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A Factorized Probabilistic Model of the Semantics of Vague Temporal Adverbials Relative to Different Event Types

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper claims that the contextual meaning of vague temporal adverbials like "recently" and "just" is captured by a factorized probabilistic model that composes a fixed per-adverbial Gaussian with a per-event Gaussian cumulative…

desk verdict Clean factorization of temporal adverbial semantics, but the parity claim is in-sample goodness-of-fit, not held-out prediction. read the letter →

arxiv 2505.01311 v2 pith:YWLIMAB2 submitted 2025-05-02 cs.CL

Svenja Kenneweg , Jörg Deigmöller , Julian Eggert , Philipp Cimiano This is my paper · ORCID
classification cs.CL
keywords vaguetemporaladverbialscompositionalsemanticsprobabilisticreferenceclasseventtypesGaussiandistributionsvaguenessreasoning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the contextual meaning of a vague temporal adverbial such as "recently" or "just" can be captured by composing two fixed probabilistic parts: an event-specific Gaussian cumulative distribution that encodes how an event's temporal signature scales with elapsed time, and an adverbial-specific Gaussian density that maps that scaled value to a felicity probability. Fitted to native-speaker judgments for six events and four adverbials, this factorized model predicts applicability ratings about as well as a non-factorized baseline that learns a separate Gaussian for every event–adverbial pair, with an average absolute error of 0.2 in both cases. The paper argues that the factorized model is preferable on simplicity and extendability grounds: adding an event or adverbial costs one new function instead of a whole row or column of pairwise functions. The point of the model is to show that reference classes for vague predicates can be treated compositionally rather than as pairwise context effects.

What carries the argument

The central object is the composition $P_{\mathrm{Adv}}(P_{\mathrm{Ev}}(t))$: a per-event Gaussian cumulative distribution $P_{\mathrm{Ev}}(t)=\frac12(1+\operatorname{erf}(t/(\sqrt{2}\sigma_e)))$ feeds into a per-adverbial Gaussian density $\exp\left(-\frac12\left((x-\mu_a)/\sigma_a\right)^2\right)$. The event function carries the reference-class information — brushing teeth gets a small $\sigma_e$ (935 minutes), marriage a large one (about 2.3 million minutes) — while each adverbial gets one fixed $(\mu_a,\sigma_a)$ pair across all events. The factorization is what makes the model compositional: the adverbial's prototype does not change from event to event; only the event's scaling changes.

What would settle it

Fit event-specific standard deviations on one half of the rating data while holding adverbial parameters fixed, then test the factorized model on held-out events: if its prediction error exceeds the per-pair baseline's error by more than fitting noise, the factorization assumption fails. A simpler check is to collect ratings for a new event whose frequency and duration are known, fit only its $\sigma_e$, and test whether the predicted probabilities for all four adverbials match observed ratings within the same 0.2 error range.

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Extended reading notes

Core claim

The central claim is that the probability that a vague temporal adverbial Adv felicitously applies to an event Ev that happened t time units ago is $P_{\mathrm{Adv}}(P_{\mathrm{Ev}}(t))$. Here $P_{\mathrm{Ev}}$ is a Gaussian cumulative distribution with a single free parameter $\sigma_e$ per event, and $P_{\mathrm{Adv}}$ is a Gaussian density with a fixed mean and standard deviation per adverbial. Fitted jointly to survey data, this factorized model reaches an average absolute prediction error of 0.2, identical to a baseline that fits one Gaussian to each event–adverbial pair. The paper concludes that the adverbial's temporal meaning can remain fixed while event properties reshape it through a single event-specific scale parameter, so that the reference class of a vague predicate is modeled compositionally in the Fregean sense.

Load-bearing premise

The model assumes that a one-parameter Gaussian cumulative distribution per event, combined with a fixed Gaussian density per adverbial, fully captures how event type and adverbial meaning interact; both functional forms are stipulated rather than derived from linguistic theory or independently validated.

Editorial extensions

If this is right

  • Adding a new event to the factorized model requires one new event function rather than one per adverbial; with 16 events and 16 adverbials, the factorized model needs 32 functions versus 256 for the non-factorized baseline.
  • The model predicts applicability ratings as accurately as the per-pair baseline despite having fewer parameters, offering a simpler explanation of how event duration and frequency shape adverbial meaning.
  • Each fitted event receives a distinct standard deviation, consistent with the claim that events carry characteristic temporal signatures tied to frequency and duration.
  • Because adverbial parameters are shared across events, the model implies that "just" and "recently" have stable core meanings that are stretched or compressed by the event context.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable prediction follows: events with similar frequency and duration should receive nearly identical event functions; if their fitted $\sigma_e$ values diverge sharply, the event signature is not fully captured by duration and frequency alone.
  • The factorized structure could be used to predict ratings for unseen event–adverbial combinations by interpolating $\sigma_e$ from event properties, an extension the paper notes would require future work to avoid collecting new survey data.
  • The same composition applies to other vague predicates with reference classes, such as spatial adverbials or adjectives, because it only assumes a prototype-based modifier and a reference-class scaling function.
  • Since both models share the same 0.2 average error on the fitted data, the paper's preference for the factorized model rests on parsimony; a stricter test would hold out entire events or adverbials and compare generalization error.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a factorized probabilistic model of vague temporal adverbials such as 'just', 'recently', 'some time ago', and 'long time ago' when applied to different event types. The model represents each adverbial by a Gaussian function and each event by a Gaussian cumulative distribution function, composing them as P_adv(P_ev(t)) to predict the probability that a speaker would use a given adverbial for an event that occurred t time units ago. Parameters are fitted by least squares to survey data from Kenneweg et al. (2024) covering 6 events, 4 adverbials, and 7 elapsed times. The paper evaluates the factorized model against a non-factorized baseline that fits one Gaussian per event-adverbial pair, reporting that both achieve an average absolute error of 0.20 and that the factorized model is preferable by Occam's razor and easier to extend. The main claimed contributions are the compositional treatment of the reference class and the parameter-efficiency of the factorization.

Significance. If the central parity claim were supported by proper out-of-sample evaluation, the paper would make a useful contribution to the semantics of vague temporal expressions. The idea of separating a fixed adverbial distribution from an event-specific reference-class distribution is linguistically plausible, and the paper connects this to prototype theory and the epistemic view of vagueness in a way that goes beyond existing treatments of adjectives. The use of existing empirical data and the explicit comparison to a non-factorized baseline are also strengths. However, the current evidence for the main claim is in-sample, so the paper's contribution is not yet established; the modeling framework is interesting, but the evaluation needs to be redone with held-out data before the stated conclusions can be accepted.

major comments (4)
  1. [Evaluation, Table 3; Model Fitting] The accuracy comparison is in-sample. The model parameters are fitted by least-squares on the survey data described in the Model Fitting section, and the same data are then used to compute the 'average prediction error' reported in Table 3. These numbers are residuals of the fit, not out-of-sample prediction errors. With 14 free parameters in the factorized model and 48 in the non-factorized baseline, a difference of 0.20 versus 0.20 (rounded) on the training data does not establish that the two models have comparable predictive accuracy. The Conclusion's claim that the compositional approach 'matches the predictive accuracy of a non-factorized baseline model' is therefore not supported. The paper should report cross-validated errors, a train/test split, or at least a model-selection criterion such as AIC or BIC to support the parity claim.
  2. [Evaluation, Accuracy subsection; Table 3] No uncertainty quantification is reported for the error values. For example, the per-adverbial errors for 'Just' (0.16 vs. 0.15) and 'Long time ago' (0.18 vs. 0.20) are presented without confidence intervals or significance tests, so the reader cannot tell whether the differences reflect real model behavior or sampling noise. Since the overall values are rounded to two decimals and the data consist of 100 judgments per condition, a bootstrap or per-condition variance estimate is needed before any comparative statement about accuracy is made.
  3. [Compositional Model; Model Fitting] The functional forms of the two components are assumed rather than derived or independently validated. The event function is fixed as a one-parameter Gaussian CDF with a single sigma_e, and the adverbial function is fixed as a Gaussian in the CDF value. These choices are not justified by linguistic theory or by comparison with alternative forms (e.g., log-normal or Weibull CDFs for events, or a logistic function for adverbials). The factorization assumption itself—that the adverbial parameters and event parameters interact only through the composition P_adv(P_ev(t))—is also untested. A concrete test would be to fit a more flexible model that allows event-dependent adverbial means or interaction terms and compare held-out predictive accuracy; without such a test, the central structural claim remains an assumption.
  4. [Evaluation, Extendability subsection; Discussion] The extendability argument is only a parameter-count comparison. Table 4 shows the number of functions needed for x events and y adverbials, but the paper does not demonstrate that the factorized model can actually be extended to a new event or adverbial without collecting new survey data. The Discussion concedes that inducing parameters for new adverbials and events would require additional data from a study like Kenneweg et al. (2024). Thus, 'easier to extend to new events and adverbials' in the Conclusion overstates what the paper shows; the practical advantage in data cost is not quantified or tested.
minor comments (5)
  1. [Introduction] There is a typo in 't times unites ago' in the Introduction; it should read 't time units ago'.
  2. [Compositional Model] The notation P_adv(P_ev(t)) is described as a probability, but P_adv is defined as an unnormalized Gaussian function of the form exp(-0.5((x-mu_a)/sigma_a)^2). This function is not a probability density and its values are not bounded by 1 in general; the paper should clarify whether the output is intended as a degree of applicability rather than a probability, and how the normalization is handled in the least-squares fit.
  3. [Model Fitting] The text says '16.800 data points' with a European decimal separator; the comma should be used consistently (16,800), and the paper should state whether fitting was performed on individual Likert responses or on per-condition means, since this affects the reported errors.
  4. [Model Fitting] The conversion of time units is described only as '1Month corresponding to 43800 minutes'; the paper should state the exact set of elapsed times used in the survey (e.g., minutes, hours, days, months, years) so that the fitted sigma_e values in Table 1 can be interpreted.
  5. [References] Some references are incomplete or inconsistently formatted (e.g., Bouraoui and Schockaert 2018 lacks a venue or page range; Qing and Franke 2014 lists a volume but no pages). These should be checked against the publisher's records.

Circularity Check

1 steps flagged · score 6.0 of 10

The central parity claim rests on in-sample fit residuals, not held-out prediction: Table 3's 'predicted value' is produced by parameters fitted to the same votes it is compared against.

  1. fitted input called prediction [Model Fitting; Evaluation, Accuracy (Table 3)]
    "For fitting, we used least-squares optimization to minimize the residuals, i.e., the difference between the observed and modeled probabilities. ... To evaluate the accuracy, we predict an adverbial's probability for a given elapsed time point of an event using our model and compute the average absolute difference between the predicted value and all votes from the empirical data."

    The parameters of P_Adv and P_Ev are obtained by least-squares fitting against the Kenneweg et al. (2024) survey votes. The accuracy evaluation then 'predicts' probabilities for the same time points and compares them with 'all votes from the empirical data' — the very data used for fitting. Thus the reported average absolute differences (e.g., 0.20 overall for both models) are residuals of the training fit, not predictions on unseen data. The central claim of equal 'predictive accuracy' therefore reduces by construction to a comparison of in-sample goodness-of-fit; without a train/test split or cross-validation it cannot distinguish generalization from memorisation. This is a fitted input renamed as a prediction.

full rationale

The model parameters are fit by least-squares minimization of residuals between observed and modeled probabilities over all data points (Model Fitting). The accuracy evaluation then 'predicts' the adverbial's probability for the same elapsed time points and computes the average absolute difference against 'all votes from the empirical data' (Evaluation, Accuracy). No train/test split, cross-validation, or uncertainty interval is reported. Therefore the 0.20 vs 0.20 averaged errors in Table 3 are in-sample training errors of the two models, not out-of-sample prediction errors; the claim that the compositional model 'matches the predictive accuracy of a non-factorized baseline model' is not supported by the reported evaluation. The extendability argument in Table 4 is a function count, and the Discussion concedes that inducing parameters for new events/adverbials would require new survey data; this is a limitation rather than a circularity. No other circular steps were found: the Gaussian ansatze are stated assumptions, and the prior self-citation (Kenneweg et al., 2024) is an empirical dataset, not an unverified result that the paper's argument reduces to.

Assumptions & free parameters 14 free parameters · 4 assumptions · 0 invented entities

The model introduces 14 free parameters fitted to the authors' earlier survey data. The Gaussian-CDF form for events and Gaussian-density form for adverbials are assumed, not derived; the factorization itself is the central hypothesis. No new entities (particles, forces, dimensions) are posited.

free parameters (14)
  • sigma_a for Just = 0.04
    Fitted width of the adverbial Gaussian for 'just' on the event-CDF input scale.
  • mu_a for Just = 0.48
    Fitted center of the adverbial Gaussian for 'just'.
  • sigma_a for Recently = 0.09
    Fitted width of the adverbial Gaussian for 'recently'.
  • mu_a for Recently = 0.45
    Fitted center of the adverbial Gaussian for 'recently'.
  • sigma_a for Some time ago = 0.19
    Fitted width of the adverbial Gaussian for 'some time ago'.
  • mu_a for Some time ago = 0.78
    Fitted center of the adverbial Gaussian for 'some time ago'.
  • sigma_a for Long time ago = 0.23
    Fitted width of the adverbial Gaussian for 'long time ago'.
  • mu_a for Long time ago = 1.00
    Fitted center of the adverbial Gaussian for 'long time ago'.
  • sigma_e for Brushing Teeth = 935 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the brushing teeth event.
  • sigma_e for Birthday = 314830 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the birthday event.
  • sigma_e for Vacation = 396579 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the vacation event.
  • sigma_e for Sabbatical = 798494 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the sabbatical event.
  • sigma_e for Year Abroad = 1240803 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the year abroad event.
  • sigma_e for Marriage = 2334869 minutes
    Fitted per-event standard deviation in the Gaussian CDF for the marriage event.
assumptions (4)
  • domain assumption Vague predicates have crisp but unknown boundaries (epistemic theory of vagueness, Williamson 1998).
    Grounds representing vagueness as probability; invoked in Background and Compositional Model sections.
  • ad hoc to paper The event-specific reference class can be modeled as a Gaussian CDF with a single per-event standard deviation sigma_e.
    Functional form assumed in the Compositional Model section; no derivation or empirical validation of the CDF form is provided.
  • domain assumption Adverbials can be modeled as Gaussian distributions around a prototype, following Bouraoui and Schockaert (2018).
    Imported from prior work; the Gaussian form for P_adv depends on this assumption.
  • ad hoc to paper The composed function P_adv(P_ev(t)) yields the probability of felicitous use, and the event and adverbial functions are independent (factorization).
    This compositional structure is the paper's core proposal; it is assumed rather than derived from theory or data.

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Cite this review

Pith. "Pith review of A Factorized Probabilistic Model of the Semantics of Vague Temporal Adverbials Relative to Different Event Types." pith.science (2026). https://pith.science/paper/YWLIMAB2

@misc{pith2026250501311,
  author       = {Pith},
  title        = {Pith review of: A Factorized Probabilistic Model of the Semantics of Vague Temporal Adverbials Relative to Different Event Types},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YWLIMAB2}},
  note         = {Machine review of arXiv:2505.01311}
}
read the original abstract

Vague temporal adverbials, such as recently, just, and a long time ago, describe the temporal distance between a past event and the utterance time but leave the exact duration underspecified. In this paper, we introduce a factorized model that captures the semantics of these adverbials as probabilistic distributions. These distributions are composed with event-specific distributions to yield a contextualized meaning for an adverbial applied to a specific event. We fit the model's parameters using existing data capturing judgments of native speakers regarding the applicability of these vague temporal adverbials to events that took place a given time ago. Comparing our approach to a non-factorized model based on a single Gaussian distribution for each pair of event and temporal adverbial, we find that while both models have similar predictive power, our model is preferable in terms of Occam's razor, as it is simpler and has better extendability.

Figures

Figures reproduced from arXiv: 2505.01311 by the authors.

Figure 1
Figure 1. Event-specific functions and adverbial-specific functions for all fitted events and adverbials. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

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