Dynamic topic model
Model Families AIMech:DynamicTopicModel DRAFT
Aliases: DTM
A time-sliced topic-model family that links the softmax natural parameters of corresponding topic-word distributions across slices through Gaussian state transitions, allowing a fixed set of topics to change over time.
Identity Notes & Concept Scope
Scoped to Blei and Lafferty's ICML 2006 dynamic topic models. Topic-word distributions evolve, unlike a static topic model with only changing document proportions. The full formulation also evolves the logistic-normal mean for document-topic proportions; the inference exposition explicitly simplifies that part to a fixed Dirichlet prior. Variational Kalman and wavelet approximations are fitting choices, not synonyms for the model family or neural state-space layers. No normalized identity match was found across all 442 pinned AIO labels and scoped synonyms and 423 preceding native IDs, names and aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main. Ten matched lines in each checkout reduce to nine unique line contents: prior frontier references, copied discovery context and cached web-result mentions. Every matching concept excerpt was inspected; these are not maintained or imported identities. All 200 semantic label/synonym hits were read. Eighteen exact annotated AIO CLASS nodes and outgoing edges were inspected, including 14 verified unchanged from prior reading and four newly read. Thirty contextual YAMLs comprise those 18 AIO records and 12 native neighbors: six fully read here, 23 byte-verified after prior reading and the updated APM verified against its fully reviewed round100 bytes. Absence is bounded to the pinned snapshot, maintained corpus and inspected semantic neighborhood.
Claims & Grounded Evidence
2 Claims
Mechanism
#temporal-law
For fixed topic count K and vocabulary, the basic model evolves each topic logit vector as beta_tk|beta_(t-1)k~N(beta_(t-1)k,sigma² I) and maps it through softmax to word probabilities. In the full generative description, alpha_t|alpha_(t-1)~N(alpha_(t-1),delta² I) evolves the document-topic logit mean. Each document draws eta~N(alpha_t,a² I), then topic assignments from softmax(eta) and words from the selected time-specific topic. Initial-state distributions and variance settings must be specified. Documents are grouped into ordered slices; conditional within-document word exchangeability remains. The inference example beginning on p.3 retains evolving topics but fixes a Dirichlet document-proportion prior, a stated simplification rather than an equivalent formula for the entire full model.
Mechanism
#structured-approximation
The published approximation uses Gaussian topic trajectories conditioned on optimized pseudo-observations, retaining time dependence within each topic chain while separating it from document-level latent factors. Gaussian forward filtering and backward smoothing compute the surrogate trajectory moments; a wavelet-regression approach is presented as an alternative. Expected topic-word counts connect document updates to trajectory fitting. Exact Kalman recursions for this Gaussian surrogate do not yield the exact nonconjugate multinomial posterior. The auxiliary expected-log-normalizer bound and numerical optimization introduce approximation; smoothing over a fitted interval can use later observations and must be distinguished from forecasting beyond that interval.
⚠️ Curated Limitations & Negative Results
- The basic random-walk model fixes topic count and vocabulary and does not create or remove topics. Richer drift, heteroscedasticity and topic birth/death processes are proposed extensions. Time-slice choice and Gaussian innovation assumptions matter; temporal association is not a causal account of scientific change.
- Softmax logits are invariant to a common shift. Fixed topic indexing links trajectories, while label permutation and model fitting can still limit semantic identification. The presented isotropic document-logit law does not itself fit the full static CTM covariance or evolving correlations.
- Appendix A's displayed expected transition quadratic omits adjacent-time posterior covariance terms, and its entropy display does not give the joint correlated Gaussian entropy. A correct Gaussian-chain calculation uses cross-time covariance and the joint covariance determinant. With fixed surrogate variances some omitted terms are constant for mean optimization, but the printed expressions are not certified as exact complete objectives when variances change.
- The reported next-year Science comparison uses a variational likelihood bound, as stated in Figure 5, rather than computed exact predictive likelihood. The illustrative wavelet approximation and historical results are not a universal accuracy or convergence guarantee. No author implementation or benchmark was executed.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:Model
Model
|
broad_match | The local identity is a specified probability-model family; the pinned Model class is broader. |
AIO:ProbabilisticTopicModel
Probabilistic Topic Model
|
related_match | The local generative model supports topic modeling. This pinned AIO target is task-scoped, so related match preserves the model-versus-task distinction. |
AIO:TimeSeriesAnalysis
Time Series Analysis
|
related_match | The model analyzes temporally organized document collections. The broader AIO time-series task differs in abstraction from this particular probability-model family. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
David M. Blei, John D. Lafferty
|
primary paper
full_text
|
sha256:0af8ce7a05e1…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T23:45:21Z
Updated: 2026-10-11T23:45:21Z
Source File:
data/curated/DynamicTopicModel.yaml