Neural Exposure Interaction Search (NEXIS)

• NEXIS is a causal discovery method that recasts heterogeneous treatment effect characterization as a minimal Markov blanket recovery problem.
• It leverages pretrained representations and sparse autoencoders to extract interpretable direct treatment interactors from complex pre-treatment data.
• Empirical validations on synthetic and field applications show high recall and precision, demonstrating NEXIS’s policy-relevant insights for heterogeneous treatment effects.

Neural EXposure Interaction Search (NEXIS) is a method for identifying a causal and interpretable characterization of heterogeneous treatment effects (HTEs) when the true effect modifiers are latent and only complex pre-treatment measurements are observed. It is developed primarily for controlled experiments with a binary treatment and perfect compliance, and its central contribution is to reframe HTE identification as a Markov blanket discovery problem over a learned representation of pre-treatment data. In that formulation, the goal is not merely to estimate a flexible conditional average treatment effect, but to recover a minimal, non-redundant set of treatment-interacting representation coordinates that can support causal and policy-relevant interpretation (Cadei et al., 15 Jun 2026).

1. Causal target and problem formulation

NEXIS is built around a distinction between predictive heterogeneity and causal heterogeneity characterization. For units $i=1,\dots,n$, the observed data consist of a binary treatment $T \in \{0,1\}$, an outcome $Y \in \mathbb R$, and pre-treatment measurements $\bm X \in \mathcal X$. Potential outcomes are $Y(0)$ and $Y(1)$, under SUTVA, and the individual treatment effect is

$\tau := Y(1)-Y(0).$

The method introduces a latent vector $\bm W^{\mathrm{dir}} \in \mathbb R^r$ of direct effect modifiers, also called latent interactors. These are the primitive drivers of treatment-effect heterogeneity. The target characterization is

$$\tau(\bm w) := \mathbb E[\tau \mid \bm W^{\mathrm{dir}} = \bm w] \qquad \forall \bm w \in \mathrm{supp}(\bm W^{\mathrm{dir}}),$$

with corresponding interventional counterpart

$$\tau^{do}(\bm w) := \mathbb E[\tau \mid do(\bm W^{\mathrm{dir}} = \bm w)] \qquad \forall \bm w \in \mathrm{supp}(\bm W^{\mathrm{dir}}).$$

This target is motivated by the effect-modifier taxonomy of VanderWeele and Robins. Besides direct modifiers $T \in \{0,1\}$0, there may be indirect modifiers, proxies, and common-cause modifiers. All of these may display observational effect modification, but only direct modifiers support the causal policy reading that NEXIS seeks. A central implication is that a variable can be highly predictive of subgroup differences and still be a poor policy lever if it is only a proxy or a common-cause companion rather than a direct interactor (Cadei et al., 15 Jun 2026).

The recoverability requirement is stated as Measurement Sufficiency,

$T \in \{0,1\}$1

If this fails, the paper argues that full causal HTE characterization is impossible. In that case, one can at best characterize heterogeneity through non-direct modifiers.

A further conceptual contribution is the critique of marginal effect-modifier search. The paper defines the set of all coordinates that exhibit marginal effect modification as

$T \in \{0,1\}$2

Typically $T \in \{0,1\}$3, where $T \in \{0,1\}$4 is the desired principal proxy set. Because correlated companions and proxies inherit marginal heterogeneity signal, increasing experimental power can enlarge $T \in \{0,1\}$5 without bringing the analyst closer to the causal target. The paper terms this the experimental power paradox (Cadei et al., 15 Jun 2026).

2. Representation learning and principal proxy coordinates

NEXIS does not search directly over raw pre-treatment input space. Instead it assumes a representation map

$T \in \{0,1\}$6

where $T \in \{0,1\}$7 is typically constructed from a frozen pretrained encoder followed by a sparse autoencoder or related dictionary-learning layer. The paper’s applications use a geospatial foundation model, Prithvi-EO, on Landsat imagery, followed by a TopK sparse autoencoder trained on held-out national grids. Active SAE atoms are then pooled with structured survey covariates and supplied to NEXIS as candidate coordinates (Cadei et al., 15 Jun 2026).

Two assumptions govern the representation stage. The first is Representation Sufficiency,

$T \in \{0,1\}$8

This requires the learned representation to preserve all HTE-relevant information contained in $T \in \{0,1\}$9.

The second is Principal Alignment. There must exist a unique injective map

$Y \in \mathbb R$0

such that for each $Y \in \mathbb R$1,

$Y \in \mathbb R$2

The resulting set

$Y \in \mathbb R$3

is the set of principal proxy direct effect modifier coordinates. Each selected coordinate $Y \in \mathbb R$4 is the dominant dictionary coordinate for one latent direct modifier.

This representation design is what underlies the paper’s phrase “From Tokens to Policy.” The raw observations may be multimodal and semantically diffuse, but the dictionary stage is intended to produce sparse, localized, and post hoc interpretable coordinates. In the geospatial applications, interpretation of selected SAE atoms is carried out using top-activating examples and VLM descriptions. The policy claim is therefore not that tokens themselves are actionable variables, but that learned concept coordinates can serve as human-understandable proxies for latent treatment interactors (Cadei et al., 15 Jun 2026).

3. Conditional treatment-interaction testing and the NEXIS procedure

The atomic primitive of NEXIS is a CATE-equivalence test. For a candidate coordinate $Y \in \mathbb R$5 and a current selected set $Y \in \mathbb R$6, the null is

$Y \in \mathbb R$7

A valid $Y \in \mathbb R$8-value $Y \in \mathbb R$9 is computed for this null. If the null holds, $\bm X \in \mathcal X$0 is conditionally redundant once $\bm X \in \mathcal X$1 is known; if it fails, $\bm X \in \mathcal X$2 contains residual heterogeneity information.

NEXIS adapts forward-backward Markov blanket discovery in an IAMB-style loop. Given data

$\bm X \in \mathcal X$3

significance level $\bm X \in \mathcal X$4, and a CATE-equivalence test, the procedure initializes $\bm X \in \mathcal X$5 and iterates until the selected set no longer changes. In the forward step, it computes $\bm X \in \mathcal X$6 for all unselected coordinates, chooses

$\bm X \in \mathcal X$7

and adds $\bm X \in \mathcal X$8 if

$\bm X \in \mathcal X$9

In the backward step, it checks each selected coordinate and removes $Y(0)$0 whenever

$Y(0)$1

Bonferroni correction is the default multiple-testing control, though the paper notes that FDR alternatives can be substituted (Cadei et al., 15 Jun 2026).

The backward step is theoretically essential. A forward-only procedure may include a proxy coordinate before the true principal proxy enters the model. Once the principal coordinate is added, the proxy should become conditionally null. Backward pruning is what removes such now-redundant variables.

The default concrete test is a linear treatment-interaction regression,

$Y(0)$2

with a partial $Y(0)$3-test on $Y(0)$4. The paper describes this as computationally cheap and effective when residual heterogeneity is approximately linear in the learned sparse codes.

For nonlinear alternatives, the paper proposes a doubly robust generalized covariance measure construction. It defines the residualized pseudo-outcome

$Y(0)$5

where $Y(0)$6 is known by design in an RCT and $Y(0)$7 estimates $Y(0)$8. After residualizing both $Y(0)$9 and $Y(1)$0 on $Y(1)$1, it forms

$Y(1)$2

with statistic

$Y(1)$3

Quadratic or LightGBM nuisance models may be used.

An optional spectral-gap gate is also proposed: $Y(1)$4 This is explicitly described as a heuristic rather than part of the core theorem. The recommended default is $Y(1)$5. Its purpose is to improve precision when residual entanglement in the dictionary allows proxy features to survive conditional testing (Cadei et al., 15 Jun 2026).

4. Markov blanket theory, recovery guarantees, and causal identification

The theoretical core of NEXIS is the claim that under Principal Alignment, the principal proxy coordinates form the minimal sufficient representation of treatment-effect heterogeneity inside the learned dictionary. The appendix establishes two key properties.

First, sufficiency: for any $Y(1)$6,

$Y(1)$7

Second, non-redundancy: for any $Y(1)$8 and any $Y(1)$9,

$\tau := Y(1)-Y(0).$0

These two statements make $\tau := Y(1)-Y(0).$1 a Markov blanket of the conditional mean of $\tau := Y(1)-Y(0).$2 within the dictionary. This is the formal justification for treating HTE characterization as a Markov blanket recovery problem rather than as a marginal screening problem (Cadei et al., 15 Jun 2026).

The theorem requires several layers of assumptions. At the experimental level, treatment is randomized, the treatment is binary with perfect compliance, and SUTVA holds. At the representational level, Measurement Sufficiency and Representation Sufficiency must hold. At the alignment level, Principal Alignment must hold. The paper also introduces a mean-faithfulness condition,

$\tau := Y(1)-Y(0).$3

for any random variables $\tau := Y(1)-Y(0).$4. This excludes conditional-mean cancellations that would obscure relevant coordinates.

In addition, the conditional tests used by NEXIS must satisfy asymptotic null validity and consistency against fixed alternatives. Under these assumptions, the main result states that the NEXIS output $\tau := Y(1)-Y(0).$5 obeys

$\tau := Y(1)-Y(0).$6

If Measurement Sufficiency and Representation Sufficiency also hold, then the selected representation recovers the causal heterogeneity characterization: $\tau := Y(1)-Y(0).$7

The paper further notes that if $\tau := Y(1)-Y(0).$8 slowly, one can upgrade the result to strict consistency,

$\tau := Y(1)-Y(0).$9

In practice, however, a fixed $\bm W^{\mathrm{dir}} \in \mathbb R^r$0 is preferred as a false-discovery budget (Cadei et al., 15 Jun 2026).

A recurring misconception addressed by this framework is that pointwise causal effect estimation automatically yields a causally meaningful heterogeneity characterization. NEXIS explicitly rejects that equivalence. The method is designed to identify treatment-interactive coordinates that are minimal and non-redundant, not merely variables that improve prediction of $\bm W^{\mathrm{dir}} \in \mathbb R^r$1.

5. Empirical validation and policy applications

The paper evaluates NEXIS in both semi-synthetic and applied settings. The semi-synthetic benchmark is based on CelebA images as high-dimensional pre-treatment covariates. Two known binary attributes, Wearing Hat and Eyeglasses, are designated as ground-truth direct modifiers. Images are embedded with SigLIP patch tokens, then a TopK SAE with $\bm W^{\mathrm{dir}} \in \mathbb R^r$2 is learned. The outcome is generated as

$\bm W^{\mathrm{dir}} \in \mathbb R^r$3

This produces a setting with known ground-truth modifier structure.

The reported findings are that NEXIS achieves high recall and precision as either sample size $\bm W^{\mathrm{dir}} \in \mathbb R^r$4 or effect size $\bm W^{\mathrm{dir}} \in \mathbb R^r$5 grows, while marginal screening loses precision as power increases, confirming the experimental power paradox. Sparse post-TopK codes outperform dense pre-activations, $\bm W^{\mathrm{dir}} \in \mathbb R^r$6 sparse coding outperforms a too-sparse $\bm W^{\mathrm{dir}} \in \mathbb R^r$7 configuration, and the linear interaction test outperforms more flexible GCM tests when the true heterogeneity is linear in the learned representation. The paper also reports that FWER and FDR are similar when $\bm W^{\mathrm{dir}} \in \mathbb R^r$8 is small, whereas omitting correction inflates false positives. In the easiest synthetic settings the backward step is empirically near-neutral because the learned dictionary is nearly orthogonal, although it remains theoretically important (Cadei et al., 15 Jun 2026).

The applied studies concern two anti-poverty programs in Africa. In both cases, standard survey data are augmented with satellite imagery, embedded by Prithvi-EO, dictionary-learned by a TopK SAE, and then searched by NEXIS.

Study	Candidate representation	Selected modifiers
YOP in Uganda	Active SAE atoms, spectral indices, survey covariates	Perennial river presence; vegetation spatial heterogeneity; NDVI / vegetation greenness; structured agricultural landscape; three ethnolinguistic-group interactions
LEAP 1000 in Ghana	131 learned atoms plus 24 household covariates	Ephemeral waterways; closed-canopy forest

In Uganda, the Youth Opportunities Program application yields distinct modifier sets for different outcomes. For skilled employment, NEXIS selects three ethnolinguistic-group interactions and two satellite-derived environmental modifiers: perennial river presence and vegetation spatial heterogeneity. For business assets, it selects NDVI / vegetation greenness and structured agricultural landscape. The substantive interpretation offered in the paper is that skilled-employment effects are dampened in regions with viable subsistence outside options such as fishing or bush-based livelihoods, while business-asset effects are amplified in greener productive landscapes and dampened in areas with more structured incumbent agriculture. A notable empirical result is that demographic covariates do not survive selection, suggesting that impact heterogeneity in this setting is primarily environmental rather than demographic (Cadei et al., 15 Jun 2026).

In Ghana, the LEAP 1000 study is not a pure RCT but a quasi-experimental setting based on RDD plus DiD local ATT logic. The paper extends its argument under conditional parallel trends and local as-if randomization near the cutoff. From 131 learned atoms and 24 household survey covariates, NEXIS selects two satellite-derived modifiers and no demographic covariates: ephemeral waterways and closed-canopy forest. The interpretation advanced in the paper is that seasonal water corridors may enable households to convert transfers into irrigation-season agriculture, while forest-edge households may have complementary non-timber livelihood opportunities. The estimated effects in these active communities are reported to be many times larger than the overall average effect. Temporal VLM analysis is described as supporting the waterways interpretation by showing cropland expansion and denser riparian vegetation between baseline and endline (Cadei et al., 15 Jun 2026).

Across both African applications, the absence of demographic discoveries is treated as substantively informative rather than as a null result. The paper’s reading is that, within the targeted poor populations studied, environmental context appears to dominate household-demographic variables as a source of treatment-effect heterogeneity.

6. Adjacent methods, conceptual boundaries, and limitations

NEXIS is positioned against three literatures. First, flexible black-box HTE estimators such as causal forests, generalized random forests, BART, meta-learners, and deep HTE models can estimate $\bm W^{\mathrm{dir}} \in \mathbb R^r$9, but they do not generally recover a minimal causal heterogeneity characterization. Second, interpretable subgroup and rule-based methods can provide readable partitions, but they usually operate on curated structured covariates and do not distinguish direct modifiers from proxies or common-cause companions. Third, representation-based deep methods can ingest images or text, but typically remain black-box with respect to the effect modifiers they rely on (Cadei et al., 15 Jun 2026).

Several nearby works illuminate NEXIS by contrast. "Neural Network-based Partial-Linear Single-Index Models for Environmental Mixtures Analysis" introduces an interpretable neural single-index mixture model, NeuralPLSI, in which exposures are compressed into

$$\tau(\bm w) := \mathbb E[\tau \mid \bm W^{\mathrm{dir}} = \bm w] \qquad \forall \bm w \in \mathrm{supp}(\bm W^{\mathrm{dir}}),$$0

and passed through a nonlinear univariate link $$\tau(\bm w) := \mathbb E[\tau \mid \bm W^{\mathrm{dir}} = \bm w] \qquad \forall \bm w \in \mathrm{supp}(\bm W^{\mathrm{dir}}),$$1. That framework can accommodate nonlinearity and some implicit interaction through a one-dimensional index, but it does not estimate explicit pairwise terms, rank interactions, or recover an interaction set or graph. It is therefore conceptually related to interpretable neural mixture modeling, but not a direct exposure interaction search method in the NEXIS sense (Do et al., 12 Dec 2025).

Bhaskar Mitra’s dissertation on exposure-aware information retrieval treats exposure as rank-dependent visibility and develops stochastic learning-to-rank for target exposure. Its relevance is conceptual: it formalizes exposure allocation as an optimization target in neural search systems. However, its notion of exposure concerns document visibility in IR, not treatment-effect heterogeneity or causal modifier discovery (Mitra, 2020).

"Efficient Neural Interaction Function Search for Collaborative Filtering" studies search over user-item interaction functions in recommendation. It is relevant as an interaction-function NAS design, especially in its micro/macro decomposition and one-shot bilevel optimization, but it does not model exposure, propensity, or causal treatment interaction (Yao et al., 2019). "Model Selection for Exposure-Mediator Interaction" is closer in scientific target: it develops XMInt, a high-dimensional, hierarchy-preserving selector for $$\tau(\bm w) := \mathbb E[\tau \mid \bm W^{\mathrm{dir}} = \bm w] \qquad \forall \bm w \in \mathrm{supp}(\bm W^{\mathrm{dir}}),$$2 interactions in linear mediation models. XMInt offers a classical template for exposure-centered interaction search, but its formulation is linear, mediation-specific, and does not use learned representations or Markov blanket recovery (Li et al., 2023). "NEX: Neuron Explore-Exploit Scoring for Label-Free Chain-of-Thought Selection and Model Ranking" uses “exposure” and “interaction” language in a different sense, detecting newly activated neurons and their reuse across exploration and exploitation phases. It is a white-box scorer for reasoning traces and model variants rather than a causal HTE discovery method (Chen et al., 5 Feb 2026).

The limitations of NEXIS are mostly assumption-driven. If Measurement Sufficiency fails, no method can recover the true causal heterogeneity from the available measurements. If Representation Sufficiency fails, the encoder discards relevant HTE signal. If Principal Alignment fails, the target of discovering one dominant coordinate per direct modifier becomes ill-posed. The method also inherits the strengths and weaknesses of its conditional tests: linear interaction tests are powerful under approximately linear residual heterogeneity, whereas GCM-style tests are more robust but more data-hungry and computationally expensive. The selection stage itself is reported to take minutes on CPU once the candidate dictionary is built, but foundation-model embedding extraction, SAE training, and VLM-based interpretation are the major computational costs. The paper also notes open problems around multilevel testing in field data and the fact that identifying the joint interventional characterization does not automatically identify all marginal intervention effects on individual modifiers unless additional independence or no-interaction conditions hold (Cadei et al., 15 Jun 2026).

Taken together, these boundaries define NEXIS as a causal feature-discovery algorithm for HTEs rather than a general-purpose HTE predictor. Its distinctive claim is that modern pretrained representations and sparse dictionaries make it possible to search for latent direct treatment interactors in a way that is simultaneously expressive, interpretable, and, under stated assumptions, causally meaningful (Cadei et al., 15 Jun 2026).