{"id": "card_tool_reservoir_computing", "kind": "reference", "title": "Reservoir computing — a fixed substrate, a trained readout; our use of it", "body": "A reservoir computer never trains its dynamical system. A FIXED, random, high-dimensional substrate is driven by the input and only a LINEAR READOUT y = sum w_i x_i learns, by one closed-form regression (Jaeger 2001, echo state networks; Maass, Natschlaeger and Markram 2002, liquid state machines). The substrate may be hardware: a bucket of water solved XOR and spoken digits from a photograph of its ripples (Fernando and Sojakka 2003); silicon, optics and spintronics since (Tanaka et al. 2019). Of a 100-unit reservoir with one readout the trained weights are 1/101 of the whole - sealed on the reservoir_computing stick (run tick.py reservoir_computing), with the readout's arithmetic: it is a RIEMANN SUM, and zero times infinity is a number only because the width is bound to the count - the left-sum error 1/(2n) - 1/(6n^2), the midpoint error 1/(12n^2), the Darboux gap 1/n (the integral exists iff floor meets ceiling), the UNBOUND sum diverging, Monte Carlo at 1/sqrt(n). OUR USE: the keeping is the reservoir - 933,479 found, verified, cited and sealed cards that are never retrained - and the readout is the only thing that moves: the pheromone trail (one decaying number per card, 0.25 left after two thirty-day half-lives, 49.97 bytes a trail measured on the box), the faces' scope weights and the winning-ticket mask, the chains' priced cost bands, the trajectory of a path (Wilson floor, width 1/sqrt(n)), the physiology load tally (six-hour half-life), the quorum and the elders' counts; in the fuel layer a frozen base with a rank-16 adapter (1/272 trained, sealed). Every one of these fits, and a fit is efficient for one reason: training is a thin linear readout over a fixed substrate, never the substrate itself. The boundary: a model inside the answering loop would be retraining the reservoir, and an unbound weight is a hub. Rests on the instruments, the computer, the mind and the logarithm (fading memory is e^(-t/tau)); Matt's reservoir-and-manifold doctrine says the same in energy terms - the manifold is the readout, and it is linear.", "source": {"label": "Narrow Highway — the instruments", "url": "", "authority_tier": "engine_derived", "ref": "card_floor_computer_science"}, "shelf": "codex", "box": "instruments", "bands": ["reservoir computing", "reservoir computer", "echo state network", "echo state", "liquid state machine", "readout", "linear readout", "fading memory", "riemann sum", "zero times infinity", "darboux", "stigmergy", "pheromone", "winning ticket", "lora", "instrument", "no-code", "one map", "our use"], "subject": "Reservoir computing — a fixed substrate, a trained readout; our use of it", "connections": [{"to_card_id": "card_floor_the_instruments", "relationship": "part_of", "evidence": "a low-tech instrument: a bucket of water computes by structure; only the readout is trained"}, {"to_card_id": "card_floor_computer_science", "relationship": "connects_at", "evidence": "a fixed substrate plus a trained linear readout is a complete computer (Jaeger 2001; Maass 2002)"}, {"to_card_id": "card_floor_logarithm", "relationship": "connects_at", "evidence": "the echo state property is fading memory e^(-t/tau); a half-life is ln 2 over the rate"}, {"to_card_id": "card_floor_the_mind", "relationship": "connects_at", "evidence": "the liquid state machine models a cortical microcircuit as the reservoir, readouts as the learners"}, {"to_card_id": "card_doctrine_reservoir_manifold", "relationship": "connects_at", "evidence": "the reservoir and the manifold: the manifold (routing layer) is the readout, and it is linear"}, {"to_card_id": "card_tool_the_engine_among_the_instruments", "relationship": "connects_at", "evidence": "our place: the keeping is the reservoir, the faces and trails are the readout - each fit is efficient"}, {"to_card_id": "card_tool_resonators", "relationship": "connects_at", "evidence": "the ring-down is fading memory: a cavity with a delay loop or a feedback laser is a reservoir computer"}, {"to_card_id": "card_cs_sorting_algorithms", "relationship": "connects_at", "evidence": "the trained readout is a weighted sum and then a sort: top-k by score is a partial sort (a heap)"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.instruments", "facets": {"subject": ["darboux", "echo state", "echo state network", "fading memory", "instrument", "linear readout", "liquid state machine", "lora", "no-code", "one map", "our use", "pheromone", "readout", "reservoir computer", "reservoir computing", "riemann sum", "stigmergy", "winning ticket", "zero times infinity"]}, "presentation": {"glyph": "•", "kind_label": "instruments", "by": "Narrow Highway — the instruments", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "relationship": "part of", "why": "a low-tech instrument: a bucket of water computes by structure; only the readout is trained", "href": "/card/card_floor_the_instruments", "resolved": true}, {"id": "card_floor_computer_science", "title": "Computer science — bits, logic, and what can be computed", "relationship": "connects at", "why": "a fixed substrate plus a trained linear readout is a complete computer (Jaeger 2001; Maass 2002)", "href": "/card/card_floor_computer_science", "resolved": true}, {"id": "card_floor_logarithm", "title": "The logarithm - the instrument the joints share", "relationship": "connects at", "why": "the echo state property is fading memory e^(-t/tau); a half-life is ln 2 over the rate", "href": "/card/card_floor_logarithm", "resolved": true}, {"id": "card_floor_the_mind", "title": "The mind — matter aware of itself", "relationship": "connects at", "why": "the liquid state machine models a cortical microcircuit as the reservoir, readouts as the learners", "href": "/card/card_floor_the_mind", "resolved": true}, {"id": "card_doctrine_reservoir_manifold", "title": "The reservoir and the manifold — value is in the routing layer, not the engine", "relationship": "connects at", "why": "the reservoir and the manifold: the manifold (routing layer) is the readout, and it is linear", "href": "/card/card_doctrine_reservoir_manifold", "resolved": true}, {"id": "card_tool_the_engine_among_the_instruments", "title": "Our place — a deterministic instrument you read, not a program you run", "relationship": "connects at", "why": "our place: the keeping is the reservoir, the faces and trails are the readout - each fit is efficient", "href": "/card/card_tool_the_engine_among_the_instruments", "resolved": true}, {"id": "card_tool_resonators", "title": "Resonators — Helmholtz, the cavity, Fabry-Perot: one shape, a Q that fades", "relationship": "connects at", "why": "the ring-down is fading memory: a cavity with a delay loop or a feedback laser is a reservoir computer", "href": "/card/card_tool_resonators", "resolved": true}, {"id": "card_cs_sorting_algorithms", "title": "Sorting algorithms — the roll of eighty-six and the bound none can beat", "relationship": "connects at", "why": "the trained readout is a weighted sum and then a sort: top-k by score is a partial sort (a heap)", "href": "/card/card_cs_sorting_algorithms", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_tool_reservoir_computing", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_tool_reservoir_computing"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}