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).
84 of 1352 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-058 v2 | Mental disorders are maintained by self-reinforcing causal loops rather than expressing a latent common cause, which is how they can outlast their triggers | Three traditions that do not cite one another for it put self-sustaining loops where a latent cause would be. Borsboom (LIT-547) makes disorder an alternative stable state of a strongly connected symptom network, kept up by hysteresis after its trigger has gone. Salkovskis, Sighvatsson and Sigurdsson (LIT-538) make it a threat meaning protected by the behaviour it drives. Kendler (LIT-539) finds causal loops across levels, from genes to culture. The convergence is real; the evidence is indirect, simulated or clinical, and none of it is an individual time series showing hysteresis, so the account is Proposed. It says nothing about what starts a disorder. | Proposed |
| THEORY-133 v2 | In List and Menzies’s account of causes as difference-makers, a higher-level property that makes a difference to an effect is its cause, and its realizer is not, exactly when in some nearest situation without that realizer the property is realized differently and the effect still occurs; which holds depends on each causal system’s counterfactual structure, not on levels a priori | List & Menzies (2009), LIT-722. Take causes to be difference-makers. Then Kim’s exclusion principle fails, and a revised one holds or fails system by system. Given that a higher-level property makes a difference to an effect, its realizer is not a cause exactly when some nearest situation without the realizer has the property realized otherwise and the effect present; the record re-derived this. The claim that higher-level relations are typically insensitive to their realizers is an observation about scientific practice, and Pernu disputes the paper’s main example. Which systems meet the condition is QUESTION-213. | Active |
| THEORY-138 | X is a cause of Y exactly when some intervention on X with respect to Y would change Y, where an intervention is an exogenous causal process that alone sets X (M1), affects Y only through X (M2), is not caused by anything that affects Y by another route (M3), and leaves Y’s causes off the path through X unchanged (M4); so defined, causation is not reduced to non-causal facts but is not viciously circular, and needs no human agent | Woodward, “Causation and Manipulability” (SEP, 2001; revised 2023), LIT-713. A cause is what changes the effect under a surgical, exogenous intervention, defined relative to the effect by M1–M4. The account separates total from direct causes by combining interventions, and treats natural experiments as interventions. Active as the standard the record uses for what a causal claim asserts. This statement says nothing about invariance, proportionality or levels. | Active |
| THEORY-171 v3 | When the causal constraints on events depend on context, deterministic assignments that are causal in each context can fail to glue into one causal assignment, so causal structure is itself a source of contextuality | From Gogioso & Pinzani’s trilogy: The Topology of Causality, LIT-808, read in NOTE-612, with the definitions of The Combinatorics of Causality, LIT-800 (NOTE-635). Over a space of input histories with the lowerset topology, causal functions form a separated presheaf, and on the space Θ₃ it is not a sheaf: two causal assignments on disjoint opens give one event two outputs on their common extension. That example was checked here, and it settles the claim. The source’s Theorem 2.34, that the presheaf is a sheaf exactly when no two contexts impose incompatible causal pasts on a common event, is reported as the source’s. Its proof was not read, and it is QUESTION-143. It does not say any physical or quantum data display the effect. | Active |
| THEORY-177 v2 | In a binary cyclic system, the Contextuality-by-Default measure of signalling is twice the sum, over contents, of the least direct influence of context that a canonical causal model of the data must place on each content, and each content’s least influence is the total-variation distance between its two marginals | Wang, Sadrzadeh, Abramsky & Cervantes (2021), LIT-851, Proposition 1. It joins CbD’s maximal couplings (LIT-777, Theorem 3.3) to Jones’s 2019 correspondence between couplings and canonical models, which the paper quotes and the record derives independently. The result measures signalling. Its minima are per content, each reached in its own model; one model reaches them all only if the system is noncontextual. It says nothing about contextuality beyond the bound that a rank-2 system with Δ ≥ 2 cannot be contextual, and identifies no particular causal model. | Active |
| THEORY-222 v5 | With uniform interventions imposed separately at each level, a coarse-grained macro description of a known discrete mechanism can have more effective information than the micro description it supervenes on, so the level at which effective information is highest can be a macro level | Hoel, Albantakis & Tononi (2013), LIT-1038, read in NOTE-726. Effective information is effectiveness (determinism minus degeneracy) times the log of the state-space size, measured under uniform interventions. Coarse-graining always loses size and can gain effectiveness; when the gain wins, causal emergence CE = EI(macro) − EI(micro) is positive. Four toy systems give 0.40 to 2.92 bits. The arithmetic is exact. The reading that the EI peak marks where causation happens rests on imposing a uniform distribution at each level, which the paper adopts and does not test; the title does not claim it. Promoted on 2026-10-20 on a construction. Whether the gain survives one intervention distribution at both levels is QUESTION-204. | Active |
| THEORY-231 v3 | Within classical realism, a generalized-noncontextuality no-go refutes Leibnizian representations, not realist representations as such; it rests on a stronger assumption than a Bell-like no-go and so applies where none exists, as in prepare-measure scenarios, but only Leibnizianity implying noncontextuality is proved | Schmid, Selby and Spekkens (2020), LIT-945, §VI.C, §VIII (Eqs. 200, 214, 215), read in part in NOTE-737, which is Skimmed: §§II–IV and the proofs in Appendices C–G were not read. A Leibnizian classical realist representation implies a generalized-noncontextual one, so every noncontextuality no-go is a no-go for Leibnizian representations. The converse is Conjecture 1′, so a Leibnizianity failure is not shown to be a noncontextuality failure. The prepare-measure claim is stated, not derived, in the text read. | Active |
| THEORY-243 v3 | In the three-unit identity network x ↦ x(1, 0, 1) ↦ (0, 2, 1)·h, aligning the input with the third unit and aligning it with the direction (h₁ + h₂)/√2, two alignments related by an orthogonal change of basis, pass every interchange intervention on the input equally, so interchange interventions on that variable alone do not fix which internal direction mediates it | Wu et al. (2024), LIT-961, Appendix A, and Makelov et al. (2023), LIT-968, Appendix A.3 and §8, read in NOTE-809 and NOTE-782. Both rotate the same three-unit identity network. The input aligns with h₃ in one basis and with (h₁ + h₂)/√2 in the other, equally well under interchange interventions on the input (re-derived 2026-10-20). The reply says intervening on further variables separates them; that was not checked. Makelov et al. rest their verdict on component boundaries; the reply rests its on the interventions performed. Shown exactly for one constructed network only; whether trained networks have such ties is open (QUESTION-234). | Active |
| THEORY-275 v5 | In two optically trapped beads with a symmetric hydrodynamic coupling, one trap moved by a recorded noise drive, time-delayed mutual information and transfer entropy follow the drive’s path rather than the coupling’s symmetry: the flow between the beads reads two-way under moderate drive, in experiment and numerics, and one-way under strong drive, in numerics of the fitted model only | Das, Manikandan and Banerjee (2025), LIT-947, read in NOTE-788. Two colloids are coupled by the fluid through a symmetric tensor, and recorded noise moves one trap. Time-delayed mutual information and transfer entropy give drive → driven → other, with backflow at moderate drive. In numerics only, flow is one-way at strong drive. With no drive the coupled particles are independent at steady state. The paper does not test an unrecorded drive shared by both units, and it does not claim that the measures reveal coupling architecture. Whether the same holds in other reciprocally coupled systems is QUESTION-186. | Active |
| THEORY-282 v2 | A subspace intervention can reproduce the output effect of changing a variable without localizing it, by pairing a direction that varies with the variable but cannot reach the output with one that can reach the output but does not vary on the data | Makelov, Lange and Nanda (2023), LIT-968, read in NOTE-782. Proved for the construction (§3.2, Lemma A.1); shown in GPT-2 Small’s MLP8 on IOI (46.7% FLDD, falling to 13.5% without the null-space component, 4.2% interchange accuracy) and in GPT2-XL MLPs on factual recall, where a residual-stream direction passes the same test. It does not say that subspace patching is unreliable in general, nor that a found direction with a null-space component is spurious: in a one-dimensional readout the test passes both kinds. The reply (LIT-961) contests the label, not the measurements. | Active |
| THEORY-287 | Internal variables located by interchange intervention as mediating a language model’s in-distribution behaviour predict whether its outputs stay correct under shifts that keep the task’s mechanism better than output confidence or probes of the rest of the representation | Huang, Tao, Icard, Yang and Potts (2025), LIT-987, read in NOTE-765. In Llama-3-8B-Instruct over five tasks and ten shifts, counterfactual simulation is best 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. It does not say that the located variables are constitutive, that causal features always win, or anything about shifts that change the mechanism. | Proposed |
| THEORY-410 | Brain–computer interface decoding does not show intentions to be causes distinct from their neural realisers: what is many-to-one realised there is a coarse cortical variable over single-neuron patterns, and each intention matches one value of it, so under proportional difference-making the evidence fits identifying the intention with that variable | Pernu (2018), LIT-147, read in NOTE-091. A conceptual argument that turns on an empirical premise the paper asserts and does not examine: that each intention corresponds to one ensemble-average firing value. Real decoders are not simple averages, and whether the mapping holds across sessions or subjects is not checked. It is scoped by its own footnote 1 to difference-making with proportionality. | Proposed |
| THEORY-419 v2 | In a structural causal model of autonomous equations, with intervention do(X = x) defined, as Pearl defines it, as a surgery that deletes X’s own equation, sets X to x and solves the rest, and with observing X = x violating no equation and amounting to ordinary conditioning, models that agree on every observational distribution can disagree on the effect of an intervention, and in a structural equation y = βx + ε the coefficient β is the rate of change of E[Y | do(x)], which equals the regression slope of Y on X only when X is uncorrelated with ε | Pearl (2009), LIT-894, skimmed in NOTE-696 from four excerpts the author posts: the contents, the second-edition preface, §§5.3.2–5.4.1 and the Epilogue, 46 of some 480 pages. The account is well established and the excerpts state it in full; Proposed because it rests on a skim. The surgery needs autonomous equations and a diagram saying which equation belongs to which variable. The excerpts state the three rules of the do-calculus without derivation, and contain no three-level hierarchy of association, intervention and counterfactual. | Active |
| THEORY-424 v2 | Mutual-information measures of individuality that read a system’s next state off its present one measure association, not propagation: I(S_{t+1}; S_t) can be positive when the environment alone drives the system, and conditioning on the environment does not recover the interventional quantity, which can be zero where the conditional measure is one bit | Bourrat (2024), LIT-005, read in NOTE-027, against Krakauer et al.’s (2020) measures. A* = I(S_{t+1}; S_t) is confounded when the environment is a common cause (his Fig. 2), and his interventional  = I(S_{t+1}; Ŝ_t) is zero there. His claim that  equals Krakauer’s conditional A = I(S_{t+1}; S_t | E_t) is false in general: NOTE-027’s XOR system has A = 1 bit and  = 0.  itself depends on an intervention distribution the paper leaves open, and neither it nor the paper’s two ETI criteria is computed on any system. | Active |
| THEORY-446 | Organism–environment reciprocal causation, taken diachronically, unrolls into an acyclic sequence of organism, environment and experienced-environment states joined by interventionist arrows; on that representation each niche-construction type has a characteristic causal pattern, and multi-species cases come apart only if organism and environment are kept distinct | Baedke, Fábregas-Tejeda & Prieto (2021), LIT-110, read in NOTE-111. A conceptual and visual model, worked by example for each type of niche construction and for two multi-species cases. There is no formal semantics, no completeness result and no empirical test; formalization is deferred. It sets synchronic co-constitution aside rather than refuting it, and the claim that the boundary is an “epistemic necessity” is stronger than the argument, which shows only that the model can draw one usefully. | Proposed |
| THEORY-451 | A singular causal claim, that C will contribute or did contribute to E in a particular setting, is warranted only by joint evidence on each step of the causal process there, its causal principle, its support factors and the absence of its derailers, which no single method supplies; a well-run RCT secures at most the study population’s average effect, and often not even that rigorously, and its result is not by its method evidence about any other population | Cartwright (2021), LIT-213, read in NOTE-161. The point that RCT results are not by the method evidence about another population (save under random sampling from it) is strong and standard. That no method or handful of methods can warrant a singular claim is argued from the diversity of facts a causal-process theory of change needs, with one illustrative case. That such theories yield reliable predictions is asserted, with no track record; the paper gives no method for weighing the evidence and little on transport. The critique of RCT rigour is internal to the author’s own reconstruction of “rigour”. | Proposed |
| THEORY-485 | Wave-function realism falsifies causal closure restricted to spacetime but is compatible with closure relative to fundamental physics, so quantum ontology opens no causal gap for non-physical causes; what it forces on the physicalist is a criterion of the physical and a bridge from dynamical to causal completeness | Poltorak (2026), LIT-164, an unrefereed preprint read in full in NOTE-112. “Every physical effect has a sufficient physical cause” has two tacit parameters, a domain and a completeness relation. With the domain set to spacetime the principle fails under wave-function realism; with it set to the ontology of a complete fundamental theory it survives. The move to a breach needs a premise that wave-function realists deny. The conclusions are modest and close to analytic once the terms are defined. The target is conceded to be a picture, not a published argument, and the dynamical-to-causal bridge is asserted, not argued. | Proposed |
| THEORY-491 | Of the five standard arguments that randomisation gives a clinical trial special evidential weight, only the selection-bias argument is sound, and it supports only taking allocation out of the experimenters’ hands; given balance on plausible confounders, a placebo or active control and blinding, randomisation is argued to add nothing, since balance on unknown confounders is not even probable in the one division a trial makes | Worrall (2007), LIT-175, read in NOTE-126. The case against the unknown-confounders argument is conceptual: frequentist balance is a long-run claim about repeated divisions, and a trial divides once. It does not show that randomised designs are no more reliable in practice than matched ones, and the meta-research cited is mixed. The selection-bias argument is conceded as “cast-iron”, so the account does not say randomisation is worthless. Haphazard allocation is asserted to serve as well, without discussing whether such rules are predictable. | Proposed |
| THEORY-497 v3 | A macro feature can supervene on a system’s present state and still carry information about its future that no small set of parts carries, because supervenience is instantaneous and prediction runs across time; on the integrated-information-decomposition account a system can host such a feature of order k exactly when its dynamics carry k-th-order synergy about their own future, relative to a fixed partition into parts and a chosen redundancy function | Mediano et al. (2022), LIT-025, read in NOTE-010, a review of Rosas et al. (2020), which the record does not hold. A feature V_t is causally emergent of order k iff Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0, and a system has one iff Syn⁽ᵏ⁾(X_t; X_t′) > 0, split as downward causation plus causal decoupling. The review proves none of this and names no redundancy function. The quantities change with the partition, which the review calls intended, and they are predictive, not interventional, unless p(X′ | X) is a do()-distribution. | Proposed |
| THEORY-527 v5 | If agents are the systems that would adapt their policy were their actions to affect the world differently, then in mechanised causal games meeting Kenton et al.’s five assumptions (one agent per connected component of the decision–utility graph, best response to every mechanism intervention, a fixed tie-breaking order, terminal edges only into decision mechanisms, and mechanism interventions able to set any deterministic function) the game graph, with its decisions, utilities and agents, is recovered exactly from interventions on mechanisms | Kenton, Kumar, Farquhar, Richens, MacDermott & Everitt (2022), LIT-909, read in NOTE-707. The recovery result (Theorem 1) is proved under five assumptions, including the availability of interventions on mechanisms, and was re-derived on promotion (2026-10-20). The definition is a proposal; the verdicts on thermostats and RL are argued from it, and “reliably classifies humans as agents” is asserted. The labels depend on the chosen variables, which the paper states. | Active |
| THEORY-580 v2 | On any cover of a space of input histories, the empirical models compatible with a causal structure are exactly the points of a polytope cut from a product of simplices by linear causality equations, so how much of a model a causal structure can explain is a linear program; causal separability is relative to an assumed ambient structure, and the causally separable fraction is never less than the separable local fraction | Gogioso and Pinzani (2023), LIT-788, skimmed in NOTE-624, with the proofs of the causaltope theorems (2.18, 2.19, 2.25) and of the lower bound (2.29) read and checked on promotion (2026-10-20), against the definitions they take from The Topology of Causality. The proofs are short because the work is in the definitions; the one step left implicit closes. The quantum switches witness indefinite order only relative to an ambient space with known no-signalling constraints, not absolutely. | Active |
| THEORY-612 | Natural selection cannot be both a cause and an effect of a process such as niche construction: if selection is an emergent population-level process, niche construction partly composes it, and a whole and its parts are not independently fixable and so not causally related; if selection is not emergent, it is either no cause at all or incoherently individual-level. Niche construction can still cause the product of selection | Hazelwood (2023), LIT-156, read in full in NOTE-137. A dilemma against strong reciprocal causation in the extended evolutionary synthesis, aimed at Laland and colleagues. Emergence is Wilson’s synchronic dependence plus autonomy, cashed out as composition; causation is Woodward’s interventionism with independent fixability. Its force rests on a process/product split for selection and a compositional reading of realization, both defended by citation and flagged as contestable, and its second horn considers only two non-emergent options. The weak sense, that organisms and environments affect each other, is granted as unobjectionable. | Proposed |
| THEORY-674 v2 | In Garg and Fetzer’s GPT-4o-mini extraction from NBER and CEPR working papers, edges kept in at least 4 of 9 passes and never checked against human labels, the mean per-paper share of edges labelled as backed by difference-in-differences, instrumental variables, an RCT, regression discontinuity or synthetic control rose from 7.7% in 1990 to 31.7% in 2020, at every overlap threshold; the paper’s per-decade slope fell from +0.0187 to +0.0011 once method mix and graph volume were controlled | Garg & Fetzer (2024; arXiv v2 2026), LIT-079, read in full in NOTE-083. GPT-4o-mini, nine passes per paper over the first 30 pages of 44,852 working papers, edges kept in at least 4 of 9 passes. The direction of the trend holds across overlap thresholds, its level does not (mean causal share 0.152 at EO = 1, 0.270 at EO = 9), and it nearly vanishes once method mix and graph volume are controlled. Validation covers paper-level method labels only, with RCT precision about 0.02. The association of causal structure with top-five publication rests on year-fixed-effect regressions over different subsamples and is not part of this claim. Promoted 2026-10-20 on the measurement alone (ADR-047 v3); the economics claim is held as THEORY-824. | Active |
| THEORY-700 | For jointly Gaussian stationary processes, Granger causality in Geweke’s generalized-variance form is exactly twice the transfer entropy, conditional and multivariate, at the regressions’ lags, because least-squares residual covariance is the partial covariance and a Gaussian’s conditional entropy is half its log-determinant plus a constant | Barnett, Barrett & Seth (2009), LIT-1171, read in full in NOTE-934. F_{Y→X|Z} = 2T_{Y→X|Z}, exactly, for population quantities. The proof is two identities and was checked. Sample agreement depends on the entropy estimator. Both quantities are predictive; the authors keep them apart from physical causation. | Active |
| THEORY-701 | Transfer entropy from J to I is the Kullback entropy of assuming that I’s next state, given its last k states, does not depend on J’s last l states, so it is zero exactly when J’s past leaves I’s transition law unchanged; unlike time-delayed mutual information it is directional and zero for static correlation, and it removes a common input only when that input is conditioned on | Schreiber (2000), LIT-1177, read in full in NOTE-940. The definition and its zero condition are exact. The comparison with delayed mutual information rests on two coupled-map lattices built with a known direction. The continuum-limit claim is asserted. The Letter’s tent-map coefficient appears to be twice what Eq. 4 gives. | Active |
| THEORY-703 | Weak emergence of a macro variable from micro variables can be measured as its Granger autonomy from them times their mean Granger causation of it, which is zero if it is independent of them or fully predicted by them; in a boids model this measure, and Granger causation from the flock’s centre of mass to each boid, are higher for flocking than for random or rigid motion; the measure is relative to the regression model and the variables included | Seth (2010), LIT-1170, read in full in NOTE-935. The definitions are exact; the evidence is two hand-built agent-based models. Seth concedes that the measure is epistemic: positive with missing micro factors or a limited predictor, zero with the system as predictor. Proposed until it is tested against an independent criterion. | Proposed |
| THEORY-704 | In a stationary multivariate time series whose components include every relevant process, with interventions that are isolated exogenous changes and no instantaneous causation, a missing Granger-causal edge from a to b means intervening on a has no effect on b at the next step, non-ancestry means no effect at any horizon, and a set whose observed past blocks every back-door path into b’s ancestors identifies the effect from observational data, as a multi-step linear-predictor coefficient in the Gaussian case | Eichler & Didelez (2007), LIT-1164, read in full in NOTE-941. The back-door results are proved; the edge-to-effect statements in the conclusion are said to follow by the same reasoning; the front-door proof is deferred. All conditions are sufficient, and Assumption 2.3 is untestable from observational data. Two worked effects were checked. | Active |
| THEORY-707 | Transfer entropy is not a measure of information flow, if flow means information in the target attributable solely to the source’s past: as a conditional mutual information it equals the source’s unique information plus its synergy with the target’s past, so it can credit a full bit to a source that carries none alone (Y_t = X_{t−1} ⊕ Y_{t−1}) and report zero from each of two sources that jointly fix the target (Z_t = X_{t−1} ⊕ Y_{t−1}); conditioning on further series, as causation entropy does, has the same fault | James, Barnett & Crutchfield (2016), LIT-1165, read in full in NOTE-945. Both examples are exact and were recomputed. The decomposition holds for any PID satisfying the consistency equations. The conclusion is relative to the authors’ definition of flow; transfer entropy as predictive improvement is untouched. The claims about directed information, interventional flow and Gaussian systems are cited or conjectured. | Active |
| THEORY-710 | In a finite causal Bayesian network, a set of nodes is causally independent of another, imposing a third, for every choice of mechanisms exactly when every directed path between them passes through the third; information flow, conditional mutual information computed from interventional instead of observational distributions, vanishes under causal independence, and it can differ from transfer entropy and conditional mutual information in either direction | Ay & Polani (2008), LIT-1174, read in full in NOTE-946 from the 2006 preprint. Theorem 2 and Prop. 3 are proved; Examples 3–6 were recomputed. Example 6’s one bit holds at k = 1 and fails for k ≥ 2 as stated. The measure needs the mechanisms, and estimation and identification are not addressed. | Active |
| THEORY-711 | Directed information from an input sequence to an output sequence, the sum over time of the information the inputs up to now carry about the current output given the past outputs, is at most their mutual information and equal to it when the channel is used without feedback; in a causal system it bounds what the output reveals about the source, so feedback cannot raise a memoryless channel’s capacity; and the usual definition of a memoryless channel holds only without feedback | Massey (1990), LIT-1166, read in full in NOTE-939 from the author’s preprint. Three short theorems, all checked; the feedback inequality also checked numerically. “Causal” is Massey’s factorization condition, not intervention. That directed information is full-history transfer entropy plus instantaneous terms is the record’s derivation. | Active |
| THEORY-764 | For a deterministic supervenient feature V of a Markov system, Rosas et al.’s practical emergence criterion Ψ equals the parts’ whole-minus-sum information about V’s next value minus V’s one-step dynamical dependence I(V_t′; X_t | V_t), so dynamical independence raises Ψ but neither implies emergence nor is implied by it, and the paper’s sufficient test for causal decoupling can pass a feature that is not dynamically independent | Rosas et al. (2020), LIT-1244, read in NOTE-987, with Barnett and Seth’s dynamical independence (LIT-979, THEORY-257). By the chain rule, Ψ(V) = [I(X_t;V_t′) − Σ_j I(Xʲ_t;V_t′)] − I(V_t′;X_t|V_t). The subtracted term vanishing implies Barnett–Seth independence for Markov X. Examples show each condition without the other. The independent sum of AR(1) channels has both, with no interaction. The identity concerns Ψ, the paper’s practical criterion; it says nothing about the PID quantities themselves. | Active |
| THEORY-787 v2 | A system’s causal structure can be most effective at a macro scale, so that causation emerges at a coarse-grained level and the macro description is the one at which the system’s causes are found, as Hoel, Albantakis and Tononi propose from effective information | Hoel, Albantakis and Tononi (2013), LIT-1038, argue that macro can beat micro: the scale at which effective information peaks is where a system’s causal structure is, so causation can emerge at a macro level. The record holds as shown, in THEORY-222, only the arithmetic: under uniform interventions imposed separately at each level, a macro description can have more effective information. This is the causal thesis, filed under ADR-047 v4 when the narrowing dropped it. | Rejected — Rejected on 2026-10-30, at the owner’s direction, by its own refutation condition: the macro advantage disappears whenever the same intervention distribution over micro states is used at both levels. THEORY-1167 proves this for a coarse-graining of one transition, by data processing, and Comolatti and Hoel concede it (LIT-1843). The independent interventionist test the promote_when asks for, causal feature learning (LIT-1833), can confirm that a macro is proportionate but never that it beats the micro (THEORY-1169). What the record holds instead is CLAIM-497, by ARG-041. Hoel’s temporal and spatio-temporal macros, which the bound does not reach, are QUESTION-335. The arithmetic it rested on, THEORY-222, stands. |
| THEORY-801 v2 | Agents are the systems that would adapt their policy were their actions to affect the world differently, so the agent is wherever that adaptation is: a thermostat is not an agent while it together with its design process is, an RL training process is while its learnt policy generally is not, and humans are | The definition and verdicts THEORY-527’s title carried before the promotion audit (batch 055) narrowed it to the recovery theorem. Kenton, Kumar, Farquhar, Richens, MacDermott and Everitt (2022), LIT-909, propose the definition and argue the verdicts from it in §1 and §4; that it “reliably classifies humans as agents” is asserted. The verdicts are relative to the variables chosen, which the paper states. Filed under ADR-047 v4. | Proposed |
| THEORY-802 v2 | In trained networks as in constructed ones, interchange interventions on a fixed set of variables can be satisfied equally by alignments related by a change of basis, so which internal direction mediates a high-level variable is fixed only relative to a chosen decomposition into units, and complex models will generally have several distinct, fully correct abstractions | The general reading that THEORY-243 held before the promotion audit narrowed it to the three-unit network it proves (batch 062). Wu et al. (2024), LIT-961, conjecture that complex models have “multiple distinct fully correct abstractions” and that the causal-abstraction framework cannot settle structural equivalence; Makelov et al. (2023), LIT-968, §8, grant that crossing component boundaries makes “illusory” tenuous, and answer by privileging components. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. Its only support is the constructed tie. | Proposed |
| THEORY-820 v2 | For a stationary discrete-valued process X and any coarse-graining Z of its past, informational closure at every horizon is the same condition as zero one-step transfer entropy from the micro past, Barnett and Seth’s dynamical independence, and as causal closure, Z’s ε-machine coinciding with its υ-machine; for a coarse-graining of the present state it also makes Z’s causal states a coarse-graining of X’s, which does not imply closure, and the closed coarse-grainings are not closed under common refinement | Rosas et al. (arXiv 2024), LIT-1306, read in NOTE-1030, with Barnett and Seth’s definition (LIT-979). For discrete stationary processes, the information-theoretic criterion of emergent closure (dynamical independence), the interventionist one (the macro’s own causal states are all the micro distinctions that matter for it) and, for maps of the present state, a computational one are nested as stated. The first two are one condition. It says nothing about approximate closure. It does not make closure a mark of unity. “Causal” is only in the Granger sense unless X is fully observed. | Active |
| THEORY-824 | Economics working papers increasingly back their claims with design-based identification: in NBER and CEPR working papers the share of claims supported by difference-in-differences, instrumental variables, an RCT, regression discontinuity or synthetic control rose about fourfold from 1990 to 2020 | Garg and Fetzer (2024; arXiv v2 2026), LIT-079, read in full in NOTE-083, read the rise in their extraction’s design-backed share as a change in economics: “economic papers have increasingly incorporated causal inference methods to substantiate their claims over the past three decades”. The record holds as shown, in THEORY-674, only the extraction’s series, whose edges were never checked against human labels and whose per-decade slope nearly vanishes with method-mix and graph-volume controls. This is the paper’s reading, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-839 | A model optimal for the distribution its own deployment induces, a performatively stable point, need not minimize the risk it actually incurs, and the gap is bounded: for a loss that is L_z-Lipschitz in the data and γ-strongly convex in the parameters, and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, every stable point lies within 2L_zε/γ of every performative optimum; in a biased-coin example the stable point is µ/(1 − ε) and the optimum µ/(1 − 2ε), equal only when the prediction has no effect | Perdomo, Zrnic, Mendler-Dünner and Hardt (2020), LIT-1336, read in NOTE-1044. Self-consistency under one’s own influence and the best outcome under that influence are different targets. The bound says they are close when the influence is weak relative to the loss’s curvature. It does not say how to find the optimum, which needs the distribution map away from the deployed model. | Active |
| THEORY-843 | Beckers, Eberhardt and Halpern’s approximate abstraction error, the least over surjective context maps of the worst case over allowed interventions and contexts of the high-level distance between the coarse-grained low-level outcome and the high-level outcome, is zero exactly for τ-abstraction; an abstraction followed by an α-approximation of the high-level model is within α, an α-approximation of the low-level model followed by an abstraction only within kα, k the worst-case ratio of high- to low-level distances, and an approximate abstraction need not factor into an exact abstraction and an approximation | Beckers, Eberhardt and Halpern (2020; arXiv 2019), LIT-1310, read in NOTE-1045, on Beckers and Halpern’s τ-abstraction (LIT-1316). The error is relative to a metric the user chooses, takes the worst case over interventions, and minimizes over context maps, so like exact abstraction it is zero for a coarse-graining whose dropped detail the high-level noise can hold. It does not measure the governance deficiency Γ. | Active |
| THEORY-847 | In a linear structural equation model whose exogenous micro-causes W₁, …, W_n drive effects Z = AW + F, with interventions that set all of W, all of Z or both, averaging each block is an exact transformation onto Ẑ = (an/m)Ŵ + F̂ if and only if every column of A sums to the same a, the column-equitability of the block of A from W to Z; the transformation is exact only for those whole-block interventions | Rubenstein et al. (2017), LIT-1334, read in NOTE-1037, with Beckers and Halpern’s restatement (LIT-1316, Example 3.3). Averages of linear micro-variables form a causally consistent macro model exactly when each micro-cause has the same total effect on the effect block. It says nothing about interventions on single micro-variables, which break exactness, nor about nonlinear or approximate aggregation. | Active |
| THEORY-848 | In an acyclic structural equation model, marginalising a variable that no declared intervention sets is an exact transformation, provided the coarse model’s exogenous noises may be dependent; so exactness does not require the dropped variable to be causally idle, and it can drop a variable that decides how its children respond to an intervention that is declared | Rubenstein et al. (2017), LIT-1334, read in NOTE-1037. Exact transformation asks only that the coarse model reproduce the push-forward of each declared interventional law, so a never-intervened variable can be substituted out and its randomness folded into noise, whatever it does. Applied to the hidden governance bit, the coarse-graining that CLAIM-407 shows to lose the response to h is exact. It does not say that the coarse model keeps any one system’s response. | Active |
| THEORY-849 | For deterministic causal models with a countable set of allowed interventions, a high-level model reproduces the coarse-grained interventional law of a low-level one for every distribution on contexts exactly when some map τ_U on contexts commutes with every allowed intervention, τ(M_L(u, i)) = M_H(τ_U(u), ω(i)); exactness for one distribution is strictly weaker, since a well-chosen distribution lets unrelated models match, and τ-abstraction and strong abstraction are strictly stronger; the context map is only required to exist, so high-level exogenous variables may carry what the coarse state drops | Beckers and Halpern (2019), LIT-1316, read in NOTE-1032, on Rubenstein et al.’s exact transformation (LIT-1334). Uniformity over distributions turns a distributional match into a context-by-context commuting condition. It does not make the coarse endogenous state carry the high-level context, which is what governance-response sufficiency would need. | Active |
| THEORY-861 | When a deployed model changes the distribution it is scored on, retraining on the distribution the last model induced contracts at rate εβ/γ, for a β-jointly smooth, γ-strongly convex loss and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, and so converges to a unique performatively stable point when ε < γ/β; each condition is needed, since dropping strong convexity, joint smoothness or the bound on ε each admits a case where retraining never converges | Perdomo, Zrnic, Mendler-Dünner and Hardt (2020), LIT-1336, read in NOTE-1044. Retraining under performativity is a fixed-point iteration, and these are the conditions for it to settle. Its fixed point is self-consistent, not optimal (THEORY-839), and outside the conditions there may be several or none. | Active |
| THEORY-889 v2 | In Acharya, Blackwell and Sen’s analysis, white Southerners surveyed in 2006 to 2011 who live in counties where a larger share of the 1860 population was enslaved are, with state fixed effects and 1860 county controls, somewhat less Democratic, less supportive of affirmative action and more racially resentful, by about 0.09 to 0.13 standard deviations per standard deviation (about 20 points) of slave share, and in 1984 to 1998 survey data colder toward black Americans, by about 0.32; a cotton-suitability instrument gives larger estimates; the direct effect estimated with present black share held fixed is about as large; and in county presidential vote, which counts black voters until disenfranchisement, the difference appeared after Reconstruction rather than before the war | Acharya, Blackwell and Sen (2016), LIT-1388, read in full in NOTE-1089 from the journal PDF on the second author’s site, without the online appendix. The association is well supported; the causal reading rests on 1860 controls, a cotton-suitability instrument with an untestable exclusion restriction, and a direct-effect estimate. The transmission mechanism has the weakest evidence: a parent–child correlation in 241 Southern respondents not linked to county slavery. | Active |
| THEORY-965 | Sparse-autoencoder features of a large language model’s residual stream are units the model computes with: they track abstract concepts across languages, modalities and concrete or abstract instances, and intervening on one changes the model’s behaviour in the way its label predicts, better than directions found from a few labelled examples | Templeton et al. (2024), LIT-1533, read in NOTE-1178, with Bricken et al. (2023), LIT-1545, for the one-layer case. The thesis of both papers: features are the model’s own units, shown by steering. The authors’ own hedges: steering needs features clamped beyond their observed range; the reconstruction error rides along; “we haven’t rigorously evaluated our features against other steering methods”. The record holds a result against it for known causal variables (THEORY-968). | Proposed |
| THEORY-966 | Greedy edge pruning of the ACDC kind, which removes each edge whose removal changes the output metric by less than a threshold given the edges already removed, keeps only one input of a redundant OR gate, and which input it keeps depends on the order in which edges are visited, so when a model has redundant sufficient paths the circuit it returns is one of several sufficient subgraphs | Conmy et al. (2023), LIT-1547, Appendix M, read in NOTE-1170. For out = 1 − ReLU(1 − x − y) with x = y = 1, removing either input alone leaves the output at 1, so the first one visited is pruned and the second is then kept; visiting y first keeps x instead. It does not say how common redundant paths are in trained models, nor that any other method does better: HISP keeps neither input. | Active |
| THEORY-968 | In the Mechanistic Interpretability Benchmark’s causal-variable localization baselines on Gemma-2 2B and Llama-3.1 8B, features of the public Gemma Scope and Llama Scope sparse autoencoders, selected by a learned binary mask, never gave a higher mean interchange-intervention accuracy than the same mask over the model’s own hidden dimensions, in all sixteen task–variable cells and by 1 to 14 points, while distributed alignment search, trained against the causal model it is scored on, gave the highest mean in fifteen of them | Mueller et al. (2025), LIT-1550, read in NOTE-1169. Unsupervised SAE features were worse units than neurons for known task variables across ARC, MCQA, two-digit addition and RAVEL. It does not say SAE features are never causal units: the comparison is on residual streams, under one selection method, with the base reconstruction error carried into every intervention, and the best method is supervised by the hypothesis it is scored against. | Active |
| THEORY-970 | On three language-model tasks whose circuits earlier manual work reported, indirect object identification and Greater-Than in GPT-2 Small and Python docstrings in a four-layer attention-only model, ACDC run with resampled corrupted activations against KL divergence ranked the reported edges with areas under the ROC curve of 0.85 to 0.98, above head-importance pruning and subnetwork probing on all three; on two compiled tracr programs it ranked them poorly with corrupted activations, 0.68 and 0.20, and exactly with zero activations | Conmy et al. (2023), LIT-1547, read in NOTE-1170. Edge AUCs with corrupted activations and KL: Docstring 0.982, Greater-Than 0.853, IOI 0.869 for ACDC, against 0.805, 0.693, 0.789 for HISP and 0.937, 0.806, 0.823 for SP. It does not say ACDC finds the true circuit: the reported circuits are incomplete, the results depend on metric, ablation and parent order, and negative components are missed at sparse thresholds. | Active |
| THEORY-974 | When a transformer’s MLP sublayers are replaced by transcoders and the attention patterns and LayerNorm scales on a prompt are held fixed, the contribution of an earlier transcoder feature at the same token to a later one’s pre-activation is the earlier feature’s activation times the dot product of its decoder with the later feature’s encoder, scaled by one LayerNorm constant per token, so the weight factor is fixed by the trained weights and holds on every input | Dunefsky, Chlenski and Nanda (2024), LIT-1554, read in NOTE-1174, Eq. 7 and App. D.2–D.4, re-derived here. The weight factor is a weight of the replacement model, not of the original, and it is exact only for the replacement. It says nothing about why attention attends where it does, and “input-invariant” holds only up to a per-token LayerNorm scalar and only while the later feature is active. | Active |
| THEORY-978 v2 | Causal scrubbing scores a hypothesis through the partitions of the dataset that its interpretation nodes induce, so two hypotheses that assign different features to a node but induce the same partition on the dataset, such as two features perfectly correlated on it, receive the same score | Chan et al. (2022), LIT-1549, read in NOTE-1168. In the causal-scrubbing algorithm an interpretation node enters only through sample_agreeing_x, which draws a datum with an equal value of that node, so only the equivalence classes the node induces on the dataset matter. The authors say it themselves: the method “doesn’t allow us to distinguish between two features that are perfectly correlated on our dataset”. It does not say that a passing hypothesis is otherwise wrong, nor anything about features correlated only imperfectly. | Active |
| THEORY-979 | On one prompt, a transformer whose MLPs are replaced by a cross-layer transcoder, with its attention patterns and normalization denominators frozen and each MLP’s reconstruction error added back as a constant, reproduces the model’s activations and outputs exactly and is linear between features, so each active feature’s pre-activation is the sum of its attribution-graph edges and constants; a perturbation that clamps MLP outputs up to the target feature’s encoder layer then confirms a direct edge by construction, and tests only knock-on effects and the output | Ameisen et al. (2025), LIT-1552, read in NOTE-1185: the local replacement model, the edge formula and the appendix on steering, re-derived here. It is a statement about what an attribution graph is exact for, not about the model: exactness holds at the unperturbed point only, the error terms are constants with no inputs, and the frozen attention patterns are the part of the computation the graph does not explain. | Active |
| THEORY-980 | In GPT-2 small on fifteen templates of indirect object identification, a circuit of 26 attention heads in seven classes, found by path patching, keeps 87% of the model’s mean logit difference when every other head is mean-ablated; knocking out its three main name mover heads costs only 5%, because other heads take over, and knockout sets found by greedy search make the circuit and the full model differ by up to 87% of the logit difference, so the circuit is faithful on average and incomplete under knockouts | Wang et al. (2022), LIT-1540, read in NOTE-1167: §§3–4 and the appendices. The circuit implements “identify the names, remove the duplicated one, output the rest” through duplicate-token, induction and previous-token heads, S-inhibition heads and name movers, with negative and backup name movers. The faithfulness, completeness and minimality tests are the paper’s own. It says nothing beyond these templates and this model, it treats MLPs as given, and its greedy search is printed in a form that does not match its description. | Active |
| THEORY-983 | In Geiger et al.’s three-layer feed-forward network trained on hierarchical equality and in BERT fine-tuned on monotonicity inference, interchange interventions on subspaces found by a learned rotation aligned the hypothesised two-variable causal models with interchange intervention accuracy of 1.00 on the rotation’s training data, where the axis-aligned alignment closest to the learned rotation reached 0.73 and 0.51; in BERT, the learned lexical-entailment subspace was in turn aligned, at 0.97 to 0.98, with a model holding only the identities of the two words | Geiger, Wu, Potts, Icard & Goodman (2024), LIT-1551, read in NOTE-1192. Layer 1 of the equality network (1.00 with |N| = 16 and two 8-dimensional subspaces) and layer 9 of BERT’s [CLS] vector (1.00 with two 256-dimensional subspaces). It does not say the networks implement the algorithms in any stronger sense than interchange accuracy on training pairs, nor that the learned subspaces are unique: every rotation within them gives the same interventions. | Active |
| THEORY-987 | In Claude 3 Sonnet’s middle-layer residual stream, on two prompts for which every active sparse-autoencoder feature was ablated, how strongly a feature was active predicted its ablation effect on the answer poorly (correlation about 0.12) while its gradient attribution predicted it well (about 0.81), and on the multi-step prompt only three of the ten most active features were among the ten with the largest ablation effect | Templeton et al. (2024), LIT-1533, read in NOTE-1178: Features as Computational Intermediates and the appendix on ablations and attributions. On “The capital of the state where Kobe Bryant played basketball is” (Sacramento against Albany), the five features with the largest ablation effect, Kobe Bryant, California, capital, Los Angeles and the Lakers, rank as low as 70th to 162nd by activation. It does not say how often this holds beyond the two prompts, and for other prompts the authors found no intermediate features at this layer. | Active |
| THEORY-994 | In Ameisen et al.’s evaluations, the local replacement model of their 18-layer language model, built from a 10-million-feature cross-layer transcoder, responded to small perturbations much as the model did one layer after the intervention and increasingly differently over later layers, more in the size of the effect than its direction and slightly more for larger dictionaries, and over 20 prompts the graph’s influence of one feature on another ranked the effect of ablating the first on the second with a Spearman correlation of 0.72 | Ameisen et al. (2025), LIT-1552, read in NOTE-1185. It is the method’s own measurement of where a circuit read off its stand-in stops being the model’s: close for a layer, diverging with depth. It does not say how faithful the circuits of any case study are, which were chosen and validated separately, and it is measured on 18L, not on Claude 3.5 Haiku, where the companion’s case studies were run. | Active |
| THEORY-995 | The attention heads in GPT-2 small that take over the indirect-object prediction when its main name mover heads are knocked out exist because the model was trained with dropout, which optimized it to be robust to disabled components, as Wang, Variengien, Conmy, Shlegeris and Steinhardt hypothesize | Wang et al. (2022), LIT-1540, read in NOTE-1167, §3.4: “We hypothesize that this compensation phenomenon is caused by the use of dropout during training. Thus, the model was optimized for robustness to dysfunctional parts.” The compensation is real (a 5% loss of logit difference after knocking out the three name movers); the cause is not examined. Appendix F: “Both the reason and the mechanism of this compensation effect are still unclear.” | Proposed |
| THEORY-996 v2 | On Pythia language models from 410M to 12B parameters, in three single prompt pairs and two small prompt distributions, verifying attention or neuron nodes by activation patching in the order given by attribution patching, a first-order gradient estimate of each node’s noising effect, found the nodes with the largest effects at about 2 to 50 times the cost of an oracle ordering, below unordered patching, subsampling and block search in every setting; its misses were concentrated in queries and keys behind saturated attention and in nodes whose direct and indirect effects nearly cancel | Kramár, Lieberum, Shah & Nanda (2024), LIT-1531, read in NOTE-1190. Ground truth is each node’s exact single-node noising effect on the clean prompt’s negative log probability. Recomputing the softmax for queries and keys removes many misses; dropping one layer’s gradient at a time helps on single prompt pairs but not on the distributions, where AtP with the softmax fix or plain AtP is cheapest. It says nothing about coarser nodes, other model families, effect magnitudes or false positives. | Active |
| THEORY-998 v2 | In GPT-2 XL, for 1000 facts the model knows, restoring single clean hidden states into a run whose subject tokens were noised recovers the most of the correct object’s probability at two sites, middle layers at the last subject token, where MLP outputs carry most of the effect, and late layers at the last token, where attention does; and a rank-one edit of one middle MLP output matrix keyed on the last subject token inserts counterfactual facts that generalize to paraphrases and spare neighbouring subjects better than the fine-tuning, knowledge-neuron and hypernetwork editors tested, working best at that token and in middle layers | Meng et al. (2022), LIT-1536, read in NOTE-1166: §§2–3, Tables 1 and 4, and Appendices A, B and E. Causal traces: ATE 18.6%; the mid-layer MLP effect at the last subject token peaks at AIE 6.6% against 1.6% for attention. CounterFact on GPT-2 XL: ROME’s score 89.2 (efficacy 100.0, paraphrase 96.4, neighbourhood 75.4), next best 66.9. It does not say where facts are stored: a rank-one edit with the same output exists for any one-dimensional fact patch (LIT-968). | Active |
| THEORY-1000 v2 | For fine-grained nodes of transformer language models generally, attribution patching corrected for attention saturation is a reliable prefilter for activation patching: nodes it ranks low rarely have large single-node patching effects, so verifying nodes in its order finds the important ones at a small multiple of the cost of an oracle, as Kramár et al. expect | Kramár, Lieberum, Shah & Nanda (2024), LIT-1531, read in NOTE-1190. The measured case is four Pythia models, three prompt pairs and two small distributions. The paper’s own diagnostic is what would let a single new setting be checked without exhaustive patching. | Proposed |
| THEORY-1002 | On frozen randomly initialized feed-forward networks at chance on hierarchical equality, with 16 input dimensions, distributed alignment search for the two-equality causal model reached interchange intervention accuracy of 0.50 to 0.51 at hidden sizes up to 256 but 0.55 at 1,028 and 0.64 at 4,096, so in a hidden layer much wider than the input a learned rotation can produce above-chance interchange accuracy for an algorithm the network does not implement | Geiger, Wu, Potts, Icard & Goodman (2024), LIT-1551, §4.4, read in NOTE-1192. A random network cannot implement hierarchical equality, so any IIA above 0.5 is made by the search. At widths near the input’s there is none; at 4,096 there are 14 points. It does not say DAS results on trained networks are artefacts: the trained equality network reached 1.00 at width 16, where the random one stayed at 0.50. | Active |
| THEORY-1007 | On four subject–verb agreement tasks in Pythia-70M and Gemma-2-2B, circuits of sparse-autoencoder features and autoencoder error nodes, selected by linear estimates of indirect effect, carried half or more of the behaviour on held-out pairs with about 100 and 500 nodes, where circuits of neurons needed about 1,500 and more than 30,000; with the error nodes removed, the same feature circuits carried little of it, under about a quarter in Pythia and almost none in Gemma | Marks et al. (2025), LIT-1532, read in NOTE-1187: §§2–3.2, Figure 3 and Appendices A, B and H. Faithfulness is (m(C) − m(∅))/(m(M) − m(∅)) with nodes outside the circuit mean-ablated, scored on the latter two thirds of each circuit only. The features plus the dense error terms are a small circuit; the features by themselves are not. It says nothing about what the error terms hold, and it does not compare features with neurons on equal terms, which the authors say cannot be done. | Active |
| THEORY-1011 v3 | In autoregressive transformer language models, factual associations are stored in middle-layer MLP modules as linear key–value memories: the MLP takes a key encoding the subject at its last token and returns a value encoding its attributes, which late attention moves to the prediction, and any middle layer could store a given fact equally, as Meng, Bau, Andonian and Belinkov propose | Meng et al. (2022), LIT-1536, read in NOTE-1166, §2.3 and §3: “the localized factual association hypothesis”. It localizes recall along three dimensions, “(i) in the MLP modules (ii) at specific middle layers (iii) and specifically at the processing of the subject’s last token”, and conjectures “that any fact could be equivalently stored in any one of the middle MLP layers”. The support is causal tracing and the success of rank-one edits at the traced site. | Rejected — Hase et al. (LIT-1578, THEORY-1024) meet this entry’s own refutation clause for its localization part, in GPT-J on 652 CounterFact facts. ROME rewrites a fact at over 96% at every layer but the last, and the per-fact tracing effect adds at most 3.2 points of R² to edit success. The conjecture that any middle layer could store a fact equally was split out to THEORY-1039 and stays Proposed |
| THEORY-1014 | In a language model, a behaviour that looks like one mechanism, whether picked out by one contrast or by one cluster of next-token predictions, is often carried by several distinct pathways of sparse features that converge on the output without fully intersecting, as in Pythia-70M’s agreement across a relative clause, its prediction of “to” before an infinitival object, and its incrementing of sequences | Marks et al. (2025), LIT-1532, read in NOTE-1187: §3.3, §5 and Appendix C. Agreement across a relative clause: subject-number features promote verb forms directly, and a second pathway carries the number to the clause’s end through PP/RC boundary features. Cluster 475: one mechanism detects verbs and adjectives that take infinitival objects, another nominal objects before an object complement. Cluster 382: general succession features and token-specific induction features. “While the clusters … seem at first to each represent a single mechanism, circuit-level analysis reveals in both cases a union of distinct mechanisms.” | Proposed |
| THEORY-1020 | In a two-layer attention-only language model, on tokens where induction helps, the standard induction circuit (queries and values from the token embedding, keys from the previous-token head) accounts for 35% of the loss its two induction heads contribute, and a hypothesis that adds three-token matching, layer 0’s average effect and three layer-0 heads acting as if they attended to the current token accounts for 86% | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), LIT-1579, read in NOTE-1196. Percentages are of 0.053 nats, the loss the induction heads 1.5 and 1.6 contribute on next-token examples whose last token is on an induction-favouring whitelist, measured by causal scrubbing. The naive story’s shortfall is mostly in the queries (51% alone) and keys (79%), not the values (90%). It does not say what fraction of the model’s whole loss, or of its in-context learning, the circuit explains, nor anything about models with MLPs. | Active |
| THEORY-1021 | In transformer language models, attribution patching agrees well with activation patching for small patches of single heads and their queries, keys, values and attention patterns, for nodes late in a circuit relative to the metric, and for circuits that route information through attention, and agrees badly for large patches such as whole residual streams, for the first MLP layer and the early layers of deep circuits, where nonlinearities move out of saturation, and where an effect needs several features at once, as Nanda proposes | Nanda (2023), LIT-1581, read in NOTE-1201. The post’s map of where the first-order estimate can be trusted. The record holds it from one task in the post, from the mathematics of the estimate (THEORY-1023), and in part from Kramár et al.’s test on Pythia (THEORY-996), which found misses behind saturated attention, as this predicts, and tested no residual-stream nodes. | Proposed |
| THEORY-1023 | Attribution patching estimates the effect of patching an activation from a clean run into a corrupted run as the difference between the two activations dotted with the gradient of the metric on the corrupted run, so the estimates for every activation come from two forward passes and one backward pass and add over sub-components; the estimate is exact when the metric is affine in the activation, gives no effect for a nonlinearity in saturation whatever the true change, and through LayerNorm ignores the component of a patch along the vector being normalized | Nanda (2023), LIT-1581, read in NOTE-1201: the estimate and its mathematical properties, not its accuracy in any model. The cost is fixed (about four forward passes for all patches), the estimate is linear and so additive, and its blind spots follow from linearity: saturation, interaction between features, and LayerNorm’s scale invariance. | Active |
| THEORY-1024 | In GPT-J, for 652 CounterFact facts the model knows, the per-fact causal-tracing effect at an MLP layer adds at most 3.2 points of explained variance in the success of editing that fact at that layer, beyond what the choice of layer alone explains, across ROME, MEMIT and constrained fine-tuning and five editing objectives; ROME rewrites the fact at over 96% at every layer but the last, including layers where tracing does not place it, and the only reliable link appears when the edit is made on the noised input that tracing uses | Hase et al. (2023), LIT-1578, read in NOTE-1194: §§4–5, Tables 1–8 and Appendices A–C. For ROME at GPT-J’s layer 6, ρ = −0.13 between rewrite score and tracing effect; R² 0.947 from the layer, 0.948 with tracing added. Over twenty method–objective pairs the largest gain is 0.032 (fine-tuning on five layers, Fact Forcing). It does not say that facts are stored nowhere in particular, nor that the layer does not matter: the layer explains most of the variance, and ROME is best on average at the layer tracing favours on average. | Active |
| THEORY-1025 | The inputs causal scrubbing samples for a treeified hypothesis are the unique maximum-entropy distribution, on finite inputs, among those that give the inputs of every interpretation node the joint distribution they have on the data, so whatever the hypothesis does not claim is resampled as independently as the claims allow | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt et al. (2022), LIT-1583, read in NOTE-1202, §5. Every node’s datum is distributed as D, so each node’s scrubbed inputs are jointly as on the data, and among all distributions with that property the algorithm’s has the greatest entropy. It characterizes the sampling, not the score: it does not say that a hypothesis whose score matches the model is true, and the same appendix’s §7 builds one that is false. | Active |
| THEORY-1026 | In transformer language models, locating where a forward pass carries information about a fact and finding where a weight edit best changes the expressed fact are different questions, because an edit at one layer can override information accumulated across other layers, so that many layers could hold a fact and some happen to, as Hase, Bansal, Kim and Ghandeharioun propose | Hase et al. (2023), LIT-1578, read in NOTE-1194, §6: “Causal Tracing answers a question about where factual information is carried in representations in a Transformer forward pass, and this question turns out to be a different question than the editing question of where is best to intervene”; and, for why edits work where facts are not traced, “Many layers could store a fact, and it happens that some do”. The authors note that this would be surprising, since layers cannot be swapped freely. | Proposed |
| THEORY-1029 | On a three-layer parenthesis-balance classifier, causal-scrubbing hypotheses that resample the terms of one head’s input separately scored 81% and 84% of the loss recovered against 77% for the less specific hypothesis they refine, and the authors attribute the rise to resampling washing out a signal, not to a better explanation | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), LIT-1580, read in NOTE-1195. Hypothesis 3a resamples head 2.1’s input separately at each of up to 40 positions and recovers 77% (loss 0.97 ± 0.06). Hypotheses 3c and 3d also split each position’s input into terms drawn from different inputs, and recover 84% (0.69 ± 0.05) and 81% (0.81 ± 0.05). The authors call the two results not legitimate. It does not say how often this happens in other models, nor that the adversary they propose would remove it. | Active |
| THEORY-1031 | In GPT-J, inserting 10,000 CounterFact counterfactuals at once by a closed-form least-squares update of the MLP output matrices of layers 3 to 8, spread so that each layer writes a share of each fact’s required change to the subject’s hidden state, gives an editing score of 85.8 (efficacy 98.9, paraphrase 88.6, neighbourhood 73.7) with fluency kept, against 67.6 for weight-decayed fine-tuning, which breaks generation, 50.3 for ROME applied one fact at a time and 23.1 for MEND; GPT-NeoX scores 82.0, and editing late MLPs or attention instead does worse | Meng et al. (2022), LIT-1582, read in NOTE-1197: §§4–5, Tables 1 and 2, Appendices A, B and F. On 10,000 true zsRE facts in GPT-J, MEMIT scores 50.7 against FT-W 42.1, MEND 20.0 and ROME 2.6. At a handful of edits ROME generalizes a little better. It does not show where facts are stored: the layer range is chosen from traces averaged over facts, which do not predict per fact where an edit works (THEORY-1024). | Active |
| THEORY-1039 | In autoregressive transformer language models, factual associations are recalled through middle-layer MLP modules acting as key–value memories, and any fact could be stored equally in any one of the middle MLP layers, as Meng, Bau, Andonian and Belinkov conjecture | Meng et al. (2022), LIT-1536, read in NOTE-1166, §2.3: “we conjecture that any fact could be equivalently stored in any one of the middle MLP layers”. It was one clause of THEORY-1011, which is Rejected for its other part, the claim that the traced middle layers are where a fact is stored. Hase et al. (2023), LIT-1578, read in NOTE-1194, measure edits succeeding at nearly every layer of GPT-J whatever tracing says (THEORY-1024). That is what this conjecture predicts, but it is not evidence of storage, since an edit can work wherever a layer can write the needed output (LIT-968). | Proposed |
| THEORY-1061 | Flack makes downward causation operational as components tuning their behaviour to their own estimates of aggregate variables they collectively compute: weak (apparent) when at least one component tunes to a variable slower than the behaviour producing it, strong (effective) when the variable is predictive, robust, used nearly universally, agreed on and gaining mutual information with the microscopic behaviour; she speaks of a new level only at the strong form, and regeneration of the variable by its use is not among her criteria | Flack (2017), LIT-1630, read in NOTE-1216, §1, §3 and §7. Active as a reading of what the paper proposes, which its text states as lists. It does not say the proposal is right, that it meets any definition of causation (the paper sets that aside), or that the macaque system meets the strong criteria; the evidence for that is in earlier papers not reproduced here. The sharp edge for the record: what reinforces itself in Flack is the convergence of members’ estimates, not the variable’s persistence. | Active |
| THEORY-1123 | In COTA’s formulation of causal abstraction learning as multi-marginal optimal transport, the term meant to impose do-calculus relations between the transport plans of comparable interventions depends only on the plans’ marginals and on normalisers built from them, which the transport constraints fix to the empirical distributions, so it is constant on the feasible set; its weight changes the solution only by rescaling the cost and entropy weights, and the paper’s evidence that the constraints help, a sweep over that weight, cannot separate the two | Felekis, Zennaro, Branchini and Damoulas (CLeaR 2024), LIT-1806, eqs. (6), (9), (10), (12) and Appendices A–B, read in NOTE-1342 from the arXiv preprint v1. A derivation from the paper’s own equations, which state the term as a divergence between column (or row) sums of two plans; Theorem 1’s proof writes it the same way. Active as mathematics about the problem as written. The released code, read but not run, builds a different problem for posets with several chains, in which the term acts on copies of plans that carry no marginal constraints. | Active |
| THEORY-1125 | For discrete X and Y, with an intervention on a variable abstraction T of X defined as the mixture of interventions on X weighted by Bayes inversion of the encoder under a protocol prior, no abstraction gains causal information about Y over X itself, and at full weight on causal control the causal information bottleneck is optimised by the partition of X by p(y | do(x)), mapped one class to one value of T, uniquely up to relabelling when T has exactly as many values as there are classes; these are Chalupka et al.’s causal macrovariables | Simoes, Dastani and van Ommen (UAI 2025), LIT-1802, Proposition 20 with its proof (pp. 14–15), read in NOTE-1347 from the arXiv preprint v5. Active: the proof is a strict-concavity argument, checked here on the paper’s Genetic Mutations SCM. It is the interventional counterpart of THEORY-743, and unlike the bottleneck there it reaches the partition exactly, because γ = 1 drops the compression term. It holds for the paper’s stipulated intervention on T and a fixed protocol; it says nothing about intermediate γ. | Active |
| THEORY-1137 | When an abstraction map between two causal models is learned by optimal transport from paired interventional distributions, a transport cost that rewards pairs of states compatible with the same paired interventions gives much lower held-out abstraction error than a Hamming cost when the intervention set is rich, and higher error when it holds only a few, because with few interventions the compatibility cost is nearly uniform | Felekis et al. (CLeaR 2024), LIT-1806, §§4.2 and 6 and Appendices C and E, read in NOTE-1342. Two synthetic models (STC, LUCAS) and one real two-lab dataset (EBM), all discrete, evaluated by leaving one intervention pair out. The ω-cost wins on STC with parent-free interventions and on LUCAS, loses on STC with two interventions on tar and on EBM. The explanation, a nearly uniform cost when interventions are few, is argued and fits the four cases. Proposed. | Proposed |
| THEORY-1146 v2 | Under confounding the partition of a variable X by what it predicts about a target Y can differ from its partition by what setting it does to Y, so the information bottleneck at full sufficiency can learn distinctions no intervention could use and miss ones only intervention reveals, as it did in two confounded toy models, while the causal information bottleneck, computed from observational data through a backdoor set, recovered the causal partition in all three toy models, projected gradient search finding it in 95 to 100 percent of runs | Simoes, Dastani and van Ommen (UAI 2025), LIT-1802, §8 and Appendices E–F, read in NOTE-1347. Three SCMs with 7, 4 and 16 values of X; ensembles of 4 to 12 optimisers; a penalty against unused values of T was needed at full control. The difference between the partitions follows from the definitions; what the experiments add is that the search finds the causal one, in toy problems only. Active as a report (ADR-065); whether search finds it at scale is QUESTION-346. | Active |
| THEORY-1167 v2 | When one intervention distribution over micro states is used at both levels, the effective information of a coarse-graining of a discrete mechanism, with each macro intervention realized by that distribution within its block, cannot exceed the micro effective information; so a positive causal emergence of effective information, scored with a uniform distribution at each level, equals the micro gain from changing the distribution minus a non-negative loss, and is a gain from the change of distribution | The test QUESTION-204 asks for has an answer that needs no system: with one distribution over micro states at both levels, EI(macro) = I(f(X); f(Y)) ≤ I(X; Y) = EI(micro) by data processing. Hoel’s causal emergence uses the uniform distribution at each level, which is a non-uniform micro distribution whenever blocks differ in size, so its positive values come from the micro chain scored under that other distribution. Comolatti and Hoel (LIT-1843) concede the stationary case; Eberhardt and Lee (LIT-1839) name the distribution as the source of the artefact. It says nothing about measures that data processing does not bound, nor about whether EI’s level agrees with an interventionist test. | Active |
| THEORY-1169 | For a discrete mechanism scored with one full-support intervention distribution over micro causes at both levels, a coarse-graining of cause and effect keeps all of the micro effective information if and only if it merges only causes with identical rows P(Y | do(x)) and only effects with proportional columns, whatever the distribution; so the coarsest coarse-graining that ties the micro is the causal partition of causal feature learning, with effects grouped by normalized likelihood, and any merge of causes with different effects loses information under every such distribution | Causal feature learning (LIT-1833, LIT-1834) defines macro causes as classes of micro states with the same interventional effect, with no distribution over interventions. Under one full-support distribution w at both levels, the loss of effective information from a coarse-graining (f, g) is I(X; Y | g(Y)) + I(X; g(Y) | f(X)), and both terms vanish exactly when f merges only equal rows and g only proportional columns, for every w. So the ties that THEORY-1167 allows are the causal-feature-learning partitions and their refinements: on which coarse-graining loses nothing, EI under a common distribution and the interventionist test agree, and the agreement is distribution-free. How much a merge loses still depends on w. Hoel’s EI, uniform at each level, parts from it on Eberhardt and Lee’s (13), (14) and note 6. | Active |
| THEORY-1225 | Among white Southerners today, those living in counties where a larger share of the 1860 population was enslaved are somewhat less Democratic, less supportive of affirmative action and more racially resentful, by about a tenth of a standard deviation per standard deviation of slave share, and colder toward black Americans, by about a third; the difference is not accounted for by the present black share of the population, and in voting it appeared after Reconstruction rather than before the war, which supports its origin in the incentives that emancipation gave planters to repress black labor and votes, and its local transmission thereafter | The wide form of Acharya, Blackwell and Sen (2016), LIT-1388, kept here when the status review of 2026-10-30 narrowed THEORY-889 to what the analysis measured and promoted it (ADR-065; ADR-047, kind 1). The paper argues that the attitude difference originated in emancipation’s incentives to repress black labor and votes and was transmitted locally. The causal reading rests on an untestable exclusion restriction, residence stands in for descent, and the transmission evidence is not tied to county slavery. | Proposed |
| THEORY-1287 | The experiments mechanists use to find a mechanism’s components (correlation, lesion, stimulation, and intervening on the whole while recording the parts) run in both directions between part and whole and, by Craver and Bechtel’s own account, show only prima facie that an item is a component, because an item not interactively integrated into the system could be a background condition; they give no test of integration, so the experiments do not by themselves fix where a mechanism ends | Craver and Bechtel (2007), LIT-1928, pp. 553–554, read in NOTE-1491. The four kinds of interlevel experiment “share a form with Mill’s methods” and are symmetrical. A lesion deficit is “only prima facie” evidence of componency, since a part “not interactively integrated” may be a background condition (n. 10). “Integrated” is never defined, and nothing in the four experiments tests where the system’s edge is. That leaves the mechanism’s boundary to be fixed some other way. | Active |
| THEORY-1288 | If a mechanism’s behaviour supervenes on its constituents’ behaviours and constitution is not causal, every cause of that behaviour is also a cause of some constituent along another path, so no intervention can change the whole without separately changing a part; mutual manipulability by ideal interventions is then unsatisfiable, and once interventions are relaxed to admit these common causes, every model with constitutive dependence has a model without it that implies the same correlations under every manipulation, even in ideal experimental conditions | Baumgartner & Gebharter (2016), LIT-1934, pp. 10–13, 18–20, and Baumgartner & Casini (2017), LIT-1939, pp. 6–11; restated by Baumgartner, Casini & Krickel (2020) as Systematic Fat-Handedness. Read in NOTE-1493 and NOTE-1490. Active as a conditional: valid on supervenience and non-causal constitution, and checked step by step. It does not say that constitution cannot be known, only that no finite set of manipulations of whole and part shows it; and it is about simultaneous whole–part dependence, not about a diachronic cause inside a system, which can be intervened on surgically. | Active |
| THEORY-1291 | Within levels of mechanisms, apparent top-down and bottom-up causes can be read as mechanistically mediated effects, intralevel causation among components together with the constitution of the whole by them, so that the relation between levels is constitution and not causation; Craver and Bechtel show the translation for six cases, on the assumption, not argued, that every higher-level cause has a mechanistic explanation | Craver and Bechtel (2007), LIT-1928, read in NOTE-1491. Parts and wholes are not distinct events. So, given transmission, distinctness or asymmetry views of causation, they cannot be cause and effect, and the symmetry of interlevel experiments is explained by constitution. The six worked cases translate. The account says nothing about whether a feedback loop crossing the mechanism’s boundary changes the analysis, and its generality is assumed. | Proposed |
| THEORY-1293 | Given that every change in a phenomenon is simultaneously realized by some constituent on every lower level, that simultaneous changes are not causally related, that co-occurrence is transitive, and that the parts and their levels are already known, a single intervention that changes a part and the phenomenon simultaneously while directly changing at most one behaviour on each lower level shows that the part is a constituent; the condition presupposes the boundary and the level hierarchy it is applied to and cannot supply them | Baumgartner, Casini & Krickel (2020), LIT-1924, §§3–4, read in NOTE-1494. Active as a conditional: the eight-line reductio is valid on Universal Constitution, Simultaneity and transitivity of co-occurrence, and checked. It does not say such interventions exist in any real system, that the condition is necessary, or where the boundary lies; and its line between causation and constitution is simultaneity, which is sharp only at a fixed time resolution. | Active |
| THEORY-1294 | Constitution is best inferred, and only abductively, from the failure to break a coupling: a set of parts constitutes a phenomenon when every cause of the phenomenon is also a cause of some member of the set, no smaller set does as much, and no expansion of the variables studied turns up a cause of the phenomenon that spares them all, so constitutive relevance is fixed by the set a part belongs to and no finite series of experiments settles it | Baumgartner & Casini (2017), LIT-1939, §§4–5, their No De-Coupling account, developing the fat-handedness criterion of Baumgartner & Gebharter (2016), LIT-1934, pp. 20–22. Read in NOTE-1490 and NOTE-1493. Proposed: a definition offered with no operationalization and no case from practice, which the authors say themselves. It does not say how far a variable set must be expanded, and it takes parthood as given. | Proposed |