters and decision cycle

The protocol selects sources from measured responses, alternates two needs through sensing, reading, scoring, and correction, and writes records by combining outcomes with traces of recent link activity. The resulting credit allocation is task-dependent, and inactive traces decay so their negative writing is finite.

Selection, parameters and decision cycle

  • Source selection favours stronger relative responses while retaining uniform exploration; the maximum selection probability is about 0.933 even with perfect sensing contrast.The reference settings are N_K = 3, β_s = 8, and ε_x = 0.1.Source: Selection, parameters and decision cycle · p. 14
  • Each run begins with unformed records, then alternates needs in 22-unit cycles containing sensing, reading, scoring delay, correction, and quiet time.Hidden values flip with probability 0.1 after each reading and each cycle; a copied valid reading succeeds with probability 0.9.Source: Selection, parameters and decision cycle · p. 14
  • One action in five is a designated fair guess that updates the chance baseline without triggering writing; other actions are scored and can trigger an outcome pulse.A tie-break for a near-zero memory output remains a non-guess action and triggers writing.Source: Selection, parameters and decision cycle · p. 14

Writer and traces

  • Each link’s trace weights the common outcome signal and decays when its drive ceases, while activity traces measure cavity presence, reader admission, and memory-directed use.The acting-need gate restricts admission and use drives, and it is off during the outcome pulse so writing uses the trace left by reading.Source: Writer and traces · p. 15
  • When hidden values are redrawn each cycle, use produces persistent false records on 17 of 48 co-read links.The credit allocation is approximate because gating, thresholding, and rectification intervene.Source: Writer and traces · p. 15
  • When a need stops acting, its admission and use traces decay exponentially, leaving only a finite amount of negative writing that can erode records.During reading, reader inputs drive the memory; the work-balance terms are rates in an effective potential, not physical energy-transfer rates.Source: Writer and traces · p. 15

Learned relevance, tests and statistics

Learned relevance is defined by five tests of how outcomes form and use records, alongside preregistered tests and statistical procedures. Derived bounds specify when valid sources are selected, stored answers are protected yet revisable, and where those guarantees apply.

Learned relevance, tests and statistics

  • Outcomes must form records matching source validity without relying on signal co-occurrence, and each record must improve sensing and evidence influence while meeting separation and locality criteria.The validity assignment is not supplied to the network; switching the acting need changes preferences without changing records, while reassignment changes only affected records.Source: Learned relevance, tests and statistics · p. 15
  • The seeded network is the sampling unit; exact binomial intervals, network-resampled link-rate intervals, and paired or Fisher exact tests were used as appropriate.Median waiting times used Kaplan–Meier estimates with non-crossing networks censored; reader-withdrawal effects used one-sided bootstrap intervals over paired networks.Source: Learned relevance, tests and statistics · p. 15

Functional readout bounds

  • A valid-record interval of [2.263, 3.737] suffices for target selection probability pv ≥0.9 at NK = 3, βs = 8 and ϵx = 0.1 under the stated competitor conditions.Increasing βs to 10 widens the interval to [1.976, 4.024]; limits depend on selection settings and target probability.Source: Functional readout bounds · p. 16
  • Protection and revision share the sufficient width range 0.4551 ≤w < 0.7101 under the stated record, residual, and state bounds.At w = 1, two readers at xL can reverse a stored answer; the shared range assumes ηr = 0.05, and the guarantees concern unassisted readings.Source: Functional readout bounds · p. 16
  • At w = 0.6, the full reader and memory analysis establishes sensing, protection, and revision for specified record ranges and reset states, but not arbitrary dynamical states.The argument assigns no probability to records staying within bounds, and sensing additionally requires bounded cavity-field errors.Source: Functional readout bounds · p. 16

Finite pulses and the learning target

Finite outcome pulses update records according to success weighted by local trace activity, not overall success frequency. The analysis sets a functional learning target and informs a self-limiting writer, while pulse replays and drift calculations identify conditions and constraints on that design.

Finite pulses and the learning target

  • Positive-pulse credit is exactly J = A(s −ν) in the transformed coordinate Ψ(x), with A determined by trace area over the pulse.The coordinate Ψ(x) = x + x∗ln(x/x∗) removes the factor H from the original writer; passive flow and noise contribute separately.Source: Finite pulses and the learning target · p. 16
  • Credit depends on success weighted by local activity, so equal-population links can receive different credit from the same outcome pulse when their traces differ.The learning target is functional records from the acquisition deadline through operation, but sampled readings do not certify continuous survival; with the original writer at w = 0.6 and Λ = 5, all tested continuations lost sensing within 151 cycles.Source: Finite pulses and the learning target · p. 17
  • The original writer at w = 0.6 and Λ = 5 lost sensing within 151 cycles in every tested continuation from learned states.Loss was mostly through the upper boundary of the sensing interval; operation checks sampled readings rather than continuous survival.Source: Finite pulses and the learning target · p. 17

Matched outcome-pulse intervention

  • Matched pulse replays reproduced selected sensing-loss events with full pulses, while half or absent writing altered only the writer term after the pulse.The test supports causation in the selected events but does not estimate how often this mechanism occurs.Source: Matched outcome-pulse intervention · p. 17

Construction of the self-limiting writer

  • The proposed writer controls write power through the local trace and positive outcome signal, with filling proportional to the absorption line aw(x).Representative formation pulses require write power of order ten times holding power during a two-unit pulse, without saturating the cavity or shared reservoir.Source: Construction of the self-limiting writer · p. 17
  • The capacity factor stops positive writing above xc, but noise carried validation records to 3.63–3.66 despite xc = 3.60.Deterministic confinement also requires reader absorption and field-transient filling to remain within the margin; the factor is phenomenological and needs a separate fast-following filling channel.Source: Construction of the self-limiting writer · p. 17
  • Under use statistics, formation and confinement overlap narrowly: formation requires Λ ≳7.4 under measured admission statistics, whereas confinement below x+ requires Λ ≲5.5 in this approximation.Keeping the equilibrium below the upper edge of the proved reader window requires Λ ≲4.9. At Λ = 5, the admission calculation predicts slightly negative drift through part of the formation interval, while the use calculation lies close to its threshold and depends on how trace areas are conditioned on the outcome.Source: Construction of the self-limiting writer · pp. 17–18

Development study

A separate development implementation compared writer controls, while subsequent studies tested acquisition, full-sequence completion, an adverse-outcome susceptibility extension, and numerical sensitivity. The supplied passages specify study designs and some outcomes, but do not report the sixty-network comparison's outcome.

Development study

  • At ∆t = 0.002, the development implementation formed records faster than the original code; at ∆t = 0.0005, sampled formation-time distributions were consistent, without established trajectory agreement.Uniformly stronger writing and self-limiting gains without either population factor formed records but left no network functional at the acquisition deadline; shaping both branches erased no obsolete record.Source: Development study · p. 18
  • The development study used eight networks per writer-law and trace-rule combination with matched random streams, and its results were not pooled with validation.It checked sensing each cycle and applied protection and revision tests to applicable unassisted readings.Source: Development study · p. 18

Six-network validation

  • Six-network validation fixed six criteria before runs, including functional acquisition, operation, preservation of the unchanged need, replacement, post-replacement operation, and no persistent false records.Acquisition required sensing, protection, and revision; replacement required operation through the new source and protection against tested non-valid patterns containing the obsolete source.Source: Six-network validation · p. 18
  • The acquisition comparison of six successes against none was added after the runs; the pre-run comparisons concerned completion of the whole sequence.The acquisition comparison used Fisher’s exact test because the compared writers did not share random streams.Source: Six-network validation · p. 18

Adverse-outcome susceptibility and sixty-network comparison

  • The susceptibility extension strengthens negative writing after adverse outcomes using a local signed state, while leaving positive writing unchanged.Its parameters were fixed before the first extension simulation; the sixty-network comparison tested it against the self-limiting writer and a uniform control on ten networks per reassignment.Source: Adverse-outcome susceptibility and… · pp. 18–19
  • The sixty-network comparison required all six criteria to pass in one history and used two-sided exact McNemar tests with Holm adjustment for its two primary comparisons.Numerically unresolved histories counted as failures; superiority required statistical significance and a positive paired difference.Source: Adverse-outcome susceptibility and… · p. 19

Noise and numerical resolution

  • Aggregate verdicts in the trace-rule studies were unchanged across tested step sizes, although individual counts and short-segment quantities sometimes depended on step size.In a separate halved-step check, all 18 complete-sequence outcomes and 108 criterion labels were unchanged; this does not establish a convergence order.Source: Noise and numerical resolution · p. 19
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