Temporal Semantic Volatility (TSV)

• Temporal Semantic Volatility (TSV) is a concept that quantifies how semantic structures evolve over time across varying units such as terms, topics, statements, and relations.
• It employs methods ranging from co-occurrence rank analysis and latent topic trajectory metrics to embedding space drift and learned semantic rates.
• TSV provides actionable insights for forecasting, financial NLP robustness, and knowledge graph evolution, despite challenges in standardization and methodological heterogeneity.

Searching arXiv for the cited TSV-related papers to ground the article in current records. Temporal Semantic Volatility (TSV) denotes the temporal instability of semantic structure, but the term is not used in a single canonical way across the recent literature. In diachronic corpus analysis it refers to rank volatility of context terms; in dynamic topic models it measures change in latent topic distributions; in forecasting it can denote a text-derived volatility primitive or an embedding-space drift signal; in temporal reasoning it can quantify how contextual updates alter validity duration; and in temporal knowledge graphs it is a learned rate controlling semantic change over continuous time (Heyer et al., 2017, Wenzel et al., 2024, Pan, 12 Oct 2025, Sun et al., 30 Sep 2025, Li et al., 13 Mar 2026, Li et al., 13 Apr 2026). Taken together, these formulations treat TSV as a family of temporal-semantic diagnostics and control variables rather than a single universally standardized statistic.

1. Semantic scope and units of analysis

A useful way to organize TSV is by the object whose semantics is assumed to evolve. The literature explicitly instantiates term-level, statement-level, topic-level, document-level, time-slice-level, corpus-level, and relation-level variants. The dynamic topic framework states that TSV can be computed at topic level, document level, time-slice level, and corpus level; TVCP operationalizes it at the level of statements and contextual updates; RoMem makes it a relation-level scalar; and the earlier context-volatility line treats it as a per-term property in diachronic corpora (Pan, 12 Oct 2025, Wenzel et al., 2024, Li et al., 13 Apr 2026, Heyer et al., 2017).

Formulation	Unit of analysis	Core quantity
Context volatility (Heyer et al., 2017)	term	IQR of co-occurrence rank trajectories
Dynamic topic evolution (Pan, 12 Oct 2025)	topic, document, time slice, corpus	divergence or norm-based change in $\theta_t$
TVCP (Wenzel et al., 2024)	statement	change in expected temporal validity duration
Financial NLP robustness (Sun et al., 30 Sep 2025)	article stream or regime	mean Euclidean step in embedding space
TESS (Li et al., 13 Mar 2026)	forecast instance	gated volatility primitive from text
RoMem (Li et al., 13 Apr 2026)	relation	learned $\alpha_r \in (0,1)$ controlling rotation speed

This heterogeneity matters methodologically. Some formulations are descriptive measurements of observed drift, such as embedding displacement or co-occurrence-rank instability. Others are latent-state diagnostics derived after model training, such as changes in topic distributions. Still others are control variables internal to the model, as in RoMem’s semantic speed gate. A recurrent source of confusion is the assumption that all TSV definitions estimate the same object; the cited work does not support that reading.

2. Co-occurrence volatility and latent topic dynamics

The earliest explicit precursor in the supplied corpus is “context volatility,” introduced for diachronic corpora as a measure of how the significant co-occurrences of a term change rank over time (Heyer et al., 2017). Let $C_t$ denote the time-slice-specific term-term co-occurrence matrix with significance weights, and let $r_t(w,c)$ be the rank of context term $c$ for target term $w$ in slice $t$. The global volatility of a term is given as

$$S_w = \frac{1}{|C_{w,T}|} \sum_{i=1}^{|C_{w,T}|} \mathrm{IQR}\big(\mathrm{Rank}(C_{w,i}, T)\big).$$

The windowed form computes

$$CV_{w,T}(i,t) = \mathrm{IQR}\big(\{ r_{t'}(w,c_i) \mid t' \in [t-h+1, t] \}\big),$$

followed by

$$S_w(t) = \frac{1}{|C_{w,T}|} \sum_{i=1}^{|C_{w,T}|} CV_{w,T}(i,t).$$

In that formulation, TSV is not a distance in embedding space and not a topic divergence; it is the average dispersion of rank trajectories of significant co-occurrences. The paper uses the log-likelihood significance measure, monthly slices for volatility in the case study, and a history window $\alpha_r \in (0,1)$0 months (Heyer et al., 2017).

The 2025 dynamic topic evolution framework moves TSV into a latent-topic setting based on time-aware LLM representations (Pan, 12 Oct 2025). Text is encoded as

$\alpha_r \in (0,1)$1

with exponential temporal decay

$\alpha_r \in (0,1)$2

and time-aware attention

$\alpha_r \in (0,1)$3

The topic distribution is then

$\alpha_r \in (0,1)$4

and dynamics are governed by

$\alpha_r \in (0,1)$5

The joint objective is

$\alpha_r \in (0,1)$6

Within this framework, TSV is derived from changes in $\alpha_r \in (0,1)$7. The paper explicitly lists norm-based change,

$\alpha_r \in (0,1)$8

topic-level change,

$\alpha_r \in (0,1)$9

and a transition-induced quantity

$C_t$0

The interpretation is direct: higher $C_t$1 yields smoother trajectories and lower TSV; larger $C_t$2 down-weights distant context more aggressively and also yields lower TSV (Pan, 12 Oct 2025).

These two lines of work share the assumption that semantics is temporally legible through relational structure—either co-occurrence neighborhoods or topic-mixture trajectories. They differ in whether TSV is computed from observed lexical ranks or from latent state evolution after representation learning.

3. TSV as a forecasting primitive extracted from text

In TESS, TSV is one of four interpretable temporal primitives in the Temporal Evolution Semantic Space: mean shift, volatility, shape, and lag and decay (Li et al., 13 Mar 2026). Here the volatility primitive is explicitly defined as a regime shift in dispersion between observation and forecast windows. With realized volatilities on first differences,

$C_t$3

the relative volatility shift is

$C_t$4

The discretization uses five classes: surge, rise, stable, fall, and calm (Li et al., 13 Mar 2026).

Extraction is performed by a frozen LLM under a strict structured prompt. For each primitive $C_t$5, the model yields log-likelihood scores

$C_t$6

and a temperature-scaled categorical distribution

$C_t$7

The volatility class is $C_t$8. Confidence is estimated by the log-probability margin

$C_t$9

Each predicted class is embedded as $r_t(w,c)$0, then gated by

$r_t(w,c)$1

All gated primitives are stacked as semantic prefix tokens and fused with PatchTST through

$r_t(w,c)$2

so TSV enters the forecaster as an exogenous, interpretable bottleneck (Li et al., 13 Mar 2026).

The paper is explicit that TSV in TESS is not raw realized variance from the observed series; rather, it is a text-derived volatility signal that is numerically grounded by $r_t(w,c)$3 and calibrated by confidence-aware gating. This distinguishes it from purely representation-level definitions of TSV.

4. Embedding drift and temporal validity change

A different operationalization appears in financial NLP robustness evaluation, where TSV is defined directly in embedding space (Sun et al., 30 Sep 2025). Let $r_t(w,c)$4 be a sentence embedding function, instantiated in the study as all-MiniLM-L6-v2, and let $r_t(w,c)$5 for time-ordered news items $r_t(w,c)$6. The conceptual functional is

$r_t(w,c)$7

and the practical estimator used in experiments is

$r_t(w,c)$8

This is model-agnostic and requires no latent topic structure, no prompt-based discretization, and no explicit semantic primitives. The same study complements TSV with Jensen–Shannon divergence between regime-specific TF-IDF term distributions, treating TSV as a representation-space drift indicator and JSD as a vocabulary-level drift indicator (Sun et al., 30 Sep 2025).

Temporal Validity Change Prediction defines a further semantic-temporal object: the sensitivity of a statement’s validity duration to contextual updates (Wenzel et al., 2024). Temporal validity is

$r_t(w,c)$9

and the temporal validity duration is

$c$0

Given a follow-up statement $c$1, TVCP predicts whether duration decreases, is unchanged, or increases:

$c$2

With the change operator

$c$3

the paper proposes volatility measures such as

$c$4

and, in duration-class space,

$c$5

It also defines time-indexed and survival-oriented variants. In this formulation, TSV is not drift of lexical or latent representation per se; it is the expected magnitude of context-induced change in temporal validity (Wenzel et al., 2024).

These two strands show that TSV may refer either to semantic motion through a continuous representation manifold or to the effect of newly arriving semantics on temporal validity.

5. Relation-level TSV in temporal knowledge graphs and memory

RoMem introduces a qualitatively different use of TSV: a learned relation-specific speed controlling continuous phase rotation in complex embedding space (Li et al., 13 Apr 2026). The central quantity is a per-relation scalar

$c$6

produced by the Semantic Speed Gate (SSG). High $c$7 corresponds to rapidly changing relations such as “president of,” “met with,” and “host a visit,” whereas low $c$8 corresponds to persistent relations such as “born in,” “citizen of,” and “species” (Li et al., 13 Apr 2026).

Time acts as a continuous geometric operator, and TSV enters multiplicatively in the rotation angle:

$c$9

Entities and relations live in $w$0 but are interpreted as complex vectors in $w$1, and a scalar time $w$2 applies an element-wise phase shift through $w$3. The scorer is

$w$4

SSG is pretrained by mapping relation text embeddings $w$5 to $w$6 via

$w$7

using an exponential change model

$w$8

with a BCE loss (Li et al., 13 Apr 2026).

The operational consequence is “geometric shadowing”: obsolete facts are rotated out of phase rather than deleted. Persistent facts remain aligned because $w$9 implies negligible phase drift, while dynamic facts separate quickly because $t$0 amplifies time-dependent phase mismatch. In this formulation, TSV is neither a post hoc volatility score nor a drift diagnostic. It is a learned semantic prior on temporal change rate.

6. Empirical findings, limitations, and standardization issues

Across domains, TSV is typically justified by non-stationarity, semantic drift, or temporal conflict, and the associated empirical results are correspondingly heterogeneous.

In the dynamic topic model, evaluation on 20 Newsgroups reports the following comparative results: Ours achieves Perplexity 598.2, Diversity 0.78, Topic Coherence 0.57, and Topic Stability 0.69, compared with LDA at 950.3, 0.62, 0.41, 0.48, BERT at 730.5, 0.68, 0.46, 0.55, DeBERTa at 702.7, 0.71, 0.50, 0.60, Topic audiolization at 680.4, 0.71, 0.50, 0.60, and T3 at 655.8, 0.73, 0.52, 0.62. The same study reports that Perplexity and Coherence improve up to sequence length approximately 200, Diversity peaks at medium lengths, and Topic Stability increases steadily with longer sequences (Pan, 12 Oct 2025).

In TESS, experiments on four real-world datasets report up to a 29.1% MSE reduction relative to the best baseline on Bitcoin, with financial datasets showing particularly strong gains under pronounced non-stationarity. Scenario analyses for volatility change, mean shift, and shape transition subsets show MSE improvements of 21–52% over multimodal baselines and 21–45% over unimodal baselines. Primitive ablation on FNSPID indicates that each primitive contributes, while gating assigns median weights approximately 0.65–0.78 to correctly extracted primitives and approximately 0.21–0.40 to incorrect ones (Li et al., 13 Mar 2026).

In RoMem, relation-level TSV supports state-of-the-art TKGE on ICEWS05-15 with 72.6 MRR, 66.8 Hit@1, 75.9 Hit@3, and 83.7 Hit@10 for RoMem-ChronoR, versus 68.4 MRR for ChronoR. In agentic memory, the MultiTQ results under GPT-5-mini plus text-embedding-3-small report MRR 0.337 vs 0.203, Acc@5 0.366 vs 0.112, and Acc@10 0.392 vs 0.102, while DMR-MSC shows slight improvement over HippoRAG with MRR 0.856 vs 0.848 and Acc@5 0.862 vs 0.852 (Li et al., 13 Apr 2026).

In financial NLP robustness, TSV peaks align with crisis periods. The study states that the COVID regime exhibits the highest TSV and the largest errors; JSD peaks around major regime transitions; matched events have TSV around 0.9 within regime and around 1.8 across regimes; JPM and AAPL show COVID TSV peaks of approximately 2.10 and 2.30; and feature augmentation reduces TSV from 2.07 to 1.76 while improving NLICS from 0.49 to 0.56 (Sun et al., 30 Sep 2025).

In TVCP, the dataset contains 5,055 target-context samples derived from 1,685 target statements, with three follow-ups per target. The strongest benchmark reported is SelfExplain with 88.5% accuracy and 69.8% exact match, while multitask duration prediction improves EM in all models except S-BERT (Wenzel et al., 2024).

A consistent limitation across these lines of work is that TSV is definition-dependent. In co-occurrence analysis it is sensitive to slice sparsity and rank instability; in latent-topic models it depends on $t$1, $t$2, time slicing, and the learned transition matrix; in TESS it depends on discretization thresholds, LLM extraction accuracy, and confidence calibration; in embedding-space monitoring it depends on the embedding function $t$3 and on regime partitioning; in TVCP it depends on duration taxonomies and contextual annotation; and in RoMem it depends on the calibration of $t$4 from relation text and on the assumption that relation-level volatility is the right granularity (Heyer et al., 2017, Pan, 12 Oct 2025, Li et al., 13 Mar 2026, Sun et al., 30 Sep 2025, Wenzel et al., 2024, Li et al., 13 Apr 2026).

The broader implication is that TSV is best understood as an umbrella concept for temporally indexed semantic instability. What remains invariant across the surveyed literature is the target phenomenon: semantic structure changes with time, and those changes can be quantified or controlled. What varies is the carrier of semantics—co-occurrence ranks, latent topic vectors, LLM-extracted primitives, statement-validity durations, dense embeddings, or continuous-time KG phases—and that choice determines both the mathematics and the interpretation.