Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Causality — causation and the structure of causal relations — causal order, definite and indefinite, and its combinatorics, topology and geometry; sheaf- and process-theoretic accounts of causality; causal models, causal inference and interventionist accounts of what a causal relation is; and the metaphysics of causation — exclusion, mental causation, causal emergence and closure, reciprocal causation (ADR-035).
79 of 2004 LIT documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| LIT-005 v3 | Adding causality to the information-theoretic perspective on individuality | Bourrat (2024), DOI-10.1007/s13194-023-00566-1. Of Krakauer et al.’s (2020) three mutual-information “individuality” terms (A* = I(S_{t+1}; S_t), A = I(S_{t+1}; S_t | E_t), nC = I(S_{t+1}; E_t | S_t)), Bourrat argues that nC and A* are not individuality measures. He then proposes the interventional  = I(S_{t+1}; Ŝ_t) (Eq. 6) and two ETI criteria: C1, a normalised Â_{S2}/H(Ŝ2) ≥ Â_{S1}/H(Ŝ1)|θ₀, and C2, low Var(Â_{S2} | Ê2 = ê2k). None of these is computed on any system. The paper’s claim that  ≡ I(S_{t+1}; S_t | E_t) = A in Krakauer’s model is false in general. | Proposed — read in full 2026-09-25 (NOTE-027); a clear conceptual argument that information-theoretic individuality should be interventional. It is unproven as a measure. Three things would settle it: a worked computation of Â, C1 and C2 on an explicit model (for example Black et al.’s ecological-scaffolding model); a corrected account of how  relates to the observational A; and a correct adjustment set for its own Fig. 3 example. |
| LIT-025 v4 | Greater than the parts: a review of the information decomposition approach to causal emergence | Mediano et al. (2022), ARXIV-2111.06518. A review, with no new theorem, of the ΦID theory of causal emergence. A supervenient feature V_t is k-th-order causally emergent iff Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0. A system hosts such features iff Syn⁽ᵏ⁾(X_t; X_t′) > 0 (cited as Rosas et al. 2020, Theorem 1), and Syn⁽ᵏ⁾ = D⁽ᵏ⁾ + G⁽ᵏ⁾ (downward causation plus causal decoupling). The review’s own additions are interpretive: the formalism is neutral between Granger and Pearl, coordinate dependence is defended as a feature, and it rebuts the charge that the theory makes no macro-versus-micro comparison. | Active — read in full 2026-09-25 (NOTE-010); a short, accurate map of the ΦID emergence formalism and the right entry point to Rosas et al. 2020, which a reader will still need for the proofs, the assumptions and the redundancy-free practical criteria. None of these is stated in the review. |
| LIT-038 v2 | The Relativity of Causal Knowledge | D’Acunto & Battiloro (2025), ARXIV-2503.11718. The paper defines SCMs as functors I → Prob and interventions as natural transformations (which requires invertible mixing functions). It encodes each non-intervened SCM as the convex space Δ(V, Ω) of all probability measures on its endogenous space, and puts these spaces on a graph as stalks of a network sheaf and cosheaf. The restriction maps are interventionally consistent α-abstractions and the extension maps are unspecified affine maps. “Relative causal knowledge” is the image of alternating restriction and extension along a path (Def. 11). The two substantive-looking theorems are either unsound or vacuous. Theorem 1 (every convex combination of a model’s interventional measures is a soft-interventional measure of it) rests on a proof step that is false. Theorems 2 and 3 hold for any pushforward map, so interventional consistency does no work in them. There are no results about the sheaf. | Rejected — read in full 2026-09-25 (NOTE-050); Not worth a reader’s time as a source of results. Its one non-trivial theorem is unsound as proved and false in general, its encoding theorem is vacuous, and §4 contains definitions only. A reader wanting category-theoretic causal abstraction should go to Rischel’s thesis or Beckers–Halpern. A reader wanting sheaves on networks should go to Curry or Hansen–Ghrist. |
| LIT-048 v3 | Transfer Entropy as a Log-likelihood Ratio | Barnett & Bossomaier (2012), ARXIV-1205.6339. For a parametric Markov model f(x_t | x^k_t, y^k_t; θ) of X, the likelihood-ratio estimator T̂ = −(1/(n−k)) log Λ for the null “no dependence on Y’s past” converges almost surely to the transfer entropy T_{Y→X} (Theorem 1a). Under the null, 2(n−k)T̂ is asymptotically χ²(d), with d the difference in parameter counts (Theorem 1b). For finite-state chains the ordinary plug-in estimator is exactly this estimator, with d = (a−1)a^k(b^k−1). For a linear Gaussian VAR, T̂ is half the Granger-causality statistic. | Active — read in full 2026-09-25 (NOTE-053); a short, correct letter and the standard citation for reading transfer entropy as a log-likelihood ratio. The consistency proof is informal, and the χ² results are cited to Wald (1943) rather than proved, but the identity itself is exact and still the one to cite. |
| LIT-079 v2 | Causal Claims in Economics | Garg & Fetzer (2024), ARXIV-2501.06873. GPT-4o-mini is run in nine passes per paper over the first 30 pages of 44,852 NBER/CEPR working papers. Edges kept in at least 4 of 9 passes, JEL-mapped, give “claim graphs” in which the share of edges backed by DiD/IV/RCT/RDD/synthetic control rises from 7.7% (1990) to 31.7% (2020). In year-fixed-effect-only regressions, doubling causal edges is associated with +1.36 pp top-five probability and +11.2% citations, while non-causal counterparts are flat or negative. The validation checks paper-level method labels, and only weakly: RCT and field labels have precision ≤ 0.10. It never checks the edges themselves against human labels. | Proposed — read in full 2026-09-25 (NOTE-083); a promising, openly released claim-extraction infrastructure whose headline associations rest on edges never validated against human labels and on regressions with year fixed effects only. An edge-level human-annotated audit, and outcome regressions with field and method controls on a common sample, would settle it. |
| LIT-110 v3 | Unknotting reciprocal causation between organism and environment | Baedke et al. (2021), DOI-10.1007/s10539-021-09815-0. The paper gives an epistemic, not a metaphysical, tool for organism–environment reciprocal causation. The loop is “unrolled” into two ordered series of states, O_n and E_n, joined by interventionist (Woodward) causal arrows, and an experienced-environment node Ex_n is added as the interface. Its authors argue that this one diagram keeps an epistemically set organism–environment boundary and maps constitutive, mediational, relational, relocational and physical niche construction onto shared causal patterns. They support this with worked cases, including two multi-species ones (bumblebee–eggplant; rumen microbes–ruminant host). | Active — read in full 2026-09-26 (NOTE-111); worth reading as the clearest statement of the “keep the boundary, unroll the loop” position in the niche-construction reciprocity debate, and as the natural counterpart to Hazelwood (LIT-156); its model is illustrative, not formalized or tested, and the formalization it promises is deferred to later work. |
| LIT-132 v2 | Luck and Intentional Action: A Causal Account | Quillien (2026), DOI-10.1162/OPMI.a.361. Across three Prolific studies (N = 198, 673, 142; Likert 1–7), judgments that “X happened because the agent wanted X” track intentionality judgments under manipulations of luck. Causation is the strongest predictor of intentionality: standardized β = .46, .56, .53, against know-how β = .33, .20, .27 and probability-raising β = .14, .16, .10. Across the 12 condition means, r = .98. Causation only partly mediates the effect of luck (64%, 45% and 49%; exploratory analyses). As the causal account predicted, Study 3 found that the effect of Process (normal vs mix-up) on intentionality is larger when the agent knows how the buttons work (interaction F(1, 423) = 32). In the morally neutral Kraemer vignette, intentionality and causation came apart. | Active — read in full 2026-09-26 (NOTE-092); Worth reading as the cleanest current statement and test of the causal (desire-causes-outcome) account of folk intentionality under luck. It has pre-registered designs, open data and an honest discussion of the half-mediation and the Kraemer divergence. Its evidence is correlational and its “model” is verbal, not computational. |
| LIT-144 v3 | Causal Exclusion and Downward Counterfactuals | Pernu (2015), DOI-10.1007/s10670-015-9781-7. The counterfactual theory of causation can answer the causal exclusion problem without being committed to downward causation, provided the semantics of counterfactuals is handled carefully. The exclusion problem itself, however, comes in several distinct forms. | Unavailable — seeded from the abstract on 2026-09-26; a close reading was attempted the same day and no full text could be obtained (Springer paywalled on both hosts; OpenAlex and Semantic Scholar list it closed; not among the articles of Pernu’s open 2013 dissertation in HELDA, though its §5.2 covers the counterfactual response at an earlier stage; PhilPapers, ResearchGate and Academia.edu refused). It stays Unavailable until a copy is supplied. |
| LIT-147 v3 | Mental causation via neuroprosthetics? A critical analysis | Pernu (2018), DOI-10.1007/s11229-018-1713-z. The interventionist/difference-making case for nonreductive mental causation from BCIs (List & Menzies 2009; Menzies 2015; Woodward 2008a,b, 2017) misplaces multiple realisation. What the ensemble recordings show is that one cortical-level variable N (the ensemble’s average firing) is realised by many single-neuron patterns N1, N2. Each intention M corresponds to one value of N. So the counterfactual contrast “∼M □→ ∼B true, ∼N □→ ∼B false” fails, and neuroprosthetics supports mental causation only by identifying M with N, not nonreductive physicalism. | Active — read in full 2026-09-26 (NOTE-091); Worth reading as a short, precise diagnosis of a specific equivocation in the interventionist BCI argument (multiple realisation at the wrong level). Its scope is limited to difference-making with a proportionality constraint (fn 1), and its identity conclusion rests on a simplified picture of neural decoding that it asserts rather than argues. |
| LIT-156 v4 | An Emerging Dilemma for Reciprocal Causation | Hazelwood (2023), DOI-10.1017/psa.2023.124. Hazelwood defines RC as “the process of natural selection is both a cause and effect of processes such as niche construction” and EC as “natural selection is an emergent causal process”. He argues they are incompatible. Emergence here is Wilson’s synchronic dependence plus autonomy, cashed out as Pence’s composition. If EC holds, niche construction partly composes selection, so the two fail Woodward’s independent-fixability condition and cannot stand in a causal relation. If EC fails, selection is either non-causal (statisticalism) or individual-level, which is incoherent because relative fitness needs a population (Millstein, Sober). EES proponents should drop RC but can keep niche construction as a genuine cause of the evolutionary product. | Active — read in full 2026-09-26 (NOTE-137); worth reading as a tight, well-sourced argument that brings the reciprocal-causation debate into the composition, exclusion and interventionism literature. Its force depends on accepting a process/product split for selection and a compositional reading of realization, both argued briefly and flagged as contestable. |
| LIT-164 v3 | Wave-Function Realism and the Scope of Physical Causal Closure | Poltorak (2026), https://philsci-archive.pitt.edu/30720/. A closure principle has two tacit parameters, its domain and its completeness relation (causal, dynamical or explanatory). Wave-function realism falsifies spatiotemporal-domain closure (STC) but is compatible with fundamental-physical closure (FPC), so there is no “trans-domain causal breach”. The physicalist is left with a dilemma: STC is too narrow, and FPC needs an independent criterion of physicality plus a dynamical-to-causal bridge. The paper tests this across primitive-ontology, spacetime-state, multi-field, Everettian, nomological and dispositional readings. | Active — read in full 2026-09-26 (NOTE-112); worth reading as the clearest statement of what quantum ontology does and does not do to causal-closure arguments. Its conclusions are modest, and it concedes that its main target is a picture rather than a published argument. Unrefereed. |
| LIT-713 | Causation and Manipulability | Woodward, “Causation and Manipulability”, Stanford Encyclopedia of Philosophy (2001; revised 2023). Causes are handles for manipulation: X causes Y iff some intervention on X, an exogenous change meeting conditions M1–M4 relative to Y, would change Y. The account is non-reductive but not viciously circular, needs no human agent, and distinguishes total, direct and contributing causes by combining interventions. Invariance and levels are not treated here. | Active — read 2026-10-05 (NOTE-585): in full, from the Stanford Encyclopedia of Philosophy’s own open page (2023 revision). Worth reading as Woodward’s compact statement of the interventionist account: X causes Y when an intervention on X, a surgical exogenous change defined by conditions M1–M4, would change Y. It answers the circularity and anthropocentrism objections and separates total, direct and contributing causes. Limits: it is a survey, and this version does not treat invariance, proportionality or levels of causation; for those the book (LIT-723, unread) is needed. |
| LIT-723 v2 | Making Things Happen: A Theory of Causal Explanation | Woodward (2003; Crossref print date 2004), Oxford University Press. A non-reductive, non-circular account of causation and explanation built on interventions; relationships that are stable under interventions are invariant, and invariance rather than lawhood explains causal explanation in the special sciences (per the publisher’s abstract). Unread: the account of intervention is read in his SEP entry LIT-713; chapter 6 on invariance is not. | Unavailable — registered 2026-10-05 from Crossref, not read: no lawful full text could be reached (the Oxford Academic page returned HTTP 403, and it is a subscription product). Its interventionist account is read first-hand in Woodward’s Stanford Encyclopedia entry “Causation and Manipulability” (LIT-713). The entry does not treat invariance, so chapter 6, “Invariance” (pp. 239–314), is the part the owner’s essay needs and has not read. It stays Unavailable until a copy is supplied, not on merit. |
| LIT-788 | The Geometry of Causality | Gogioso & Pinzani (2023), arXiv 2303.09017, Part 3 of the trilogy. Empirical models on any cover of a space of input histories are the points of a causaltope, a product of simplices cut by linear causality equations, so causal fractions are linear programs. Causal separability relative to a given ambient space lets entangled or contextually controlled quantum switches witness indefinite order once known no-signalling constraints are imposed, with the causally separable fraction bounded below by the separable local fraction. | Active — skimmed 2026-10-09 (NOTE-624); worth reading as the geometric half of the trilogy and the successor of the withdrawn LIT-813’s polytope and causal-fraction results: the empirical models on any cover of a space of input histories are exactly the points of a “causaltope”, the product of simplices sliced by linear causality equations derived from the space’s topology, so supported fractions and causally separable fractions are linear programs. Causal separability is defined relative to an ambient space rather than to the indiscrete one, which lets quantum switches with entangled or contextual control witness indefinite causal order once known no-signalling constraints are imposed (and not otherwise); the causally separable fraction is bounded below by the separable local fraction, and in the switch examples it tracks, and sometimes equals, the local fraction (“contextual causality”). The BFW model is 0% supported by every causally complete 3-event space and 100% by each of three indefinite orders. Read in part: introduction, causaltopes, standard causal separability and the examples. |
| LIT-800 | The Combinatorics of Causality | Gogioso & Pinzani (2022–23), arXiv 2206.08911 (v1 “The Topology and Geometry of Causality”). Generalises causal orders to spaces of input histories, sets of partial input assignments on which outputs may depend, so that causal constraints can depend on inputs. Defines causal completeness, tightness and sequential, parallel and conditional composition; proves the maximal complete spaces are the causal switch spaces; and counts 2644 causally complete spaces on 3 binary-input events (19 from definite orders), with about a billion estimated on 4. | Active — read 2026-10-09 (NOTE-635); worth reading as the paper that replaces causal orders by “spaces of input histories”: finite, join-prime sets of partial functions from events to inputs, each history being data on which the output at its tip event may depend. Order-induced spaces are a special case, and input-dependent (dynamical) causal constraints, such as a switch where one party’s input fixes the order of the other two, are first-class. Spaces form a lattice under inclusion of their extended histories; causal completeness (one tip event per history) recovers definite order; causal switch spaces are exactly the maximal complete spaces. On 3 events with binary inputs there are 2644 causally complete spaces in 102 symmetry classes, of which order-induced spaces account for 19; most are non-tight. It is the first of the three papers that supersede LIT-813, and its spaces replace that paper’s defective “locale of inputs”. |
| LIT-808 | The Topology of Causality | Gogioso & Pinzani (2023), arXiv 2303.07148, Part 2 of the trilogy. Extends Abramsky–Brandenburger from no-signalling to arbitrary, possibly dynamical or indefinite, causal structure: causality is continuity in the lowerset topology, causal functions form a presheaf that fails to be a sheaf exactly on spaces with “solipsistic contextuality”, empirical models live on any open cover, and standard empirical models on causal switch spaces (total orders included) are always local, so the Leggett–Garg model is local for its own total order. | Active — read 2026-10-09 (NOTE-612); worth reading as the direct successor of the withdrawn LIT-813’s sheaf construction, now over spaces of input histories (LIT-800) rather than a “locale of inputs”: a joint input–output function is causal when each event’s output depends only on the histories with that event as a tip, causal functions are exactly free assignments of outputs to tips (up to tip-equivalence in non-tight spaces), and an extended function is causal iff it is continuous for the lowerset topology. Causal functions form a separated presheaf that is a sheaf exactly when the space admits no “solipsistic contextuality”, so tight spaces give a sheaf and some dynamical causal structures do not, letting deterministic local data fail to glue. Empirical models are compatible families of distributions over causal functions on any open cover, from the fully solipsistic to the classical; standard empirical models on causal switch spaces, total orders included, are always local. Source of THEORY-171. |
| LIT-813 v2 | The Sheaf-Theoretic Structure of Definite Causality | Gogioso & Pinzani (2021), QPL 2021, EPTCS 343:301–324; withdrawn by the authors in 2024. Extends Abramsky–Brandenburger to a finite causal order. Inputs live on lower sets, sections are causal functions (an output depends only on inputs in its past), and an empirical model is a causal conditional distribution. Locality is a global section, equivalently a mixture of deterministic causal functions (Proposition 21). The models form a polytope cut out by linear causality equations, and pre-orders sketch indefinite causality. The construction’s “locale of inputs” is not a locale, as the authors’ withdrawal says. | Superseded — by LIT-800, LIT-808, LIT-788; read 2026-10-09 (NOTE-629), and superseded by its authors’ trilogy: LIT-800 (The Combinatorics of Causality, arXiv 2206.08911), LIT-808 (The Topology of Causality, 2303.07148) and LIT-788 (The Geometry of Causality, 2303.09017). The authors withdrew it: the arXiv record’s v3 (3 April 2024) states that the paper “has been superseded by arXiv:2206.08911v4, arXiv:2303.07148 and arXiv:2303.09017”, that its Definition 3 (the locale of inputs) “is not fit for purpose”, and that it is “unlikely to be the right reference”. The reading confirms the defect: the meet given in Proposition 5 can leave the poset, and the poset is not distributive, so it is not a locale (NOTE-629 gives a two-event counterexample). The successors replace the locale of inputs with spaces of input histories under the lowerset topology, a genuine topology; the sheaf of causal functions and locality as a global section are redone in LIT-808, and the polytope and the BFW causal fractions are proved in LIT-788. |
| LIT-843 | Combining contextuality and causality: a game semantics approach | Abramsky, Barbosa & Searle (2024), ARXIV-2307.04786, Phil. Trans. R. Soc. A 382:20230002. Adds an enabling relation to a measurement scenario and reads contextuality as a game: the Experimenter chooses measurements, Nature chooses outcomes, and Nature’s deterministic strategies replace the event sheaf. Recovers flat contextuality and Gogioso–Pinzani causal Bell scenarios, and expresses adaptive MBQC by Experimenter strategies. The strategy presheaf is not a sheaf: compatible deterministic strategies can fail to glue or glue non-uniquely. | Active — read in full 2026-10-09 (NOTE-646); worth reading as the version of sheaf-theoretic contextuality in which measurements are performed in a causal order and the choice of the next one may depend on earlier outcomes. A causal measurement scenario adds an enabling relation (Kahn and Plotkin’s information matrices renamed); Nature’s deterministic strategies over it replace the event sheaf, and the Abramsky–Brandenburger definitions of empirical model and contextuality then go through unchanged. Flat scenarios and Gogioso and Pinzani’s Bell scenarios with a causal order come out as special cases, and Experimenter strategies express adaptive measurement, as in the Anders–Browne GHZ OR-gate. Its sharpest point is that the strategy presheaf is not a sheaf: deterministic, compatible local strategies can fail to glue (Example 7.2) or glue non-uniquely (Example 7.3). A short paper; several results are deferred to an extended version. |
| LIT-894 v2 | Causality: Models, Reasoning, and Inference | Pearl (2009), second edition, Cambridge University Press. Skimmed in four excerpts the author posts: an intervention do(X = x) deletes X’s structural equation and solves the rest, while observing X = x violates no equation and is ordinary conditioning, so P(y | do(x)) and P(y | x) differ in general. A structural equation is a claim about Y under ideal control (Definition 5.4.1), and its coefficient is ∂E[Y | do(x)]/∂x, not a regression slope. The rest of the book was not read. | Active — read in part 2026-10-10 (NOTE-696); skimmed in four excerpts the author posts, the contents, the Preface to the Second Edition, §§5.3.2–5.4.1 (pp. 154–163) and the Epilogue (pp. 401–428), and nothing else. Worth reading for its operational meaning of a structural equation (Definition 5.4.1: a claim about Y under ideal control of X, not an algebraic or regression equation), for the coefficient as ∂E[Y | do(x)]/∂x, and for the Epilogue’s plain statement of intervention as surgery on autonomous mechanisms, against observation as conditioning, “given that we see”. These excerpts confirm the record’s gloss of do(). Not read: chapters 1–4 and 6–11, so not the identification results, the derivation of the do-calculus, the counterfactual semantics, the treatment of sequential plans (§4.4) or the chapter 11 discussions of whether do(x) represents practical experiments. |
| LIT-909 | Discovering Agents | Kenton, Kumar, Farquhar, Richens, MacDermott & Everitt (2022). Agents are “systems that would adapt their policy if their actions influenced the world in a different way”. In mechanised causal models, which add mechanism variables, decision and utility nodes are found from interventions on mechanisms, with proofs of recovery under five assumptions. Verdicts: a thermostat is not an agent, but the thermostat with its creation process is; humans are agents; an actor-critic is two agents. The labels are frame-dependent. | Active — read in full 2026-10-11 (NOTE-707) from the arXiv PDF (v2). Worth reading for the interventional definition of agents, as systems that would adapt their policy if their actions influenced the world differently, and for its verdicts: a thermostat is not an agent, but the thermostat with its creation process is; the training process, not the frozen policy, is the agent. It is explicit that its labels are frame-dependent, relative to the chosen variables. Its proofs assume interventional data on mechanisms. |
| LIT-945 v3 | Unscrambling the omelette of causation and inference: The framework of causal-inferential theories | Schmid et al. (2020). The paper introduces causal-inferential theories, which pair a theory of causal influences with a theory of inference and say how the two interact. In this frame it recasts operational and realist theories and characterizes the assumptions behind no-go theorems based on Bell locality and on generalized noncontextuality. It shows that the existence of a Leibnizian classical realist representation implies a generalized-noncontextual one; the converse is conjectured. Read in part. | Active — read 2026-10-14 (NOTE-737) in part, not in full: the sections that characterise generalized noncontextuality and Leibnizianity (§§V, VI, VIII, IX) were read closely, §II–IV and the proofs in Appendices C–G were not, so the NOTE is Skimmed. Worth reading as the current statement of what a generalized-noncontextuality no-go denies: a classical realist representation that preserves inferential equivalence. It also shows why a prepare-measure scenario, which allows no Bell-like no-go, can still show contextuality. Read it knowing that Leibnizianity implies generalized noncontextuality only in one direction (the converse is Conjecture 1′), that only classical inference is built, that the nonclassical realist theory it aims at is specified by desiderata only, and that it does not discuss the Kochen–Specker or sheaf notions. |
| LIT-947 v2 | Unravelling the Flow of Information in a Nonequilibrium Process in the Presence of Hydrodynamic Interactions | Das et al. (2025). Two colloidal particles in optical traps are coupled by the fluid through a symmetric tensor, and the trap of one is moved by recorded Ornstein–Uhlenbeck noise. Mutual information, time-delayed mutual information and transfer entropy, estimated from experimental and simulated trajectories, recover drive → driven particle → other particle. They show backflow between the particles at the measured drive strengths, and one-way flow at strong drive in simulation only. Stronger coupling lowers the information the driven particle shares with the drive and raises what the particles share, in parallel with a reported trend of irreversibility under coarse-graining. Without drive the particles are statistically independent. | Active — read 2026-10-14 (NOTE-788) in full; worth reading as a clean experimental benchmark for directional information measures: two colloids, symmetrically coupled by the fluid, one trap moved by recorded noise, with transfer entropy and time-delayed mutual information recovering drive → driven → other particle. Read it knowing that the drive acts on one particle and is recorded, so the measures locate where a drive enters; they do not tell a shared drive from coupling, and the direction they report changes with drive strength while the coupling stays symmetric. Held for QUESTION-063 as a limit on what such measures can see, in THEORY-275. |
| LIT-961 v2 | A Reply to Makelov et al. (2023)‘s “Interpretability Illusion” Arguments | Wu, Geiger, Huang, Arora, Icard, Potts and Goodman (2024). The authors of distributed alignment search reply to Makelov et al. (2023). They argue that the “illusion” is generic, because a direction a model uses need not be orthogonal to the null space of the next layer; that FLDD can be large with no change in behaviour; and that the factual-recall cases come from DAS trained per fact pair. Their toy counterexample holds only for an unnormalized patch. Both papers grant that alignments related by a change of basis can tie under interchange interventions. The reply’s own GPT-2 experiments agree that MLP8 carries almost no name-position information (4% IIA, against 70% for the layer-8 block output). | Active — read 2026-10-14 (NOTE-809) in full; worth reading for the point it shares with the paper it answers: interchange interventions on one set of variables can be satisfied equally by alignments related by a change of basis, so the mediating variable is fixed only relative to a choice of units. Read it knowing that its central toy computation, which claims Makelov et al.’s test rejects their own faithful direction, holds only for an unnormalized patch; patching the subspace the rowspace component spans recovers the full effect. Its own GPT-2 experiments agree that MLP8 carries almost no name-position information. The dispute is over the label, the metric (FLDD against IIA) and how DAS is trained, not over constitution against correlation. Filed, with LIT-968, as THEORY-243. |
| LIT-968 v3 | Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching | Makelov, Lange and Nanda (2023). A subspace activation patch can make a model behave as if a feature had changed while the patched direction is the sum of a part that varies with the feature but cannot reach the output (in an MLP, the kernel of the down-projection) and a part that can reach the output but is dormant on the data. Exact in a three-unit network; shown for MLP8 of GPT-2 Small on indirect object identification and for GPT2-XL MLPs on factual recall, where the effect vanishes once the disconnected part is removed. A residual-stream direction for the same feature passes the test. One-dimensional fact patches and rank-1 edits are nearly interchangeable, so a working rank-1 edit does not show the fact is stored in the edited layer. | Active — read 2026-10-14 (NOTE-782) in full; worth reading as the clearest case of an intervention that produces the predicted counterfactual output without the intervened variable carrying the feature: a subspace patch that pairs a direction varying with the feature but unable to reach the output with one that can reach it but is dormant on the data. Read it knowing that its ground truth for GPT-2’s MLP8 comes from prior component-level work, that it concedes a cancelling-subspaces reading it does not test, that its own residual-stream case passes the test, and that the reply (LIT-961) contests the label but not the MLP8 measurements. It speaks of faithfulness to a computation, not of constitution. Filed as THEORY-282 and, with the reply, THEORY-243. |
| LIT-987 v2 | Internal Causal Mechanisms Robustly Predict Language Model Out-of-Distribution Behaviors | Huang, Tao, Icard, Yang and Potts (2025; ICML 2025). Given a high-level causal model of a task and the subspace where DAS locates its key variable on correct in-distribution examples, transplanting a test input’s value of that variable into verified examples (counterfactual simulation) predicts whether the output is correct. In Llama-3-8B-Instruct, over five tasks and ten shifts that keep the task but lower accuracy, it beats output confidence and causal-agnostic probes on 8 of 10. A probe of the located variable beats a probe of its orthogonal complement on 7 of 10. Interchange accuracy and predictive power rise together only until accuracy nears 1. | Active — read 2026-10-14 (NOTE-765) in full; worth reading as a measured case in which variables located by interchange intervention as mediating a model’s in-distribution behaviour predict whether its outputs stay correct under task-preserving shifts better than output confidence or probes of the rest of the representation. Read it knowing that it is one model, two selected shifts per task and three folds without significance tests; that counterfactual simulation wins 8 of 10 shifts and the causal-variable probe beats the background probe on only 7; that its comparison features are not “merely correlated” ones; and that it claims nothing about constitution. It does not cite Makelov et al. or the reply. Filed as THEORY-287. |
| LIT-1038 | Quantifying causal emergence shows that macro can beat micro | Hoel, Albantakis and Tononi (2013), PNAS 110(49). Effective information, the mutual information between uniformly imposed interventions and their effects, equals effectiveness (determinism minus degeneracy) times the log of the state-space size. Coarse-graining always loses size and can gain effectiveness, so in four toy systems of logic gates a macro description carries 0.40 to 2.92 bits more than the micro it supervenes on. The claim that the EI peak is where causation happens rests on the uniform intervention distribution imposed at each level. | Active — read in full 2026-10-13 (NOTE-726) from the PubMed Central PDF of the published article (PMC3856819, pmc.ncbi.nlm.nih.gov/articles/PMC3856819/pdf/pnas.201314922.pdf), fetched through the Internet Archive capture of 2022-11-13 because PMC answered scripted requests with a reCAPTCHA page and pnas.org returned 403; the online Supporting Information was not read. Worth reading as the source of effective information as a measure of causal emergence: it shows exactly when a coarse-grained description of a known mechanism can carry more EI than the micro, and its macro advantage rests on imposing a uniform intervention distribution at each level. For QUESTION-093 it is an interventional criterion met with no closure and no self-individuation; it complements CLAIM-154 and THEORY-133 and is neither a case nor a rival of them; it measures a different object from the information-decomposition account of LIT-025. |
| LIT-1123 v2 | Engineering Emergence | Jansma & Hoel (2025). Scores every partition of a Markov chain’s states by CP minus the best CP of any finer partition; the partitions with positive gain form an emergent hierarchy, top-heavy, bottom-heavy or spread, whose spread peaks near linear preferential attachment in 40-state networks, and cycles can confine it to one chosen scale. | Active — read 2026-10-29 (NOTE-1359) in full, from arXiv’s own copy (v2); worth reading as the extension of causal emergence 2.0 (LIT-1136) from one path to the whole partition lattice of a Markov chain’s states, where a partition counts if its CP beats every finer partition’s, and the survivors form an “emergent hierarchy” whose spread is tied to preferential attachment and can be engineered to a single scale with cycles. Read it knowing that it searches partitions of one system’s states, not system–environment boundaries, prices nothing, drops CE 2.0’s consistency filter on “data not shown”, rests on 5- to 8-state enumerations and a 40-state greedy sampler, and that one of Figure 2’s CP values (0.13) does not follow from its own determinism and degeneracy (0.24 − 0.09). |
| LIT-1129 v2 | Dynamical Reversibility and A New Theory of Causal Emergence based on SVD | Zhang et al. (2024). Measures approximate dynamical reversibility of a Markov chain by Γ_α = Σσᵢ^α of its TPM, bounds EI by affine functions of log Γ_α, and defines causal emergence as the rise in average singular value when those at or below a threshold ε are cut: a rank test at ε = 0, threshold-relative above it. | Active — read 2026-10-29 (NOTE-1399) in full, from arXiv’s own copy (v6, with the supplement and proofs); worth reading for Γ_α = Σσᵢ^α as a measure of how near a transition matrix is to a permutation, the bounds log Γ_α − log N ≤ EI ≤ (2/α) log Γ_α, and causal emergence read off the spectrum as the gain in average singular value when values at or below ε are dropped. Read it knowing that with ε > 0 the measure depends on ε and is positive at some ε for every matrix whose singular values are not all equal, so “independent of coarse-graining” holds only for the rank test; that its Proposition 5, that its lumping commutes with the dynamics for any grouping, is false; and that the equivalence with EI maximization rests on Hoel’s Boolean-network examples. |
| LIT-1136 v2 | Causal Emergence 2.0: Quantifying emergent complexity | Hoel (2025). Along a chosen path of dynamically consistent coarse-grainings of a Markov chain, each step’s gain in CP (normalized determinism minus degeneracy, uniform interventions at each scale) is that scale’s causal contribution; causal emergence is the total gain and emergent complexity the entropy of the gains. Shown on three 8-state chains; the all-paths version is left open. | Active — read 2026-10-29 (NOTE-1387) in full, from arXiv’s own copy (v3); worth reading as the paper that recasts Hoel’s causal emergence as gains in causal primitives (determinism minus degeneracy, the effectiveness, which is EI without its size term) credited to each scale along a micro→macro path of consistent coarse-grainings, with the entropy of those gains as “emergent complexity”. Read it knowing that it is shown on three hand-built 8-state chains with no TPM printed, that the multi-path version is left open (LIT-1123 takes it up), that its claim to capture all macroscale causation rests on one manipulated family, and that its degeneracy formula is misprinted as 1 − H(E|C)/log₂ n. |
| LIT-1164 | Causal Reasoning in Graphical Time Series Models | Eichler & Didelez (2007), UAI 2007: 109–116, ARXIV-1206.5246. Defines the causal effect of an intervention on one component of a stationary multivariate time series on another at a later time, and links it to strong Granger noncausality through mixed graphs (directed edges for Granger causality, dashed edges for contemporaneous dependence). Under its intervention assumptions, which require the system to include every relevant process and exclude instantaneous causality, a missing directed edge means no effect at the next step, non-ancestry means none at any horizon, and back-door and front-door criteria identify the effect from observational data. In a Gaussian VAR the identified effect is a coefficient of the multi-step linear predictor. | Active — read in full 2026-10-16 (NOTE-941); worth reading as the short statement of exactly when a Granger-causal analysis says something about interventions: under its intervention assumptions, which need the series to include every relevant process (observed or not) and exclude instantaneous causation, a missing Granger edge means no causal effect at the next step and non-ancestry means none at any horizon, and time-series back-door and front-door criteria identify effects from observational data. Read it knowing that the front-door theorem’s proof is deferred to a paper “in preparation”, that the results are sufficient conditions, and that the examples are Gaussian VARs. Filed as THEORY-704. |
| LIT-1165 | Information Flows? A Critique of Transfer Entropies | James, Barnett & Crutchfield (2016), Physical Review Letters 116, 238701, ARXIV-1512.06479. Defines information flow from X to Y as information in Y attributable solely to X’s past, and shows with two XOR processes that transfer entropy is not it. With Y_t = X_{t−1} ⊕ Y_{t−1}, T_{X→Y} = 1 bit, yet the bit is jointly carried by both pasts (co-information −1). With Z_t = X_{t−1} ⊕ Y_{t−1}, both transfer entropies are 0 and the causation entropies are 1 bit each. By PID, transfer entropy is unique plus synergistic information; only the unique part is a candidate for flow. Conditioning is not subtraction. | Active — read in full 2026-10-17 (NOTE-945); worth reading as the short, exact case that transfer entropy is not a measure of information flow: in two XOR processes it credits a bit to a source that holds none of it alone, and reports zero for sources that jointly fix the target. Read it knowing that “flow” is defined by the authors as information solely attributable to one source’s past, that the cure it points to (unique information) has no agreed measure, and that its conjecture that directed information and Ay and Polani’s interventional flow fail the same way is a conjecture. Filed as THEORY-707. |
| LIT-1166 | Causality, Feedback and Directed Information | Massey (1990), Proc. ISITA-90, Waikiki. The usual definition of a discrete memoryless channel, P(y^N|x^N) = Π P(y_n|x_n), holds only when the channel is used without feedback; the right definition is P(y_n|x^n y^{n−1}) = P(y_n|x_n). Defines directed information I(X^N→Y^N) = Σ_n I(X^n; Y_n | Y^{n−1}), after Marko (1973), and proves I(X^N→Y^N) ≤ I(X^N;Y^N) with equality without feedback, that it bounds what the output tells about the source in a causal system, and so that feedback does not increase DMC capacity. “Statistical dependence, unlike causality, has no inherent directivity.” | Active — read in full 2026-10-17 (NOTE-939); worth reading as the short source of directed information, I(X^N→Y^N) = Σ I(X^n; Y_n | Y^{n−1}), and of the point that the usual definition of a memoryless channel silently forbids feedback because it confuses statistical with causal dependence. Read it knowing that “causal” here is a factorization condition on a system of sources and channels, not an interventional notion; that directed information conditions on the current input as well as the past, so it is not transfer entropy; and that the copy read is the author’s preprint, not the proceedings version. Filed as THEORY-711. |
| LIT-1169 | Measurement of Linear Dependence and Feedback between Multiple Time Series | Geweke (1982), Journal of the American Statistical Association 77(378): 304–313. Measures the linear dependence between two multivariate time series as the sum of three parts: feedback from the first to the second, feedback from the second to the first, and instantaneous feedback. The directed measures are log ratios of generalized variances (determinants of residual covariance matrices), have asymptotic χ² null distributions, and decompose additively by frequency. Unread; known through Barnett, Barrett and Seth and the abstract. | Unavailable — unread, registered 2026-10-16. A lawful copy was sought and not reached: OpenAlex marks it closed with no repository full text, Crossref lists only the Taylor & Francis and JSTOR copies, and web searches found no author-posted or course-hosted copy. Its generalized-variance measure and χ² asymptotics are restated by Barnett, Barrett and Seth (LIT-1171), which is how the record reads it until a copy is supplied. |
| LIT-1170 | Measuring Autonomy and Emergence via Granger Causality | Seth (2010), Artificial Life 16(2): 179–196. Defines G-autonomy, the log ratio of a variable’s prediction-error variance without and with its own past, given external variables, and G-emergence, a macro variable’s G-autonomy from micro variables times their mean Granger causality on it, so that it is zero if the macro variable is independent of the micro or fully predicted by them. In a predator–prey model an evolved controller has higher G-autonomy than a reactive rule; in a boids model, flocking has higher G-emergence and more macro-to-micro Granger causality than random or rigid motion. Measures are linear or Taylor-expanded nonlinear regressions. | Active — read in full 2026-10-16 (NOTE-935); worth reading as the source of G-emergence, the Granger-based measure the causal-emergence readings name as a rival (NOTE-726, NOTE-791, NOTE-010). Read it knowing that its measures are predictive and relative to a regression model and a variable set, as Seth himself says (§5.2), so that “downward causation” here means Granger causation from a macro variable to micro variables, and that the validation is two agent-based models with hand-chosen conditions. Filed as THEORY-703. |
| LIT-1171 | Granger causality and transfer entropy are equivalent for Gaussian variables | Barnett, Barrett & Seth (2009), Physical Review Letters 103, 238701, ARXIV-0910.4514. For jointly Gaussian stationary processes X, Y, Z, Geweke’s Granger causality F_{Y→X|Z} = ln(|Σ(X|X⁻⊕Z⁻)|/|Σ(X|X⁻⊕Y⁻⊕Z⁻)|) equals 2T_{Y→X|Z}, twice the transfer entropy, for multivariate predictor, predictee and conditioning variables. The proof is two lines: Gaussian conditional entropy is ½ln|partial covariance| plus a constant, and OLS residual covariance is the partial covariance. | Active — read in full 2026-10-16 (NOTE-934); worth reading as the short, exact source of the Gaussian equivalence the record already leans on through Barnett and Bossomaier (NOTE-053): for jointly Gaussian stationary processes, Geweke’s generalized-variance Granger causality is exactly twice the transfer entropy, conditional and multivariate. Read it knowing that the identity is about population quantities at fixed lags, that sample agreement depends on how the entropies are estimated, and that the remark that a stationary Gaussian AR process leaves nothing for nonlinear Granger causality cites unpublished work. Filed as THEORY-700. |
| LIT-1173 | Investigating Causal Relations by Econometric Models and Cross-spectral Methods | Granger (1969), Econometrica 37(3): 424–438. Proposes testable definitions of causality and feedback between stationary time series: Y causes X if the past of Y improves the prediction of X beyond what the other relevant past information gives. Shows the cross spectrum can be decomposed into two parts, one for each causal arm of a feedback loop. Unread; known through the works that restate it. | Unavailable — unread, registered 2026-10-16. A lawful copy was sought and not reached: Crossref and the Econometric Society give only the JSTOR copy (stable 1912791), behind a login; a course-hosted copy on a University of Freiburg seminar page (jeti.uni-freiburg.de, stud_sem_SS_09/grangercausality.pdf) refused this client’s connection three times and answered WebFetch with HTTP 503; a Bilkent course copy found by search returned 404. Searched again on 2026-10-17: the Freiburg host still reset the connection, and the only other copies found (ResearchGate, Scribd) are user uploads whose authorization could not be established. The record reads it through Barnett, Barrett and Seth (LIT-1171), Seth (LIT-1170) and Eichler and Didelez (LIT-1164), which restate its definition, until a copy is supplied. |
| LIT-1174 | Information Flows in Causal Networks | Ay & Polani (2008), Advances in Complex Systems 11(1): 17–41. In a causal Bayesian network, X_B is causally independent of X_A imposing X_S if setting x_A after setting x_S does not change the post-interventional distribution of X_B; this holds for every model on a DAG iff every directed path from A to B meets S (ud-separation, Theorem 2). Information flow I(X_A → X_B | X̂_S) is conditional mutual information with every probability replaced by its interventional counterpart, and is zero iff causal independence holds (under positivity of p(x_S)). Examples show it differs from mutual information and from transfer entropy: two binary chains that swap states have zero transfer entropy and one bit of flow (at k = 1, by the record’s check), and an observationally identical pair of independent inverters has zero of both. | Active — read in full 2026-10-17 (NOTE-946), from the authors’ preprint dated 12 May 2006; worth reading as the interventional counterpart of transfer entropy: information flow I(X_A → X_B | X̂_S) is conditional mutual information computed from do()-distributions instead of observational ones, it vanishes exactly under a graphical condition (ud-separation), and examples show it differs from transfer entropy and conditional mutual information in both directions. Read it knowing that it needs the full causal Bayesian network and its mechanisms, not data; that the examples are deterministic binary networks; and that its Example 6 claim of one bit holds, by the record’s calculation, only for k = 1 or when imposing X_k alone. The published version (Advances in Complex Systems 11(1), 2008) was not compared. Filed as THEORY-710. |
| LIT-1177 | Measuring Information Transfer | Schreiber (2000), Physical Review Letters 85, 461, ARXIV-nlin/0001042. Defines the transfer entropy T_{J→I} = Σ p(i_{n+1}, i_n^{(k)}, j_n^{(l)}) log[p(i_{n+1} | i_n^{(k)}, j_n^{(l)}) / p(i_{n+1} | i_n^{(k)})], the Kullback entropy of assuming that I’s transitions do not depend on J’s past, with history lengths k and l (“most natural” l = k or l = 1). Unlike time-delayed mutual information it is directional and zero for static correlation. In a tent-map lattice it is O(ε²) in the coupling while time-delayed MI is zero, and in an Ulam-map lattice it shows the coupling’s direction where time-delayed MI does not. | Active — read in full 2026-10-17 (NOTE-940); worth reading as the four-page source of transfer entropy, which the record uses in seven documents without holding it: T_{J→I} is the Kullback entropy of the transition probabilities of I with and without the past of J, at history lengths k and l that the definition leaves open. Read it knowing that “information transfer” and “exchange” are the paper’s words for a conditional mutual information, that common inputs are excluded only when they are known and conditioned on, that the continuum-limit claim is asserted, and that the evidence is two coupled-map lattices and one physiological pair, the last of which Schreiber himself says a common trigger could explain. Filed as THEORY-701. |
| LIT-1244 v2 | Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data | Rosas et al. (2020). Defines causal emergence of a supervenient feature V as unique information about the system’s future that no group of k parts holds, Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0, and proves a system has such a feature iff Syn⁽ᵏ⁾(X_t; X_t′) > 0, with the microstate as the witness. ΦID atoms split that synergy into downward causation and causal decoupling, under stated axioms on the redundancy function, which the paper says the minimum-MI decomposition meets and which identity-respecting ones fail. The practical criteria Ψ, Δ, Γ are redundancy-free and sufficient only; as proved they certify the system’s capacity, not the candidate feature. Applied to the Game of Life, boids and macaque ECoG. | Active — read 2026-10-20 (NOTE-987) in full; worth reading for the axioms the ΦID theory of causal emergence needs, the proof that a system hosts an emergent feature iff its parts carry synergy about their own future, the exact definitions of downward causation and causal decoupling, and the redundancy-free criteria Ψ, Δ, Γ. Read it knowing that the theorem’s witness is the microstate itself; that Proposition 1, as proved, certifies the system’s emergence capacity and not the candidate feature (under the minimum-MI decomposition the parity of two self-copying bits passes Ψ and is not emergent); that its axioms exclude identity-respecting redundancy measures and count aggregates of non-interacting persistent parts as emergent; and that Γ = 0 is never met in its data. |
| LIT-1306 v2 | Software in the natural world: A computational approach to hierarchical emergence | Rosas, Geiger, Luppi, Seth, Polani, Gastpar & Mediano (arXiv 2024). Defines three exact closures of a coarse-graining Z of a stationary discrete process X. In informational closure the micro past adds nothing to predicting Z’s future (Barnett–Seth dynamical independence). In causal closure Z’s ε-machine equals its υ-machine, the coarsest partition of micro pasts that predicts Z. In computational closure Z’s ε-machine is a coarse-graining of X’s. It proves informational ⟺ causal closure, and causal ⇒ computational closure for spatial coarse-grainings, not conversely. It ties these to strong and weak lumpability of the micro ε-machine. It proposes the lattice of strongly lumpable coarse-grainings of that ε-machine, modulo computational equivalence, as a system’s “functional architecture”. The case studies are cellular-automaton parity, Ehrenfest, Glauber energy, a modular random walk, agent counts and Hopfield overlaps. Most of them close by a permutation symmetry. | Active — read 2026-10-20 (NOTE-1030) in full; worth reading for three exact notions of a self-contained coarse-graining Z of a stationary discrete process X and how they relate: informational closure, I(X⃗_t; Z⃗ᴸ_{t+1} | Z⃗_t) = 0 for every horizon, which is Barnett and Seth’s dynamical independence without an environment; causal closure, the ε-machine of Z equivalent to its υ-machine (the coarsest partition of micro pasts that predicts Z’s future); and computational closure, Z’s ε-machine a coarse-graining of X’s. Theorem 1 proves informational ⟺ causal closure for any coarse-graining of the past; Theorem 2 proves causal ⇒ computational closure for spatial ones, and Counterexample 4 the converse false. Proposition 4 and Theorem 3 tie closure to Kemeny–Snell lumpability: strong lumpability gives closure, closure with a Markov Z gives strong lumpability, weak lumpability gives only computational closure. Read it knowing that the sublattice claims are asserted and, for informationally closed spatial coarse-grainings, false under common refinement (a three-bit counterexample in the NOTE); that the stated sufficient condition for the Ising energy to close (a permutation-invariant Hamiltonian) fails with a uniform field at coincident energies; that Proposition 3 is a telescoping identity whose closure hypothesis is idle; that (A.11) and Example 2 contain slips; that the modular random walk closes by symmetry of the weights and not by modularity; and that every result is exact, with nothing on approximate closure. |
| LIT-1310 v3 | Approximate Causal Abstractions | Beckers, Eberhardt & Halpern (2020; arXiv 2019). Extends exact causal abstraction to approximate abstraction: the worst case, over allowed interventions and contexts, of how far a high-level causal model’s answers depart from the coarse-grained answers of the low-level model it abstracts, under a distance the user chooses; probabilistic versions average over contexts and, given an intervention distribution, over the low-level implementations of each high-level intervention. Composing an abstraction with an approximation gives an approximate abstraction, and the converse decomposition can fail. | Active — read 2026-10-21 (NOTE-1045) in full, from arXiv:1906.11583v2; worth reading for its distance between causal models that compares answers to interventions rather than graphs, for approximate abstraction as that distance under a coarse-graining (THEORY-843), for the intervention distribution over low-level implementations of a high-level intervention, and for when an approximate abstraction factors into an abstraction and an approximation. Read it knowing that the error is a worst case over interventions, minimized over context maps and relative to a metric the user chooses, so it is zero wherever exact abstraction holds, including coarse-grainings whose dropped detail high-level noise can carry. |
| LIT-1316 v2 | Abstracting Causal Models | Beckers & Halpern (2019; arXiv 2018). A sequence of successively stronger definitions of abstraction between causal models, from Rubenstein et al.’s exact transformation through uniform transformation and abstraction to strong abstraction, which takes all potential interventions seriously, and constructive abstraction, which maps clusters of micro-variables to macro-variables; the paper says that combining micro-variables into macro-variables, and each of Rubenstein et al.’s examples, is constructive. | Active — read 2026-10-21 (NOTE-1032) in full, from arXiv:1812.03789v4; worth reading for the examples that show exact transformation too permissive, for the characterization of exactness under every distribution as a context map commuting with every allowed intervention (THEORY-849), and for the ladder τ-abstraction, strong and constructive abstraction. Read it knowing that its Theorem 3.8 omits the countability its proof uses, that the context map is only required to exist, so high-level noise may hold what the coarse state drops, and that every strong abstraction being constructive is a conjecture. |
| LIT-1334 v2 | Causal Consistency of Structural Equation Models | Rubenstein, Weichwald, Bongers, Mooij, Janzing, Grosse-Wentrup & Schölkopf (2017). Defines an exact transformation between structural equation models, under which the models agree on the effects of a declared set of interventions, and shows that marginalising variables, aggregating micro-variables into macro-variables and moving from time series to equilibrium models can each be exact for the interventions declared. | Active — read 2026-10-21 (NOTE-1037) in full, from arXiv:1707.00819v1; worth reading for the definition of an exact transformation between structural equation models, with its order-preserving map on interventions, and for its three families of exact coarse-grainings: marginalisation (THEORY-848), averaging under equal column sums (THEORY-847) and equilibria. Read it knowing that exactness is equality of push-forward laws for a declared intervention set, which Beckers and Halpern show to be too permissive and which can drop a variable that decides how a system responds; that only perfect interventions are modelled; and that the coefficient of its Theorem 11, as extracted from this copy, appears to lack a factor n. |
| LIT-1388 v2 | The Political Legacy of American Slavery | Acharya, Blackwell and Sen (2016). White Southerners in counties where slavery was more prevalent in 1860 are today somewhat more Republican, more opposed to affirmative action and more racially resentful, and present-day black population share does not explain it. The difference appeared after Reconstruction rather than before the war, and the authors argue it was amplified by planters’ post-emancipation incentives to repress black labor and votes and then passed down locally, through families and institutions they do not separate. | Active — read in full 2026-10-22 (NOTE-1089) from the journal’s typeset PDF posted by the second author (mattblackwell.org), without the online appendix; worth reading as a careful persistence study: white Southerners in counties with more slavery in 1860 are today somewhat less Democratic, less supportive of affirmative action and more racially resentful (about a tenth of a standard deviation), not accounted for by present black share, and the difference in voting appears after Reconstruction, not before the war (THEORY-889). The association is strong; the causal reading rests on an instrument with an untestable exclusion restriction; the intergenerational transmission is argued with thin evidence. What persists is attitude, not party. |
| LIT-1531 v3 | AtP*: An efficient and scalable method for localizing LLM behaviour to components | Kramár, Lieberum, Shah & Nanda (2024), arXiv:2403.00745. Attribution patching (AtP; Nanda 2023), a first-order gradient estimate of every node’s activation-patching effect, is tested against exhaustive patching on Pythia models from 410M to 12B. Verifying nodes in AtP’s order finds the largest-effect nodes far more cheaply than unordered or sampling-based search. Its false negatives come from saturated attention and from cancelling direct and indirect effects; AtP* adds an exact softmax for queries and keys and layer-wise gradient dropout, and a subsampling test bounds the size of nodes still missed. On the two prompt distributions, simpler variants are cheaper than AtP*. | Active — read 2026-10-26 (NOTE-1190) in full, from arXiv v1, with the comparison figures read from page renderings; worth reading as the systematic test of attribution patching against exhaustive activation patching on models up to 12B, for the two named causes of its misses (saturated attention, cancelling direct and indirect effects) and their fixes, and for the statistical bound on what is still missed (THEORY-996). Read it knowing that the ground truth is single-node noising on one model family and five settings, that only ranks are scored, that the numbers are only in charts, and that AtP* is not the cheapest variant on its two distributions. |
| LIT-1532 v2 | Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models | Marks et al. (2024), arXiv:2403.19647, ICLR 2025. Circuits are found over sparse-autoencoder features and autoencoder error terms of Pythia-70M and Gemma-2-2B, scoring nodes and edges by linear approximations to their indirect effects. On subject–verb agreement, small feature circuits carry much of the behaviour where neuron circuits need many more nodes, though only with the error terms kept. A human can remove features judged task-irrelevant from a classifier’s circuit (SHIFT), and the same method is run without supervision over thousands of behaviours clustered from the Pile. | Active — read 2026-10-26 (NOTE-1187) in full, from the arXiv copy (v3, the ICLR 2025 version); worth reading as the method that turned sparse-autoencoder features into circuits, by linear approximations of indirect effects over features and autoencoder errors together, and for its own evidence that the features alone are not the circuit: with the error nodes removed, its feature circuits recover little of the behaviour (THEORY-1007). Read it knowing that faithfulness is scored on the latter two thirds of each circuit only, that the interpretability of the circuits is the authors’ annotation, that the half-performance figure for Gemma neurons lies beyond its plotted range, and that its debiasing method is ML practice, which this record does not hold. |
| LIT-1536 v2 | Locating and Editing Factual Associations in GPT | Meng et al. (2022), arXiv:2202.05262, NeurIPS 2022. Causal tracing corrupts the subject’s embeddings with noise and restores one hidden state at a time: in GPT-2 XL, recall of known facts depends most on middle-layer MLP outputs at the last subject token and on attention at the last token. Treating an MLP’s output matrix as a linear associative memory, ROME inserts a fact by a closed-form rank-one update keyed on the last subject token. On the CounterFact dataset of 21,919 counterfactuals, ROME is the only editor tested with both high generalization to paraphrases and high specificity to neighbouring subjects. | Active — read 2026-10-26 (NOTE-1166) in full, from the arXiv copy (v5, the NeurIPS 2022 version); worth reading for causal tracing, a corrupt-and-restore intervention that locates where a fact’s recall depends on hidden states, for the finding that in GPT-2 XL that dependence concentrates at the last subject token in middle-layer MLPs, and for the rank-one edit that tests it (THEORY-998). Read it knowing that the storage hypothesis it draws is wider than what it shows (THEORY-1011), that LIT-968 proves a working rank-one edit does not locate a fact, and that several numbers and figure references in v5 do not match. |
| LIT-1540 v2 | Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small | Wang et al. (2022), arXiv:2211.00593. On sentences like “When Mary and John went to the store, John gave a drink to”, GPT-2 small predicts the indirect object through 26 attention heads in seven classes, found by path patching: duplicate-token and induction heads mark the repeated name, S-inhibition heads pass that on, and name mover heads copy the remaining name. Mean-ablating every other head keeps 87% of the logit difference. Knocking out the name movers costs only 5%, because backup heads take over, and a greedy search finds knockouts under which circuit and model differ by up to 87%. | Active — read 2026-10-26 (NOTE-1167) in full, from the arXiv copy; worth reading as the first end-to-end circuit for a natural behaviour in a pretrained language model, for path patching, for the backup heads that take over when the main ones are knocked out, and for its three tests of a circuit explanation, which its own circuit passes on average and fails under a greedy search (THEORY-980). Read it knowing that the behaviour is fifteen templates in one model, that MLPs are left out of the circuit though removing them breaks the task, that the dropout explanation of the backups is a hypothesis (THEORY-995), and that a few of its numbers and its greedy algorithm do not match their descriptions. |
| LIT-1541 v2 | On the Biology of a Large Language Model | Lindsey et al. (2025), Transformer Circuits Thread. Ten case studies of Claude 3.5 Haiku with the attribution graphs of LIT-1552, each validated by perturbing features in the model: two-hop factual recall through an intermediate “Texas” representation, rhymes planned before a line is written, addition features reused across contexts, a default “can’t answer” circuit inhibited by known entities whose misfire yields hallucination, unfaithful chains of thought, multilingual circuits, medical diagnosis, refusals, a jailbreak and a model with a hidden goal. The authors present each as an existence claim about specific prompts. | Active — read 2026-10-26 (NOTE-1181) in full, from the Transformer Circuits page; worth reading for ten case studies that show, on single prompts and with interventions, a two-hop intermediate in Claude 3.5 Haiku (THEORY-984), a rhyme planned on the newline before a line is written (THEORY-1017), a jailbreak whose target word is not represented before it is written (THEORY-1018), a trained-in goal represented in every Assistant context of a model organism (THEORY-976), and a default “can’t answer” circuit that known entities inhibit. Read it knowing that the authors find a satisfying graph for about a quarter of the prompts they try, that the graphs shown are curated and of a replacement model (LIT-1552), that several cruxes run through attention the graphs cannot see, and that its general statements about the model (THEORY-982) go beyond what the case studies show. |
| LIT-1547 v2 | Towards Automated Circuit Discovery for Mechanistic Interpretability | Conmy, Mavor-Parker, Lynch, Heimersheim & Garriga-Alonso (2023), arXiv:2304.14997, NeurIPS 2023. ACDC automates the patching step of circuit discovery: from the output back, it removes each edge of a model’s computational graph whose replacement by a corrupted activation raises the KL divergence from the full model by less than a threshold. Against circuits found by hand it ranks edges with AUCs of 0.85–0.98 on IOI, Greater-Than and Docstring, above two adapted pruning methods, and on Greater-Than keeps 68 of about 32,000 edges, all in the reported circuit. It is sensitive to metric, ablation and visiting order, misses negative components at sparse thresholds, and recovers compiled tracr circuits only with zero activations. | Active — read 2026-10-26 (NOTE-1170) in full, from arXiv v4, the NeurIPS 2023 version; worth reading for the workflow it names behind manual circuit discovery, for ACDC as that workflow’s patching step made into an algorithm, and for the first scoring of circuit-finding methods against circuits found by hand (THEORY-970). Read it knowing that the hand-found circuits are themselves partial, that the results move with the metric, the ablation and the order of visiting edges, that sparse runs miss negative components, that an OR gate keeps one input (THEORY-966), and that §4.1 claims a tracr-reverse lead its own Table 2 does not show. |
| LIT-1549 v3 | Causal Scrubbing: a method for rigorously testing interpretability hypotheses | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt et al. (2022), Alignment Forum (Redwood Research). Causal scrubbing tests a mechanistic hypothesis, stated as a correspondence from an interpretable computational graph into the model’s, by replacing every activation with its value on another input the hypothesis treats as equivalent and measuring how much of the behaviour survives. On a parenthesis-balance classifier, hypotheses recover 93% down to 72% of the loss as they are made more specific; on induction in a two-layer attention-only model, a naive hypothesis recovers 35% and a refined one 86%. | Active — read 2026-10-26 (NOTE-1168) in full, the main post of the sequence from the Alignment Forum; worth reading for the method that turns a circuit hypothesis into a mechanical test, for the argument for resampling ablation that later circuit work adopts, and for its own list of the ways a hypothesis can pass while wrong. Read it knowing that the test sees only the partitions of the data a hypothesis induces (THEORY-978), that its two applications are summarized here and detailed in companion posts the record has not read, and that hypotheses recovering 72% to 86% are accepted under a test that permits only exact swaps. |
| LIT-1550 v2 | MIB: A Mechanistic Interpretability Benchmark | Mueller et al. (2025), arXiv:2504.13151, ICML 2025. A benchmark with a circuit-localization track over IOI, arithmetic, MCQA and ARC, and a causal-variable-localization track that adds RAVEL, on four language models plus an InterpBench model with a known circuit. In circuit localization, edge attribution patching with integrated gradients does best on average; in causal-variable localization, supervised distributed alignment search (DAS) does best, and sparse-autoencoder features selected by a learned mask are never better than the model’s own hidden dimensions. | Active — read 2026-10-26 (NOTE-1169) in full, from the arXiv copy (v2, the ICML 2025 version); worth reading for its fixed-counterfactual design of two localization tracks, for the finding that public sparse-autoencoder features were worse units than neurons for known causal variables in every cell tested (THEORY-968), and for the carry-the-one case, where a representation that looked like the variable was the correlated output digit. Read it knowing that the best causal-variable method, DAS, is supervised by the causal model it is scored against, that the SAE comparison is on residual streams of two models under one selection method, and that the method rankings are interpretability practice. |
| LIT-1551 v2 | Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations | Geiger, Wu, Potts, Icard & Goodman (2024; arXiv 2023), CLeaR 2024. Distributed alignment search (DAS) learns, by gradient descent, an orthogonal rotation of a layer such that swapping rotated subspaces between inputs reproduces a high-level causal model’s counterfactuals, replacing brute-force search over disjoint neuron sets. In a network trained on hierarchical equality and in BERT fine-tuned on monotonicity NLI it finds alignments with interchange intervention accuracy 1.00 where axis-aligned ones reach 0.73 and 0.51; BERT’s entailment subspace decomposes into the identities of the two words, the equality network’s relation subspace does not. | Active — read 2026-10-26 (NOTE-1192) in full, from arXiv v4, the CLeaR 2024 version; worth reading for distributed interchange interventions and their training objective, for the exact example in which an algorithm fails in the neuron basis and holds after a rotation, and for the finding that BERT’s entailment subspace decomposes into the two words’ identities while an equality network’s relation does not (THEORY-983). Read it knowing that IIA is reported on the rotation’s training data, that Table 2’s brute-force row is a copy of Table 1’s, that the learned subspaces are fixed only up to rotations within them, and that its random-network control reaches 0.64 at width 4,096 (THEORY-1002). |
| LIT-1552 v2 | Circuit Tracing: Revealing Computational Graphs in Language Models | Ameisen et al. (2025), Transformer Circuits Thread. A cross-layer transcoder, whose features each read the residual stream at one layer and write to every later MLP output, stands in for a model’s MLPs. On one prompt, with attention patterns and normalization denominators frozen and error terms added back, this local replacement model reproduces the model’s activations exactly, and its attribution graph decomposes each feature’s pre-activation into linear edges. The graphs, pruned and grouped into supernodes, give hypotheses about an 18-layer model and Claude 3.5 Haiku that are then tested by perturbing features in the underlying model. | Active — read 2026-10-26 (NOTE-1185), main text in full and five appendices, from the Transformer Circuits page; worth reading for the attribution graph, a prompt’s computation rewritten exactly in sparse features of a local replacement model (THEORY-979), for its own measurements of how far that replacement responds to perturbation like the model (THEORY-994), for the parallelogram constraint on one-step sums (THEORY-971), and for a limitations section that names where the method fails: attention, error nodes, inactive features. Read it knowing that the graphs explain the replacement, not the model, that intervening confirms a direct edge almost by construction, that the replacement matches the model’s top token on about half of prompts, and that its faithfulness figures differ between the main text and the appendix. |
| LIT-1554 v2 | Transcoders Find Interpretable LLM Feature Circuits | Dunefsky, Chlenski and Nanda (2024), arXiv:2406.11944, NeurIPS 2024. A transcoder is a wide, sparsely activating ReLU MLP trained to imitate one MLP sublayer’s input–output map. With attention patterns frozen, the attribution of one transcoder feature to a later one factors into the earlier feature’s activation times an input-invariant dot product of decoder and encoder vectors, which allows weights-based circuit analysis through MLPs. On GPT2-small, Pythia-410M and Pythia-1.4B transcoders are at least on par with MLP SAEs in sparsity, faithfulness and human-rated interpretability, and they give a sparse account of MLP10 in GPT2-small’s greater-than circuit. | Active — read 2026-10-26 (NOTE-1174) in full, from the arXiv copy (v2, the NeurIPS 2024 version); worth reading as the source of transcoder circuit analysis, for the factorization of a feature-to-feature attribution into an input-dependent activation times an input-invariant weight (THEORY-974), on which the attribution graphs of LIT-1552 are built, and for its blind case studies, which grade the method against hidden prompts and report the failures. Read it knowing that the comparison with SAEs is one learning rate, one seed and three models (THEORY-1005), that Gemma Scope found the reverse on Gemma 2 2B (NOTE-482), that attention patterns are frozen and QK circuits are not explained, and that its counts of case studies disagree between sections. |
| LIT-1578 v2 | Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models | Hase et al. (2023), arXiv:2301.04213, NeurIPS 2023. On 652 CounterFact facts GPT-J knows, the layer where causal tracing places a fact does not predict at which MLP layer an edit of that fact succeeds: regressing edit success on the edit layer explains most of its variance, and adding the tracing effect adds at most 3.2 points of R², across ROME, MEMIT, constrained fine-tuning and five editing problems, and again on GPT-2 XL, zsRE and representation zeroing. Only Fact Forcing, which edits on the same noised input tracing uses, shows a small reliable relation. | Active — read 2026-10-27 (NOTE-1194) in full, from the arXiv copy (v2, the NeurIPS 2023 version); worth reading as the direct test of whether causal tracing tells where to edit a fact: in GPT-J, fact by fact, it does not. The tracing effect at a layer adds at most 3.2 points of explained variance in edit success once the edit layer is known, and ROME’s rewrite score is above 96% at every layer but the last (THEORY-1024). Read it knowing that its own account of why, that tracing and editing answer different questions, is offered and not tested (THEORY-1026), that “where a fact is stored” means where causal tracing peaks, and that its Table 3 and Figure 6 disagree on one cell. |
| LIT-1579 v2 | Causal scrubbing: results on induction heads | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), Alignment Forum (Redwood Research). In a two-layer attention-only language model with two induction heads, the standard induction story (queries and values from the token embedding, keys from the previous-token head) recovers 35% of the loss the induction heads contribute on tokens where induction helps. Letting the heads match the last three tokens, read layer 0’s average effect, and treat three layer-0 heads that attend to copies of the current token as attending to itself raises it to 86%, and to 89% with a crude model of where the previous-token head deviates. | Active — read 2026-10-27 (NOTE-1196) in full, from the Alignment Forum’s own API; worth reading as the quantified test of the textbook induction circuit in a two-layer attention-only model, pathway by pathway, and for what the refinements found: three-token matching, layer-0 heads that attend to copies of the current token, and a previous-token head that deviates on quotes, articles and punctuation (THEORY-1020). Read it knowing that its percentages are of the 0.053 nats the induction heads contribute on a filtered token subset, not of a label-shuffled loss like the paren post’s, that its headline 89% is the bonus hypothesis and the main post’s 86% the fourth, and that the model is not published. |
| LIT-1580 v2 | Causal scrubbing: results on a paren balance checker | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), Alignment Forum (Redwood Research). Causal scrubbing applied to a three-layer, two-head bidirectional transformer that classifies parenthesis strings as balanced. The high-level hypothesis (two heads carry an equal-count-and-starts-open test, one head the horizon test) recovers 88–93% of the loss; making it specific about how the heads compute their tests brings it to 72%. Two still more specific hypotheses score higher than the one they refine, which the authors judge illegitimate. | Active — read 2026-10-27 (NOTE-1195) in full, from the Alignment Forum’s own API; worth reading as the worked case of causal scrubbing on a model whose algorithm is known, with the full table of hypotheses, their losses and standard errors, and for the authors’ own finding that two more specific hypotheses scored higher for reasons they judge illegitimate (THEORY-1029). Read it knowing that the model and the prior dissection are unpublished, that every number is one run of 2,000 scrubbed samples, and that its prose states the horizon test backwards in two places. |
| LIT-1581 v2 | Attribution Patching: Activation Patching At Industrial Scale | Nanda (2023), blog post, neelnanda.io. Introduces attribution patching: a first-order estimate of every activation-patching effect at once, the difference between clean and corrupted activations dotted with the metric’s gradient on the corrupted run, from two forward passes and one backward pass instead of one forward pass per patch. On the IOI task in GPT-2 Small it approximates head-level patches well and residual-stream and first-MLP patches badly. The author offers it as an exploratory heuristic for finding what to patch, not a replacement for patching. | Active — read 2026-10-27 (NOTE-1201) in full, from the author’s own page; worth reading as the origin of attribution patching, for its derivation of the estimate and the identities that make it cheap and additive (THEORY-1023), for the account of where a first-order estimate should fail (THEORY-1021), and for its framework of what patching can and cannot show: sufficiency against necessity, specific against general understanding, and parallel against serial redundancy. Read it knowing that the author calls it an incomplete project, that its empirical evidence is one task in GPT-2 Small shown only in plots and a notebook, and that the systematic test is Kramár et al. (LIT-1531). |
| LIT-1582 v2 | Mass-Editing Memory in a Transformer | Meng et al. (2022), arXiv:2210.07229, ICLR 2023. MEMIT inserts many facts at once by treating each MLP output matrix in a range of layers implicated by causal tracing as a linear associative memory, solving a least-squares update for the whole batch, and spreading each fact’s required change over those layers. On GPT-J it inserts 10,000 CounterFact counterfactuals with score 85.8, against 50.3 for ROME applied one fact at a time, and does likewise on GPT-NeoX (82.0) and for 10,000 true zsRE facts. | Active — read 2026-10-27 (NOTE-1197) in full, from the arXiv copy (v2, the ICLR 2023 version); worth reading as ROME’s extension from one edit to thousands, by a closed-form least-squares update spread over the range of MLP layers that causal tracing implicates, and for the scaling curves that show sequential single edits failing where it holds (THEORY-1031). Read it knowing that it inherits ROME’s storage reading (THEORY-1011) rather than testing it, that its layer range is chosen from traces averaged over facts, which Hase et al. (LIT-1578) show do not predict per fact where an edit works, and that its zsRE specificity hardly moves for any method. |
| LIT-1583 v2 | Causal scrubbing: Appendix | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt et al. (2022), Alignment Forum (Redwood Research). The technical appendix to causal scrubbing. It defines ”% loss recovered” against a label-shuffled baseline and argues against zero and mean ablation with three examples. It proves that the inputs the algorithm samples are the maximum-entropy distribution preserving the joint inputs of every interpretation node, shows how a superposed toy model is explained as monosemantic terms plus an unexplained interference term, and builds a false hypothesis that scores far above the model. It proposes, without solving, adversarial validation. | Active — read 2026-10-27 (NOTE-1202) in full, from the Alignment Forum’s own API; worth reading for the details the main post defers: the definition of the metric, the full case against zero and mean ablation, how unimportant inputs are grouped, a proof that the scrubbed inputs are the maximum-entropy distribution consistent with the hypothesis (THEORY-1025), how superposition is handled, and a second constructed false hypothesis that scores above the model. Read it knowing that its Lemma 1 says “product distribution” where its proof shows the joint, and that it says both results posts use a randomized-loss baseline when the induction post does not. |
| LIT-1630 v2 | Coarse-graining as a downward causation mechanism | Flack (2017), DOI-10.1098/rsta.2016.0338, Phil. Trans. R. Soc. A 375. Downward causation, made operational: components tune their behaviour to their own estimates of coarse-grained variables they collectively compute (“endogenous coarse-graining”). In the weak, apparent form one component tuning to a variable slower than the behaviour producing it suffices, and estimates may be wrong and disagree. In the strong, effective form the variable is predictive, robust, used nearly universally, agreed on, and gaining mutual information with the microscopic behaviour; that marks a new organizational level. The macaque power distribution, computed from subordination signals that coarse-grain fight outcomes, is the example, reviewed from earlier work. Time-scale separation lets an aggregate act as a “social” environment whether or not it is accurate. | Active — read in full 2026-10-27 (NOTE-1216); worth reading as the general, operational statement of Flack’s account: downward causation as components tuning to their own estimates of aggregate variables they collectively compute, in a weak (apparent) and a strong (effective) form, with a new organizational level only at the strong form. A conceptual paper; the macaque results are reviewed, not reported. Its criteria put convergence of estimates, not regeneration of the variable, beyond use. |
| LIT-1802 v3 | The Causal Information Bottleneck and Optimal Causal Variable Abstractions | Simoes, Dastani & van Ommen (2024; UAI 2025). The causal information bottleneck learns a stochastic abstraction T of discrete variables X by trading the information T keeps about X against Ic(Y | do(T)), the entropy reduction in a target Y when T is set by intervention under a uniform protocol over X. Intervening on T is defined as a mixture of interventions on X through Bayes inversion of the encoder, and is identifiable by a backdoor formula. At full weight on control the optimum is the partition of X by p(y | do(x)), Chalupka et al.’s causal macrovariables, which the ordinary bottleneck misses under confounding. Three toy SCMs confirm it. | Active — read in full 2026-10-29 (NOTE-1347) from arXiv v5; worth reading as an exact, small-scale statement of the difference between compressing for prediction and compressing for control: at full control the optimum is the partition of X by p(y | do(x)), which the ordinary bottleneck misses under confounding. Toy problems only. |
| LIT-1806 v2 | Causal Optimal Transport of Abstractions | Felekis et al. (2023; CLeaR 2024). COTA learns a stochastic map from a low-level causal model’s states to a high-level one’s, given both DAGs, the map between their interventions and samples of each paired interventional distribution, without the structural equations. It solves one entropic optimal-transport problem per intervention, with a cost that rewards states compatible with the same paired interventions and a term meant to impose do-calculus relations between the plans. As written that term depends only on the plans’ marginals, which the transport constraints fix, so it is constant on the feasible set. The reported gains over non-causal transport come from the compatibility cost, and reverse when the intervention set is small. | Active — read in full 2026-10-29 (NOTE-1342) from arXiv v1; worth reading as the first method to learn a causal abstraction map from paired interventional samples without the structural equations, and for what it shows unintentionally: its do-calculus term is constant on the feasible set as written, so its gains come from an intervention-compatibility cost. |
| LIT-1833 v2 | Multi-Level Cause-Effect Systems | Chalupka, Perona & Eberhardt (2015; AISTATS 2016). A micro cause I and micro effect J, both discrete and possibly huge, are confounded by a hidden H. The fundamental causal partition groups i by P(J | man(i)) and j by P(j | man(i)) across all i; its classes are the fundamental cause C and effect E, and do(C = c) is any manipulation into the class. E is claimed to be the minimal sufficient partition for P(J | man(i)), and (C, E) the coarsest pair that recovers it losslessly. The fundamental causal coarsening theorem extends the UAI 2015 one to the effect side: given the observational partitions, both causal partitions fail to coarsen them only on a null set. Subsidiary variables are coarsenings of (C, E) with unambiguous effects; two that do not interact compose into the fundamental partition. A simulated 100-neuron population responding to bars in images is recovered. No distribution over interventions is assumed. | Active — read 2026-10-29 (NOTE-1420) in full, from arXiv 1512.07942v1 with its supplementary material; worth reading as the source of the two-sided form of causal feature learning that the overview (LIT-1834) restates: the fundamental cause and effect are the partitions of micro causes by P(J | man(i)) and of micro effects by P(j | man(·)), learned jointly; the fundamental causal coarsening theorem says both generically coarsen the observational partitions; and the authors decline, “following Pearl”, to put any distribution on the interventions. Read it knowing that its one demonstration is a simulated neural population, built with the macro structure it recovers; that its claim that the effect partition is the minimal sufficient partition is wrong where two effect states have proportional but unequal columns (NOTE-1420); and that it compares itself with Hoel et al. 2013 in one sentence and computes nothing on their systems. |
| LIT-1834 v2 | Causal feature learning: an overview | Chalupka, Eberhardt & Perona (2016; Behaviormetrika 2017). A review of causal feature learning (CFL). Macro variables are partitions of a micro state space. The observational partition groups micro causes h with equal p(e | h); the causal partition groups those with equal p(e | man(h)), where man() sets the micro state without touching a confounder; effect states are grouped the same way by their columns. A macro intervention do(C = c) is a manipulation to any micro state in the class, which is unambiguous because all of them have the same effect. The causal coarsening theorem: among distributions with given causal and confounding partitions, the causal partition fails to coarsen the observational one only on a Lebesgue-null set, so the observational partition is learned from data and one experiment per observational class merges it into the causal one. A toy with confounded hue and skin conductance shows the steps; open problems are continuous macrovariables, cycles and learning without experiments. | Active — read 2026-10-29 (NOTE-1415) in full, from the publisher’s PDF as posted on Frederick Eberhardt’s Caltech publications page (https://www.its.caltech.edu/~fehardt/papers/CEP2017.pdf); worth reading as the plainest statement of causal feature learning: a macro cause is a class of micro states with the same P(effect | man(state)), a macro intervention is any micro manipulation into the class, and the causal coarsening theorem says that, except on a measure-zero set, the causal partition is a coarsening of the observational one, so one experiment per observational class finds it. Read it knowing that its example is a one-dimensional toy with four hue bands; that the theorem is a genericity result, not a test, and holds only for discrete macrovariables and an acyclic micro system; that the effect classes are defined by equal likelihoods while the merging step normalizes them; that two of its displayed equations carry slips (NOTE-1415); and that it gives no measure of how much causal information a coarsening keeps. |
| LIT-1838 v2 | Radically open dialectical behaviour therapy for refractory depression: the RefraMED RCT | Lynch et al. (2018), Efficacy and Mechanism Evaluation 5(7). The full report of the RefraMED trial (250 adults, RO DBT plus usual care against usual care): 5.40 HRSD points better at 7 months, not significantly better at the 12-month primary end-point (2.15) or at 18 months, and not cost-effective (£220,000 per QALY). Its mechanism analysis, using randomised non-therapeutic features as instruments for sessions, alliance and skills, failed: the instruments were weak and the decomposition implausible. All eight serious adverse reactions were in the RO DBT arm, which the authors put down to unequal reporting. | Active — read 2026-10-29 (NOTE-1421) in full, from the NIHR Journals Library’s own PDF (open access); worth reading as the full report of the RefraMED trial and the only place its mechanism analysis is given: a trial that randomised RO DBT participants to three non-therapeutic features (therapy room, written feedback, mode of reimbursement) and to therapists, to serve as instruments for exposure, alliance and skills. The instruments were weak (Cragg–Donald statistics at most 1) and, by the authors’ own account, the instrumented estimates mean nothing. Read it knowing that the analysed mediators are sessions attended, alliance and DBT skills, not the flexibility and emotional-coping measures, that the mediators and the outcome are both at 7 months, that the unadjusted decompositions put the indirect effect several times the total with a direct effect of the opposite sign, that the planned analyses of temporal order were not reported, that its process-measure intervals are about half as wide as the BJP paper’s for the same differences, and that its adverse-event test (one-tailed Fisher, p < 0.01) does not reproduce from its own counts. |
| LIT-1839 v2 | Causal Emergence: When Distortions in a Map Obscure the Territory | Eberhardt & Lee (2022), Philosophies 7, 30. A critique of Hoel’s 2017 account of causal emergence. Effective information is scored under a uniform intervention over the states at each level, and an intervention on a macro state is a uniform average of interventions on its micro states. Two numerical results follow. EI maximization merges micro states whose effects differ widely (in a 3×3 example, rows at absolute distance 0.8), so the macro variable has ambiguous manipulations in Spirtes and Scheines’s sense. And the EI-optimal abstraction of a two-step matrix is not the square of the one-step abstraction, so abstraction and marginalization over time do not commute. The authors trace both to the maximum-entropy distribution, “extraneous to the system”, and call causal capacity a normative, potential quantity. | Active — read 2026-10-29 (NOTE-1413) in full, from the publisher’s PDF as deposited in Caltech’s CaltechAUTHORS repository; worth reading as the published case that effective-information maximization, with a uniform intervention over macro states realized as a uniform average over their micro states, merges states with different effects (ambiguous manipulations) and picks levels that change with the time step (abstraction and marginalization do not commute). Read it knowing that its target is Hoel 2017, not Hoel, Albantakis and Tononi 2013; that its examples are numerical, found by a 0.1 grid search on 3×3 matrices; that it argues the uniform distribution is extraneous but never computes what happens when one micro distribution is used at both levels; that its commutativity example is a partition that is strongly lumpable, so the coarse-graining commutes and only the EI-optimal choice does not; and that its 8-state ambiguity example is unambiguous with respect to the macro effect it is scored on. |
| LIT-1843 v2 | Causal emergence is widespread across measures of causation | Comolatti & Hoel (arXiv 2022). Twelve measures of causal strength from philosophy, statistics and psychology are written in terms of sufficiency P(e | c) and necessity 1 − P(e | C\c), or of Hoel’s determinism and degeneracy; several turn out to be the same measure (Pearl’s PNS, PN and PS are Eells’s, Lewis’s and Cheng’s). Each needs an intervention distribution P(C): observational (stationary), maximum entropy, or a local Hamming ball. On one 16-state bipartite Markov chain, whose two-state macro is a deterministic NOT gate, every measure shows causal emergence for some transitions and parameters; the system-level effective information under the stationary distribution does not, which the paper says was known. | Active — read 2026-10-29 (NOTE-1416) in full, from arXiv’s v1; worth reading as the defenders’ survey that rewrites a dozen measures of causal strength (Eells, Suppes, Cheng, Lewis, Pearl’s PN/PS/PNS, Galton, bit-flip, effect information, EI) as functions of sufficiency P(e | c) and necessity 1 − P(e | C\c), and that reports causal emergence for every measure on one bipartite Markov chain under maximum-entropy, stationary and local intervention distributions. Read it knowing that the model is built so its macro is a deterministic NOT gate whatever the micro noise; that in its symmetric version the macro distributions are the images of the micro ones, so it is a common-distribution test, and there the system-level EI cannot show emergence under either the stationary or the maximum-entropy distribution (data processing; the record’s computation agrees), which the paper concedes only for the stationary case; that “we prove” in the abstract covers rewritings of definitions, not a theorem that emergence must occur; and that the per-transition and normalized measures that do show emergence are not bounded by data processing. It does not meet THEORY-787’s promote_when. |
| LIT-1924 | Horizontal Surgicality and Mechanistic Constitution | Baumgartner, Casini & Krickel (2020). Since phenomena can be manipulated only via common causes of them and their parts, constitution must be analysed with non-ideal interventions; counting every supervenience-respecting common cause as an intervention begs the question, and admitting every common cause is a non-starter. An intervention that directly changes at most one behaviour on each lower level, and changes its target and the phenomenon simultaneously, is “horizontally surgical”; under Universal Constitution, Simultaneity and transitivity of co-occurrence, one such intervention suffices for constitution. The proof presupposes settled parthood and levels. | Active — read in full 2026-11-01 (NOTE-1494) from the authors’ penultimate draft; worth keeping as the one positive interventionist result in the debate: given that every change in a phenomenon is simultaneously realized on every lower level, that simultaneous changes are not causally related, and that parthood and levels are settled, a single intervention that changes one part per level and the phenomenon simultaneously suffices for constitution (THEORY-1293). |
| LIT-1925 | Saving the mutual manipulability account of constitutive relevance | Krickel (2018), DOI-10.1016/j.shpsa.2018.01.003. By the descriptions available, a defence of mutual manipulability against the charge that an interventionist criterion cannot define a non-causal relation: manipulability is read as a causal relation between a component and a temporal part of the phenomenon, which is represented by several variables for its phases. Unread; her co-authored 2020 paper reports the move in one sentence (NOTE-1494). | Unfetched — A lawful free copy was located 2026-11-01 and could not be fetched: the author’s final draft on PhilArchive, https://philarchive.org/archive/KRISTM-3 (also listed at https://philpapers.org/archive/KRISTM-3.pdf). Both returned HTTP 403 to this client; CORE’s copy (core.ac.uk/download/131213192.pdf) returned a Cloudflare challenge, and the Wayback capture (20240802095749) reset the connection. Neither challenge was pursued. The Elsevier version is paywalled. Free copy: https://philarchive.org/archive/KRISTM-3. |
| LIT-1928 | Top-down causation without top-down causes | Craver & Bechtel (2007; online 2006). Talk of top-down or bottom-up causation within levels of mechanisms can be translated “without remainder” into mechanistically mediated effects: intralevel causal chains combined with the constitutive relation between a mechanism and its components. Interlevel relations are constitutive only. The case rests on stated assumptions (higher-level causes exist and are all mechanistically explained), not on an argument for them. It concedes that the interlevel experiments used to find components are symmetrical and give only prima facie evidence of componency. | Active — read in full 2026-11-01 (NOTE-1491); worth keeping as the mechanist’s statement that the relation between levels is constitution, not causation, and for an admission the record needs. Interlevel experiments are symmetrical, and a lesion shows only “prima facie” that something is a component, since a part not “interactively integrated” may be a background condition (p. 553, n. 10). So the experiments do not by themselves draw the mechanism’s boundary (THEORY-1287, CLAIM-530). |
| LIT-1929 | Three Problems for the Mutual Manipulability Account of Constitutive Relevance in Mechanisms | Leuridan (2012), DOI-10.1093/bjps/axr036. By its abstract, two conceptual problems for Craver’s mutual manipulability account (constitutive relevance threatens to imply causal relevance; parthood as spatiotemporal inclusion meets a counterexample from endosymbiosis) and one methodological one (experimental underdetermination). Unread: no lawful copy reached. The works read with it report that it argues, under Woodward’s interventionism, that constitutive relevance is a form of bidirectional causal relevance. | Unavailable — Sought 2026-11-01 and not reached. The publisher’s copy (OUP, doi 10.1093/bjps/axr036) is paywalled. The one repository copy OpenAlex lists, Ghent University’s Biblio (record 2116239, file 6770914), is marked “restricted” in Biblio’s own metadata and redirected this client to an institutional sign-in, so it is not a free copy. No PhilSci-Archive or PhilArchive deposit was found. Known here only from its abstract and from what the three works read with it say of it (NOTE-1493, NOTE-1490, NOTE-1494). It stays Unavailable until a copy is supplied, not on merit. |
| LIT-1930 | Constitutive Explanatory Relevance | Craver (2007), DOI-10.5840/jpr20073241. The paper in which, by its successors’ account, Craver named constitutive relevance: what makes a component’s activity relevant to the behaviour of the mechanism it is part of, analysed as mutual manipulability between the two. Unread: no lawful copy was reached. What it is said to hold is from the abstract and from Craver, Glennan and Povich (2021), not from the text. | Unavailable — searched 2026-11-01 for a lawful full text and none reached, so it is not read and no NOTE is filed. OpenAlex reports it closed with no repository copy. The publisher, the Philosophy Documentation Center (pdcnet.org, record jpr_2007_0032_0003_0020), offers it for purchase only. Craver’s Washington University CV (philosophy.wustl.edu/media/1028/download) lists it without a link, his WashU research profile has no file, and searches of PhilArchive, PhilSci-Archive and the web found no author copy. It is not on Bechtel’s UCSD page, which hosts two other papers from this batch. It stays Unavailable until a copy is supplied, not on merit. |
| LIT-1931 | Constitutive relevance & mutual manipulability revisited | Craver, Glennan & Povich (2021), DOI-10.1007/s11229-021-03183-8. A reply to critics who say mutual manipulability (MM) conflates causation with constitution (Baumgartner and Gebharter 2016; Baumgartner and Casini 2017). It separates the semantic, epistemic and metaphysical questions of constitutive relevance, amends MM into an epistemic criterion, “matched interlevel experiments” (MIE), and grounds it in the thesis that constitutive relevance is causal betweenness. Unread: a free preprint is on PhilArchive behind a bot check. | Unfetched — searched 2026-11-01. The Springer article is paywalled (the page offers “Buy article PDF”; the PDF link returned the paywall page). OpenAlex lists an author-deposited preprint at PhilArchive, https://philarchive.org/archive/CRACRA-3 (record philarchive.org/rec/CRACRA-3), and a search engine reported it as the full text, “forthcoming in Synthese”, 10,558 words. It returned a Cloudflare “Just a moment…” challenge (403) to curl on 2026-11-01, on philarchive.org and on dc2.philarchive.org, and WebFetch got a 403; the challenge was not attempted. Butler University’s repository (digitalcommons.butler.edu/facsch_papers/1201) holds metadata only, and Glennan’s bepress page now redirects to a retirement notice. Free copy: https://philarchive.org/archive/CRACRA-3. |
| LIT-1933 | Why there isn’t inter-level causation in mechanisms | Romero (2015), DOI-10.1007/s11229-015-0718-0. By the descriptions available, it argues that mutual manipulability, Woodward’s interventionism and the denial of inter-level causation look like an inconsistent triad, and dissolves it by treating interventions on a mechanism’s levels as fat-handed: inter-level relations are explained without inter-level causation. Unread; Baumgartner & Casini and Baumgartner, Casini & Krickel cite it for the result that interventions on phenomena are necessarily fat-handed. | Unfetched — A lawful free copy was located 2026-11-01 and could not be fetched: the author’s accepted version on PhilSci-Archive, https://philsci-archive.pitt.edu/12956/1/fr_interlevelmechanisms_final.pdf. The server’s certificate chain ends in a root this client does not trust (TLS “unable to get local issuer certificate”), a second fetcher got HTTP 503, the Wayback capture (20240603160454) reset the connection, and CORE’s copy (core.ac.uk/download/157867512.pdf) returned a Cloudflare challenge, which was not pursued. The Springer version is paywalled. Free copy: https://philsci-archive.pitt.edu/12956/1/fr_interlevelmechanisms_final.pdf. |
| LIT-1934 | Constitutive Relevance, Mutual Manipulability, and Fat-Handedness | Baumgartner & Gebharter (2016). Embedded in Woodward’s 2003 interventionism, Craver’s mutual manipulability entails that no part is constitutively relevant to any whole, since every cause of a supervening behaviour is a common cause of it and of its base and so not an intervention; embedded in Woodward’s relaxed version it makes constitution causal; with a temporal clause added (causes precede effects for some intervention) it is consistent, but then mutual manipulation is fat-handed and its correlations are equally explained by a model with no constitution. Constitution gets only second-order, abductive evidence: no surgical cause of the whole is ever found. | Active — read in full 2026-11-01 (NOTE-1493) from the authors’ penultimate draft; worth keeping as the proof that, if constitution is non-causal and wholes supervene on their parts, every cause of a whole’s behaviour is a common cause of it and of some part’s, so mutual manipulability by ideal interventions is unsatisfiable and, once relaxed, gives no evidence of constitution (THEORY-1288). |
| LIT-1938 | Mutual manipulability and causal inbetweenness | Harinen (2018), DOI-10.1007/s11229-014-0564-5. By the descriptions available, mechanistic models contain non-causal relations beside causal ones, so the standard ideal intervention is the wrong notion for mutual manipulability, and an extended interventionism is proposed. Unread; Baumgartner & Casini answer it (their footnote 8) that relaxing interventions so deprives interventions on mechanisms of their inferential value. | Unfetched — A lawful free copy was located 2026-11-01 and could not be fetched: the author’s preprint on PhilSci-Archive, https://philsci-archive.pitt.edu/11083/5/Mutual_Manipulability_and_Causal_Inbetweenness.pdf. The server’s certificate chain ends in a root this client does not trust, a second fetcher got HTTP 503, the Wayback capture (20240604111239) reset the connection, and CORE’s copy (core.ac.uk/download/33752704.pdf) returned a Cloudflare challenge, which was not pursued. The Springer version is paywalled. Free copy: https://philsci-archive.pitt.edu/11083/5/Mutual_Manipulability_and_Causal_Inbetweenness.pdf. |
| LIT-1939 | An Abductive Theory of Constitution | Baumgartner & Casini (2017). Craver’s mutual manipulability ties constitution to ideal interventions that cannot exist, and relaxing them leaves only fat-handed ones, whose data a pure common-cause model fits as well as a constitutive one even in ideal settings, so constitution, unlike causation, has no crucial experiment. Their No De-Coupling account: a set of parts constitutes a phenomenon when every cause of the phenomenon is a common cause of it and some member, no proper subset does as much, and no expansion of the variable set breaks the coupling. The inference is abductive and only inductively corroborated. | Active — read in full 2026-11-01 (NOTE-1490) from the authors’ penultimate draft; worth keeping for the claim that, unlike causation, constitution has no experimentum crucis, and for its alternative: constitution is inferred abductively from a redundancy-free common-cause coupling of whole and parts that no expansion of the variable set breaks (THEORY-1288, THEORY-1294). |