{"id":"154960d0-1d33-40e1-96ad-43dcd48af650","arxiv_id":"2505.01311","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":14,"one_line_summary":"Vague temporal adverbials can be modeled as a fixed Gaussian applied to an event-specific Gaussian CDF, matching per-pair model accuracy with far fewer parameters.","lead":"This paper models vague time words like 'recently' and 'just' as a fixed curve combined with an event-specific curve for how long ago feels natural. It argues that this factorized approach matches the accuracy of more complex models while using far fewer parameters.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central parity claim is based on in-sample fit, not held-out prediction; the 'predictive accuracy' wording overstates Table 3, so the claim needs a cross-validation check before it is accepted.","rationale":"I read the paper as claiming that a fixed per-adverbial Gaussian composed with a per-event Gaussian CDF is as accurate as per-pair Gaussians while being simpler. For that claim to hold, the accuracy comparison must be a fair predictive comparison. It is not: Table 3 is computed on the fitting data. This is the load-bearing soft spot because the entire Occam's-razor argument depends on equality of predictive performance; in-sample equality with a more flexible baseline is neither surprising nor decisive. The reader's designated weakest assumption (the Gaussian CDF/density forms) is real but secondary: the functional form could be arbitrary yet still predict well, whereas without held-out evaluation the central empirical claim is unverified. The paper's own Discussion and Conclusion acknowledge that new data would be needed to obtain parameters for additional events/adverbials, which confirms that extendability is a promise, not a demonstrated result. A cross-validation experiment would settle whether the model genuinely generalizes. The paper has value in proposing a clean factorization and in reporting transparent parameter tables, but the strongest claim should be restated as 'comparable in-sample fit and fewer parameters' unless held-out evidence is added. Since this is addressable, CONDITIONAL remains the appropriate verdict.","tokens_in":8826,"tokens_out":10647,"duration_ms":115800,"concrete_test":"Perform stratified 10-fold cross-validation over the 16,800 individual Likert responses (or over the 168 condition means), refitting all parameters of both models on each training fold and computing mean absolute error on the held-out fold. Repeat with bootstrap to get 95% confidence intervals for the difference in held-out MAE. If the factorized model is not significantly worse than the baseline, the parity claim survives; if it is worse, the claim fails. A complementary leave-one-event-out check would test extendability: train the adverbial parameters on five events, fit the held-out event's sigma_e from its own data, and compare against a baseline fitted per pair on that event alone.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim is that the factorized model P_adv(P_ev(t)) 'matches the predictive accuracy of a non-factorized baseline model' (Conclusion). The evidence in Table 3 is the average absolute difference between model predictions and the responses used to fit those same parameters: an in-sample goodness-of-fit measure. No train/test split, cross-validation, or uncertainty interval is reported, and the overall values are rounded to two decimals (0.20 vs 0.20). With 14 parameters for the factorized model and 48 for the baseline, an in-sample comparison cannot establish predictive parity; the equal errors could reflect the coarse 168-condition dataset, model flexibility, or optimization details rather than generalization. The extendability argument in Table 4 is also only a function count: no held-out event or adverbial is added, and the Discussion concedes that inducing parameters for new events/adverbials would require new survey data. Consequently, the central 'simpler and equally predictive' claim is not yet supported by the reported evaluation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9158,"tokens_out":4542,"duration_ms":49478,"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":[{"comment":"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.","section":"Evaluation, Table 3; Model Fitting"},{"comment":"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.","section":"Evaluation, Accuracy subsection; Table 3"},{"comment":"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.","section":"Compositional Model; Model Fitting"},{"comment":"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.","section":"Evaluation, Extendability subsection; Discussion"}],"minor_comments":[{"comment":"There is a typo in 't times unites ago' in the Introduction; it should read 't time units ago'.","section":"Introduction"},{"comment":"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.","section":"Compositional Model"},{"comment":"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.","section":"Model Fitting"},{"comment":"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.","section":"Model Fitting"},{"comment":"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.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses an interesting and understudied phenomenon, and the factorized model is a plausible modeling idea. The main problem is methodological: the central parity claim is based entirely on in-sample residuals, which is not sufficient for the stated conclusion. The fix is straightforward in principle—add cross-validation or held-out evaluation, report uncertainty, and test the factorization assumption more directly—so I recommend major revision rather than rejection. The paper would also benefit from a clearer statement of what counts as 'prediction' versus 'fit' throughout."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nQuick take: the factorization is a genuinely neat idea, and the paper is worth engaging, but the 'predictive accuracy' claim overstates what Table 3 shows. The evaluation is in-sample, so parity with the baseline is a goodness-of-fit result, not a prediction result. The stress-test note is right.\n\nWhat's new: P_adv(P_ev(t)) is a clean compositional form—a fixed per-adverbial Gaussian acting on the output of a per-event Gaussian CDF. That's a new modeling choice for temporal adverbials, and it cuts parameters from 48 to 14 while matching the per-pair baseline's fit. The paper positions its contribution well against reference-class theories of vague adjectives, and it's honest in the Discussion that new events/adverbials would need new survey data.\n\nSoft spots: the central issue is that all parameters are fit with least squares on the same response data used to compute Table 3. Those are residuals of the fit, not predictions on held-out data. The word 'predictive' in the abstract and conclusion is an overstatement. A train/test split or leave-one-event-out cross-validation would fix it. The error differences are also small (0.19 vs 0.18, 0.21 vs 0.22) and no significance test or uncertainty interval is reported, so the parity claim is not quantitatively sharp. The extendability argument in Table 4 is only about counting functions; the authors concede they don't currently know how to set parameters for a new event without collecting new judgments. The functional forms—Gaussian CDF for events, Gaussian density for adverbials—are assumed rather than derived, but that's a modeling choice, not a flaw.\n\nNone of this is fatal. The core factorization is plausible, and the in-sample parity shows the form is expressive enough. The paper needs a proper evaluation before the parity claim is accepted.\n\nWho it's for: computational semanticists and anyone building temporal reference models for dialogue. It deserves a serious referee; I'd send it to review and ask for cross-validation as a condition of acceptance.\n\nBest,","headline":"Clean factorization of temporal adverbial semantics, but the parity claim is in-sample goodness-of-fit, not held-out prediction.","tokens_in":9628,"tokens_out":3769,"would_cite":true,"duration_ms":35552,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["vague temporal adverbials","compositional semantics","probabilistic semantics","reference class","event types","Gaussian distributions","vagueness","temporal reasoning"],"falsifier":"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.","tokens_in":8638,"feed_emoji":"🕰️","tokens_out":4353,"duration_ms":40687,"temperature":0.7,"pith_summary":"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.","feed_headline":"Two functions predict how 'recently' and 'just' scale across events","feed_subtitle":"A per-event and per-adverbial Gaussian pair matches a per-pair baseline at 0.2 average error, with far fewer parameters.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the empirical judgment dataset of native-speaker applicability ratings used for fitting and evaluating both models.","marker":"Kenneweg et al. (2024)"},{"why":"Establishes the linguistic premise that event frequency and duration determine how temporal adverbials are quantified.","marker":"Van Jaarsveld & Schreuder (1985)"},{"why":"Provides the epistemic theory that vague predicates have crisp but unknown boundaries, justifying the probabilistic treatment.","marker":"Williamson (1998)"},{"why":"Grounds the view that vague concepts can be modeled with uncertainty and prototype-based probability distributions.","marker":"Lawry & Tang (2009)"},{"why":"Licenses the use of Gaussian distributions to represent conceptual prototypes, which the adverbial-specific function relies on.","marker":"Bouraoui & Schockaert (2018)"},{"why":"Supplies the principle of compositionality that the factorized model instantiates by combining event and adverbial meanings.","marker":"Frege (1953)"}],"fun_headline_variants":["Single event scale plus fixed adverb PDF matches per-pair fits","Factorized model: one event scale, fixed adverb shapes, fewer parameters","Compositional semantics for vague adverbs via a single scale per event","Event-specific scale reshapes fixed adverb meaning, matching per-pair fits","Fewer parameters, same accuracy: factorized model of vague time words"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Single event scale plus fixed adverb PDF matches per-pair fits","Factorized model: one event scale, fixed adverb shapes, fewer parameters","Compositional semantics for vague adverbs via a single scale per event","Event-specific scale reshapes fixed adverb meaning, matching per-pair fits","Fewer parameters, same accuracy: factorized model of vague time words"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000774,"raw_usage":{"total_tokens":3397,"prompt_tokens":886,"completion_tokens":2511,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":502,"completion_tokens_details":{"reasoning_tokens":2418}},"tokens_in":502,"tokens_out":2511,"duration_ms":16300,"temperature":1.0,"reasoning_tokens":2418,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:20:34.658387+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":", Jackson, B B","cited_arxiv_id":null,"evidence_quote":"Supplies the empirical judgment dataset of native-speaker applicability ratings used for fitting and evaluating both models."},{"cited_title":"\\ Schreuder, R","cited_arxiv_id":null,"evidence_quote":"Establishes the linguistic premise that event frequency and duration determine how temporal adverbials are quantified."},{"cited_title":"APACrefauthors \\ 1998 10","cited_arxiv_id":null,"evidence_quote":"Provides the epistemic theory that vague predicates have crisp but unknown boundaries, justifying the probabilistic treatment."},{"cited_title":"\\ Tang, Y","cited_arxiv_id":null,"evidence_quote":"Grounds the view that vague concepts can be modeled with uncertainty and prototype-based probability distributions."},{"cited_title":"\\ Schockaert, S","cited_arxiv_id":null,"evidence_quote":"Licenses the use of Gaussian distributions to represent conceptual prototypes, which the adverbial-specific function relies on."},{"cited_title":"APACrefauthors \\ 1953","cited_arxiv_id":null,"evidence_quote":"Supplies the principle of compositionality that the factorized model instantiates by combining event and adverbial meanings."}],"review_version":1}