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LIT-1175: Local information transfer as a spatiotemporal filter for complex systems

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Properties5
StatusActive — read in full 2026-10-16 (NOTE-943); worth reading as the source of local transfer entropy, the pointwise log ratio whose average is Schreiber's transfer entropy, and of the split between apparent transfer entropy (conditioned on the destination's past only) and complete transfer entropy (conditioned also on the other causal parents). Read it knowing that its evidence is elementary cellular automata, where the causal parents are known by construction; that "complete" needs that knowledge; that the destination history k must be long (k ≥ 6 for rule 110, k = 16 used) and is limited by sample size; and that its closing claim to establish transfer entropy as the measure of information transfer predates the critique of James, Barnett and Crutchfield (LIT-1165). Filed as THEORY-702.
Tagscomplex-systems, information-theory
ExtendsLIT-1177 — Measuring Information Transfer
Cited as “paper” byNOTE-943 — Lizier, Prokopenko and Zomaya — Local information transfer as a spatiotemporal filter
Cited as “source” byTHEORY-702 — Transfer entropy is the average of a local transfer entropy, the log ratio at each observation of the destination's next-state probability with and without the source given the destination's past, which can be negative where the source misleads; the destination history must be long for it to exclude self-influence routed through the source; and conditioning also on the destination's other causal parents (complete) can differ sharply from conditioning on its past alone (apparent), as in elementary cellular automata, where long-history local transfer entropy picks out gliders and domain walls

Graph View

Joseph T. Lizier, Mikhail Prokopenko and Albert Y. Zomaya (2008), “Local information transfer as a spatiotemporal filter for complex systems”, Physical Review E 77: 026110 — ARXIV-0809.3275

Key takeaways

From the reading, NOTE-943.

  • Local transfer entropy (Eq. 9). T_{Y→X} = ⟨t_{Y→X}(n + 1, k, l)⟩ with t = log p(x_{n+1} | x⁽ᵏ⁾_n, y⁽ˡ⁾n)/p(x{n+1} | x⁽ᵏ⁾_n). The local value can exceed log b or be negative, where the source is “misleading”.
  • History length. Conditioning on the destination’s past removes “non-traveling” self-influence routed through the source; the correct setting is k → ∞ (Eq. 12). With k = 1 neither local MI nor local TE separates gliders from the background; k ≥ 6 does for rule 110.
  • Apparent against complete (Eqs. 13–14). Complete transfer entropy conditions also on the destination’s other causal parents; in a deterministic system it is nonnegative. In rule 18’s domain apparent TE is 0 where complete TE is about 1 bit.
  • Particles carry the transfer. Gliders (rules 110, 54) and domain walls (rules 18, 146) are where local TE is high, in their direction of motion; rule 22 shows transfer without coherent structure.
  • Averages hide it. Average TE against k for rule 110 does not reach a limit by k = 16 and says nothing about gliders (Fig. 7).

Standing in the record

Filed on 2026-10-16 and read the same day. It fixes two things the record’s transfer-entropy readings left open: the destination history length, which NOTE-788’s TE takes as a single value, and the difference between conditioning on the destination alone and on its other causes. Filed as THEORY-702. Its “apparent” against “complete” contrast is the synergy that CLAIM-335 turns on. complex-systems is primary for its question, information transfer by emergent structure; it carries no instruction for machine-learning practice.

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