When factor scores replace true latent scores in nonlinear prediction, measurement error attenuates the recoverable variance of any $k$th-order component of the regression function by $ρ^k$ -- the $k$th power of the score's coefficient of determination -- for any linear score type. This study derives the bound via Hermite polynomial expansion and proposes PV-ANN -- plausible values (posterior draws preserving latent variance) combined with artificial neural networks (learning functional form without prespecification). The bound governs recovery of the latent-scale function, not prediction of the outcome from observed indicators, for which factor scores are already sufficient; the two metrics are therefore predicted to dissociate. An 18-condition simulation supports both predictions: in the nonlinear low-reliability conditions PV-ANN closes about four fifths of the function-shape recovery gap between a factor-score learner and one given the true latent values, and the margin widens as reliability falls, while predictive accuracy is not improved, as the theory requires. A Big Five application illustrates the intended exploratory workflow and delineates boundary conditions under weak signal and measurement model misspecification.
Language models hold latent quantities in a form they can report on, and more of a quantity is present in that form when the task requires reusing it flexibly. What causes a representation to enter that form is open, and the word workspace invites an admission story: a gate that decides what gets in. Testing it on open-weight models with Jacobian lenses, over a benchmark whose five arms share an identical context, we find no gate where it predicts one. Demand raises a concept's lens visibility beyond what applying an operator to a supplied value produces: +0.050 [+0.045, +0.057] in percentile rank on our primary checkpoint, positive on all four we measure, though that arm answers at ceiling and the accuracymatched contrast is stronger under that readout. At the same time one shared linear map decodes the variable from every arm, the control included, at 6.4-9.0x its selection-corrected floor. What produces the later readable form at the queried position is attention-mediated gathering inside a mid-depth window: separating patch depth from readout depth puts transport there at least 17x above anywhere shallower under non-saturating readouts, with no tested MLP output contributing positively inside it. Under the saturating percentile rank the same grid does not localise the window, which is a fact about that measure. An arm that needs the variable for nothing concentrates sevenfold less, so the window is demand-specific. That window has two measured edges, a survival failure below and destruction above, and it falls at the same fractional depth in a 64-layer hybrid and a 62-layer dense model from another family. We localise where the variable is installed and read, not the route from the passage, which transports nothing. But the readout is not a calibrated measure of use: three components move it to within 12% of one another and differ 7.4x in what they do to the answer.
Discovering the direct causes and effects of a target variable from observational data is a fundamental problem in causal discovery, with broad applications in domains such as gene regulatory analysis and biomedical research. Existing causal discovery methods either learn a global causal structure, which incurs substantial computational cost, or assume the absence of latent variables and selection bias, assumptions that are often violated in real-world settings. Motivated by these challenges, we study local causal structure learning in the presence of latent variables and selection bias. Specifically, we first characterize a local region that enables target-specific causal discovery without recovering the entire global structure. We then establish a theoretical bridge between causal information learned from the observed distribution induced on this local region and the corresponding information in the global causal structure. Building on these foundations, we propose LoCaLS, a local causal structure learning algorithm that is sound and complete under standard assumptions and identifies the same direct causes and effects of a target variable as those identifiable by global causal discovery methods, while allowing for latent variables and selection bias. Extensive experiments on random and real-world structures demonstrate that the proposed method consistently achieves higher structural accuracy than existing local methods while requiring substantially less computational effort than state-of-the-art global methods. Furthermore, applications to two real-world gene expression datasets reveal biologically plausible target-specific causal structures, demonstrating its practical applicability in large-scale biological data analysis.
World models learn task-relevant information through many routes: observation reconstruction, recurrent state, temporal filtering, and explicit task supervision. Different routes can make different variables available. The same variable can also be available through several routes at once. When it is, looking at which route would increase the training loss most if removed does not tell you which route the model actually uses. The questions are reachability, whether a training signal can identify a task-relevant direction; admission, whether that direction is recoverable from the latent; and assignment, which eligible route carries it. We test them in environments with a known set of required coordinates. A direction cannot enter the latent unless some training signal can identify it. Reconstruction, recurrence, or filtering may already recover some of those coordinates; a reward or value head then has no residual direction to admit. For what remains, how many independent predictions the target supplies is how many coordinates install: one through four independent predictions admit one through four directions, including through the value head. Reachability is not admission: a temporal second-moment coefficient can remain absent under next-token prediction when accumulating it is a fraction of a percent of that loss, and a head that predicts the coefficient restores it. Assignment is a different test. Two routes that each carry the same variable when trained alone do not swap the carrier when we reverse which is more costly to remove. A recurrent model trained on a transformer's recorded sequences shows the same pattern. Near the point where the competing route is beginning to clear the probe threshold, independent training runs disagree. What a world model represents is therefore three questions: what information is reachable, what supervision admits, and which competing route carries it.
Henrique O. Caetano, Rafael Arone, Carlos Dias Macielcs.AI
Finding the source of failures, known as Root Cause Analysis (RCA), is essential for identifying the root causes of anomalies and maintaining the reliability of complex systems. While causal theory has advanced data-driven RCA, existing frameworks assume causal sufficiency, failing to account for the unobserved latent variables prevalent in real-world environments. To address this gap, we propose PAG-RCA. This framework models system failures as parametric interventions over Partial Ancestral Graphs (PAGs) to perform RCA in the presence of latent variables. We use standard causal identification algorithms to find the source of failures by quantifying causal effects over the PAG. When an effect is identifiable, candidate root causes are ranked based on their exact intervention effects. When effects are structurally unidentifiable, our framework (for the first time in the RCA literature) integrates partial identification to evaluate and score candidates using analytical causal bounds. By integrating latent variables and partial identification at once our framework ensures robust RCA even under data scarcity and latent-variable scenarios where traditional methods degrade. Evaluations on synthetic data, microservice anomaly benchmarks and power-grid cascading failures demonstrate that PAG-RCA consistently outperforms state-of-the-art data-driven baselines. By improving data-driven RCA performance under data scarcity, this methodology advances reliable automated diagnostics in partially observable complex networks.
We study causal discovery from observational and interventional regimes when latent variables may affect the measured system. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines a density-ratio or transport engine with a high-recall geometric screen and passes the retained arrows to a score-based or differentiable discovery method. The main formulation and experiments use known single-node intervention targets; in that regime the screen is designed to retain candidate directed effects, while a downstream learner determines the final graph or equivalence-class representation. Our second algorithm, Spectral Kernel Flow Matching (SKFM), amortizes the response fields, summarizes residual nonclosure by a spectral visible-footprint subspace, and applies an order-dependent graph extractor. Direct extraction succeeds on calibrated chains and selected motifs, but is unstable on harder random DAGs when the order must be learned. On ten-node nonlinear random DAGs, the more reliable hybrid role of the geometry is as a candidate generator: calibrated SKFM/Bridge fields followed by local BIC scoring achieve mean directed $F_1\simeq0.86$. Sachs protein signaling provides a real-data stress test and supports a diagnostic, not fully identified, interpretation. The contribution is therefore a practical interventional screening pipeline, explicit guarantees for screen retention and residual-footprint rank under stated assumptions, and a falsifiable account of the boundary between geometric diagnostics and causal identification.
Yan Zeng, Masanori Suganuma, Takayuki Okatanics.CV
This paper studies the problem of inverting the DDIM image generation process to recover latent variables, particularly the initial noise map, from a generated image. Existing methods often struggle with accuracy in this task. We propose a novel hybrid approach that combines direct inversion via gradient descent for the first step, followed by a fixed-point method for subsequent steps. Empirical evaluations across three datasets demonstrate that our method significantly improves the prediction of initial latent variables while achieving superior reconstruction accuracy. Additionally, we introduce a new evaluation, called the self-interpolation test, which assesses the quality of images generated from interpolated points between the true and predicted latent maps, offering deeper insights into performance. Our results reveal that while existing methods perform reasonably well in reconstruction, they consistently fail to accurately predict the initial latent variables, resulting in poor performance on the self-interpolation test. In contrast, our method outperforms all others across all metrics, providing valuable insights into diffusion models and enhancing their applications in image generation and editing.