TeaPT: Disambiguation Across Research Domains

• TeaPT is a polysemous research term with varied meanings in causal inference, educational AI, and materials modeling.
• In causal inference, TeaPT involves transporting treatment effects across time using semiparametric estimators and temporal scaling factors.
• In educational AI, TeaPT supports teaching excellence via LLM-powered conversational systems employing Socratic and Narrative approaches.

Searching arXiv for “TeaPT” and the cited papers to ground the article. TeaPT is an ambiguous label used in distinct research contexts rather than a single established technical term. In the material associated with recent arXiv papers, it appears in at least four different ways: as shorthand for transporting treatment effects across time in the TEA-Time framework (Parikh et al., 7 Mar 2026), as the acronym for “Teaching Excellence and Pedagogical Transformation,” an instructor-facing LLM system for pedagogical development (Chen et al., 15 Sep 2025), as a TeaNet-based “Tensor Embedded Atom Potential” in atomistic modeling derived from TeaNet (Takamoto et al., 2019), and as an informal shorthand that is explicitly not the official name of the method “Test-time Energy Adaptation” (TEA) (Yuan et al., 2023). The term therefore requires contextual disambiguation before technical interpretation.

1. Terminological scope and disambiguation

The most immediate fact about TeaPT is that it is not used uniformly across the cited literature. In the TEA-Time paper, the supplied summary explicitly states that it is “tailored for TeaPT (transporting treatment effects across time),” thereby using TeaPT as a label for a causal-inference problem setting centered on temporal transportation of treatment effects (Parikh et al., 7 Mar 2026). In the pedagogical LLM study, TeaPT is expanded as “Teaching Excellence and Pedagogical Transformation” and denotes a concrete conversational system for higher-education instructors (Chen et al., 15 Sep 2025). In the materials-science summary derived from TeaNet, TeaPT is introduced as “Tensor Embedded Atom Potential,” i.e., a TeaNet-based universal neural network interatomic potential (Takamoto et al., 2019).

By contrast, the paper on Test-time Energy Adaptation states that “TeaPT” is not an official term used in that paper. The method introduced there is TEA, and any appearance of “TeaPT” is best understood only as a shorthand for applying TEA to large pre-trained models at test time (Yuan et al., 2023). This makes TeaPT a polysemous label whose meaning is field-dependent.

This suggests that TeaPT is best treated encyclopedically as a disambiguation-sensitive research term spanning causal inference, AI for education, atomistic machine learning, and informal naming around test-time adaptation.

2. TeaPT as transporting treatment effects across time

In causal inference, TeaPT refers to transporting treatment effects across time within the TEA-Time framework, whose formal objective is temporal transportation: extrapolating treatment effects to time periods where no experiment was conducted (Parikh et al., 7 Mar 2026). The paper targets the transported average treatment effect (TATE), defined for a trial $k^\star$ as the average treatment effect that would have been observed in the trial population had treatment and measurement occurred at shifted times:

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$

The central structural assumption is the separable temporal effects assumption:

$$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$

with $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$. Under this assumption, the individual treatment effect separates into a unit-specific component and a common temporal modifier, yielding the decomposition

$$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$

The observed ATE and the transported ATE therefore differ only by a temporal ratio (Parikh et al., 7 Mar 2026).

Two identification strategies are developed. The first uses replicated trials comparing the same treatment pair across time. Under the replicated-trials assumptions, for trials $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$,

$$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$

The second uses a common treatment arm across time and adds the measurement-time structure assumption $\Lambda(t_0,t_1)=\Lambda(t_1)$. Under the common-arm assumptions,

$\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$

The first strategy is more flexible because it allows $\Lambda(t_0,t_1)$, whereas the second is more restrictive but potentially more efficient (Parikh et al., 7 Mar 2026).

The framework proceeds semiparametrically. For i.i.d. data $$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$0, the nuisance functions are

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$1

The marginal mean $$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$2 has efficient influence function

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$3

and the trial ATE has influence function

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$4

The paper then derives efficient influence functions for the TATE under both strategies and constructs plug-in doubly robust estimators using cross-fitted nuisance estimates (Parikh et al., 7 Mar 2026).

The doubly robust score is

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$5

and the TATE estimators are

$$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$6

With $$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$7-fold cross-fitting, these estimators are asymptotically linear, doubly robust, and semiparametrically efficient when all models are correct (Parikh et al., 7 Mar 2026).

3. Empirical behavior of temporal TeaPT

The TEA-Time paper studies TeaPT in both Monte Carlo experiments and an empirical A/B-testing application. In the simulation design, the temporal modifier satisfies $$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$8 with $$\tau(a_{k^\star},b_{k^\star},t_{0k^\star},t_{1k^\star},\delta_0,\delta_1) = \mathbb{E}\left[ Y_{t_{1k^\star}+\delta_1}(a_{k^\star},t_{0k^\star}+\delta_0) - Y_{t_{1k^\star}+\delta_1}(b_{k^\star},t_{0k^\star}+\delta_0) \mid S=k^\star \right].$$9, there are $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$0 trials, the target trial compares treatment $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$1 versus control at $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$2, and transport is to $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$3 with true $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$4. Nuisance models use gradient boosting with 5-fold cross-fitting; sample sizes are $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$5 with $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$6 replications (Parikh et al., 7 Mar 2026).

Across these experiments, near-nominal coverage is reported for the estimators. The paper states that Strategy 2, the common-arm approach, reduces RMSE by approximately $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$7 relative to Strategy 1 when the measurement-time-only assumption holds, and that the multi-anchor combination is slightly better than single-arm variants. The stated reason is that Strategy 2 estimates ratios from conditional means, which have lower variance than treatment contrasts (Parikh et al., 7 Mar 2026).

The applied case study uses the Upworthy Research Archive, containing more than 22,000 headline A/B tests from 2013–2015 with click-through rate as the outcome. Tests with detected randomization issues from June 2013 to January 2014 are excluded. Because treatments are unique headlines, recurring arms across time are created by clustering semantically similar headlines using Sentence-BERT embeddings with constrained clustering via Hungarian assignment, yielding 50 headline clusters appearing across multiple months (Parikh et al., 7 Mar 2026).

Two target trials from late 2013 and early 2014 are transported to later months in 2014. Strategy 1 uses replicated cluster-pair trials across months; Strategy 2 uses common arms across months and combines multiple anchors with inverse-variance weighting. The empirical findings expose a variance-bias tradeoff. Strategy 2 yields substantially smaller standard errors than Strategy 1: mean standard error $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$8 versus $$Y_{t_1}(a,t_0)=\theta_a(X)\cdot \Lambda(t_0,t_1)+\epsilon_{t_1},$$9 for Trial A, and $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$0 versus $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$1 for Trial B. However, Strategy 2 shows systematic bias, with estimates nearly constant across months while the true TATE varies and even changes sign in some months. Strategy 1, despite wider confidence bands, better tracks monthly dynamics, with correlation to the true TATE of $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$2 versus $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$3 for Trial A and $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$4 versus $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$5 for Trial B. The trial-level summaries are also reported: for Trial A, RMSE $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$6 versus $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$7 and Bias $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$8 versus $\mathbb{E}[\epsilon_{t_1}\mid X,A]=0$9 for Strategy 1 versus Strategy 2; for Trial B, RMSE $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$0 versus $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$1 and Bias $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$2 versus $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$3 (Parikh et al., 7 Mar 2026).

The interpretation offered is that bias in Strategy 2 indicates violation of the measurement-time structure assumption. In the Upworthy setting, treatment effects may depend on time since administration, such as headline novelty decay, implying that $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$4 depends on both $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$5 and $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$6 rather than only on $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$7 (Parikh et al., 7 Mar 2026).

4. Assumptions, diagnostics, and methodological position of temporal TeaPT

The TEA-Time framework is defined by a layered assumption structure. Beyond random assignment and SUTVA, the key untestable ingredient is separability, which posits multiplicative, rank-one temporal scaling common across units and treatments (Parikh et al., 7 Mar 2026). The paper explicitly states that separability is fundamentally untestable from observed-time data, though it may be probed indirectly by checking whether multiple anchors identify congruent temporal ratios.

For Strategy 2, the paper provides a specification test for the measurement-time-only assumption. If $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$8 anchor arms are available, and $$\tau_{k^\star}(\delta_0,\delta_1) = \tau_{k^\star}(0,0)\cdot \frac{\Lambda(t_{0k^\star}+\delta_0,t_{1k^\star}+\delta_1)} {\Lambda(t_{0k^\star},t_{1k^\star})}.$$9 is a contrast matrix, then

$\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$0

Rejection suggests that $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$1 depends on intervention timing, whereas lack of rejection does not establish the assumption because the test has power only when anchors yield detectably different ratios (Parikh et al., 7 Mar 2026).

The paper also states clear regularity and nuisance-rate conditions. Overlap requires $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$2 and $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$3 almost surely for some $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$4; bounded fourth moments are required; and non-degeneracy requires either $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$5 in Strategy 1 or $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$6 in Strategy 2. The nuisance estimators must satisfy

$\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$7

Under these conditions, asymptotic normality, double robustness, and semiparametric efficiency follow (Parikh et al., 7 Mar 2026).

Methodologically, TeaPT is distinguished from ordinary transportability across populations. Standard cross-population transport relies on observed covariates in source and target domains and adjusts for distributional shift through reweighting or covariate adjustment. Temporal transportation, by contrast, cannot observe outcomes at the target time by design; it instead requires structural assumptions about how effects vary over time. The TEA-Time framework uses anchor trials, possibly with different interventions, to identify temporal scaling factors and thereby extrapolate to unobserved timing configurations (Parikh et al., 7 Mar 2026).

A practical implication drawn in the paper is that Strategy 2 is preferable when common arms are frequent and the measurement-time-only assumption is plausible, whereas Strategy 1 is preferable when replicated comparisons exist or when treatment effects are expected to depend on both administration and measurement timing. Comparing the two strategies functions as a diagnostic for potential violation of the simpler temporal structure (Parikh et al., 7 Mar 2026).

5. TeaPT as Teaching Excellence and Pedagogical Transformation

In AI for education, TeaPT denotes “Teaching Excellence and Pedagogical Transformation,” an instructor-facing, LLM-powered conversational system designed to support higher-education instructors’ professional development (Chen et al., 15 Sep 2025). Its target users include faculty, teaching assistants, and staff seeking support for classroom management, student engagement, and assessment design. The stated goal is to shift LLM interaction away from direct answer delivery toward reflective diagnosis, reason exploration, and strategy planning.

The system is grounded in dialogic learning and externalized cognition. It adapts the Eberly Center’s three-step problem-solving framework—Identify the Problem, Explore Reasons, Develop Strategies—preceded by a contextual step, Greeting & Teaching Background. It is also grounded in the faculty-development resources Small Teaching and Small Teaching Online (Chen et al., 15 Sep 2025).

TeaPT implements two distinct conversational approaches. The Socratic approach uses guided questioning to scaffold reflection and metacognition. It is operationalized by a fine-tuned Llama-2-13b-chat-hf model conditioned on special step tokens <step>...</step> indicating the current phase, together with a system prompt that enforces probing-question starters, variation in phrasing, and a turn-management protocol. The representative prompt requires the model to determine whether the interaction is in Step 0, 1, 2, or 3 and to begin each response with a step marker (Chen et al., 15 Sep 2025).

The Narrative approach uses elaborated lists of strategies, examples, and mini-plans to support fast idea generation and immediate planning. It is implemented through calls to ChatGPT (gpt-4o-mini) with prompts framing the assistant as an experienced teaching expert. Responses are typically structured as lists, plans, or templates (Chen et al., 15 Sep 2025).

The overall architecture has three components: onboarding with progressive data collection and optional skipping; a chatbot interface with a text box, conversation sidebar, and challenge-to-course association; and a dashboard containing resources, data management, and scheduling for human consultations. After each conversation, ChatGPT summarizes the primary challenge and generates a tailored resource such as a rubric or quiz template, which is saved to the dashboard. A separate prompt analyzes transcripts to fill missing profile fields under explicit guardrails, including JSON structure, confidence and reasoning fields, and a rule excluding studentChallenges from the profile (Chen et al., 15 Sep 2025).

The system was designed around three needs surfaced in formative work with pedagogy experts: accommodating diverse AI attitudes and readiness through transparency and progressive data collection; emphasizing scaffolding rather than direct answers; and fostering calibrated trust by avoiding authoritative claims and linking to human experts and verifiable resources (Chen et al., 15 Sep 2025).

6. Evaluation of pedagogical TeaPT and profile-sensitive interaction

TeaPT was evaluated in a mixed-method within-subject Zoom study in August 2025. Each of the 41 higher-education instructors used both versions for 10 minutes each on the same teaching challenge, with order counterbalanced, followed by immediate surveys and a 15-minute semi-structured interview. The sample consisted of 22 faculty and 19 TAs/staff, with experience tiers from 0–1 years to 10+ years, and AI attitudes evenly split between “Open and Optimistic” and “Curious but Cautious” (Chen et al., 15 Sep 2025).

The quantitative evidence shows a strong behavioral difference between the two conversational modes. For the 39 successfully saved logs, the Socratic version yielded a median user message count of $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$8 versus $\ell,\ell'\in \mathcal{K}(a^\*,b^\*)$9 for Narrative, with Wilcoxon signed-rank $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$0 and median increase of $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$1 messages. User word count was also higher in Socratic: mean $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$2 versus $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$3, with paired $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$4, $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$5, and mean difference $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$6 words. By contrast, chatbot response word count was much larger in Narrative: mean $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$7 versus $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$8, with a median difference of $$\frac{\Lambda(t_0,t_1)}{\Lambda(t_0',t_1')} = \frac{\tau_\ell(0,0)}{\tau_{\ell'}(0,0)}.$$9 words when computed as Socratic minus Narrative (Chen et al., 15 Sep 2025).

On the 1–3 survey scales, most dimensions were statistically similar, including Clarity of Expression, Supportive & Appropriate Tone, Appropriateness of Validation, and Reflective Prompting. The exception was Actionable Guidance, which favored Narrative with $\Lambda(t_0,t_1)=\Lambda(t_1)$0, $\Lambda(t_0,t_1)=\Lambda(t_1)$1, median paired difference $\Lambda(t_0,t_1)=\Lambda(t_1)$2, and Hodges–Lehmann 95% CI $\Lambda(t_0,t_1)=\Lambda(t_1)$3 (Chen et al., 15 Sep 2025).

The subgroup analyses indicate moderation by both teaching experience and AI attitude. Junior instructors with 0–2 years of experience showed a larger increase in conversation turns for Socratic versus Narrative than seasoned instructors with 3+ years: mean difference $\Lambda(t_0,t_1)=\Lambda(t_1)$4 versus $\Lambda(t_0,t_1)=\Lambda(t_1)$5 turns, $\Lambda(t_0,t_1)=\Lambda(t_1)$6, $\Lambda(t_0,t_1)=\Lambda(t_1)$7, Holm $\Lambda(t_0,t_1)=\Lambda(t_1)$8. Curious but Cautious participants strongly favored Narrative on Actionable Guidance, with mean difference $\Lambda(t_0,t_1)=\Lambda(t_1)$9 and 93% preferring Narrative; Open and Optimistic participants leaned toward Socratic on Supportive Tone and Reflective Prompting. Among high-YOE instructors, Narrative preference on Actionable Guidance was especially strong, with median difference $\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$0, 75% preferring Narrative, and signed-rank $\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$1 after Holm correction (Chen et al., 15 Sep 2025).

The content analyses reinforce the interactional contrast. Topic 6, defined by terms such as “class, discussions, material, practice, retrieval,” was substantially more prevalent in Socratic, with $\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$2, $\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$3, Cliff’s $\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$4, and an average of 63.5% of Socratic content in that topic. Topics 2 and 3 were more prevalent in Narrative. Sentiment analysis showed no tone differences (Chen et al., 15 Sep 2025).

Qualitatively, Socratic dialogue was described as “like talking to a human pedagogy consultant” and as prompting reflection and self-explanation, whereas Narrative was valued for producing many concrete options quickly but also criticized for possible overload. The study reports that preference counts favored Narrative overall, 21 versus 13 for Socratic, but learning attribution in interviews more often favored Socratic, 18 versus 13, with exact agreement only 39%. The authors therefore argue for adaptive systems offering both styles, although dynamic adaptation was not implemented in the evaluated system (Chen et al., 15 Sep 2025).

7. Other uses of the TeaPT label: atomistic potentials and informal TEA shorthand

A third use of TeaPT appears in atomistic machine learning as “Tensor Embedded Atom Potential,” a TeaNet-based universal neural network interatomic potential associated with the TeaNet architecture (Takamoto et al., 2019). In this setting, TeaPT refers to a model intended to provide accurate energies and forces across arbitrary chemistries involving the first 18 elements, H to Ar. Its core architectural idea is to let scalar, vector, and Euclidean rank-2 tensor channels flow through a deep graph convolutional network, thereby translating angular interactions into graph convolution and mimicking iterative electronic relaxation. The TeaNet formulation uses 16-layer residual graph convolution with recurrent weight initialization and reports an energy mean absolute error of 19.3 meV/atom and force mean absolute error of 0.142 eV/Å for the 16-layer model; removing tensor channels degrades performance to 25.5 meV/atom and 0.190 eV/Å, highlighting the importance of rank-2 tensor transport (Takamoto et al., 2019). This use of TeaPT is domain-specific and unrelated to either temporal causal transport or pedagogical LLM design.

A fourth usage is negative or corrective rather than positive: in the Test-time Energy Adaptation paper, TeaPT is explicitly identified as a non-official term. The official method name is TEA, an energy-based test-time adaptation method that reinterprets a classifier as an energy-based model and adapts only normalization-layer parameters using unlabeled test data (Yuan et al., 2023). The paper notes that if TeaPT appears in this context, it should be understood only as shorthand for applying TEA to large pre-trained models at test time. TEA itself defines

$\frac{\Lambda(t_{1k^\star}+\delta_1)}{\Lambda(t_{1k^\star})} = \frac{\mathbb{E}[Y_{t_{1\ell}}\mid A=c^\*,S=\ell]} {\mathbb{E}[Y_{t_{1\ell'}}\mid A=c^\*,S=\ell']}.$5

and uses contrastive divergence with SGLD-generated negative samples for test-time adaptation, but this is a separate method with separate nomenclature (Yuan et al., 2023).

Taken together, these usages show that TeaPT does not designate a stable cross-field concept. In causal inference it names a temporal transport problem, in educational AI it is the title of an instructor-support system, in materials modeling it denotes a tensor-based interatomic potential, and in test-time adaptation it is an informal shorthand rejected by the primary paper. A plausible implication is that any technical discussion of TeaPT should begin by fixing the intended expansion and research domain before substantive analysis.