Temporal Continual Learning

• Temporal Continual Learning is a framework that leverages time-structured task streams, posterior updates, and latent memory to mitigate catastrophic forgetting.
• Its methodologies include multi-step variational objectives, temporal graph learning, and EMA-based strategies, offering versatile approaches for dynamic scenarios.
• Empirical results demonstrate improved retention, reduced drift, and efficient learning across domains such as human motion prediction, topic modeling, and graph-based tasks.

Temporal Continual Learning (TCL) denotes continual-learning settings and algorithms that exploit temporal structure in sequential data, task streams, posterior updates, or prediction horizons, rather than treating time merely as an ordering variable. Across the recent literature, the shared objective is to preserve prior competence while adapting to temporally evolving information under non-stationary distributions and catastrophic forgetting. The label encompasses several technically distinct formulations, including temporally bootstrapped variational objectives over posterior sequences, continual learning on temporal graphs with evolving old-class distributions, multi-stage horizon learning for human motion prediction, and time-sliced latent-variable models with explicit long-term memory (Melo et al., 2024, Liu et al., 3 Mar 2025, Tang et al., 5 Jul 2025, James et al., 21 Aug 2025).

1. Scope and terminology

The literature does not use TCL in a single narrow sense. In “Temporal-Difference Variational Continual Learning,” TCL refers to continual-learning strategies that explicitly leverage temporal structure in the sequence of tasks, posteriors, and updates, replacing single-step recursive regularization with multi-step temporally bootstrapped targets (Melo et al., 2024). In temporal graph continual learning, the temporal dimension is expressed through old classes that continue to evolve while new classes emerge, so the learner must retain performance on an old distribution that is itself drifting (Liu et al., 3 Mar 2025). In brain-inspired multi-cognitive learning, TCL is framed as learning across a temporally ordered sequence of Perception-Motor-Interaction tasks, with later tasks reshaping earlier modules through feedback-guided development (Han et al., 8 Apr 2025). In continual neural topic modeling, the time index is a sequence of corpora slices, and the core continual component is an online global prior that carries topic memory across time (James et al., 21 Aug 2025).

A representative cross-section of current usages is summarized below.

Instantiation	Temporal unit	Principal mechanism
TD-VCL (Melo et al., 2024)	tasks, posteriors, updates	n-step and TD($\lambda$)-style multi-posterior regularization
TGCL/LTF (Liu et al., 3 Mar 2025)	periods on temporal graphs	subset selection via proxy error and MMD
TD-MCL (Han et al., 8 Apr 2025)	ordered PMI tasks	long-range connection evolution plus pruning
CoNTM (James et al., 21 Aug 2025)	time-sliced corpora	decayed global prior update

This suggests that TCL is best understood as a family of temporally structured continual-learning problems rather than a single benchmark regime. What remains invariant is the stability–plasticity problem under temporally organized change; what varies is the object over which time is modeled: tasks, posterior estimates, class distributions, latent memories, structural modules, or future horizons.

2. Formal formulations

A recurring formulation in TCL is sequential factorization. In Bayesian continual learning, tasks arrive as datasets $\mathcal{D}_t$, model parameters are $\theta$, and the posterior update follows the recursion

$$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$

with variational continual learning optimizing

$$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$

The temporal issue identified in this formulation is that the entire history is transferred through the most recent approximation $q_{t-1}$, making posterior error compounding a first-class TCL concern (Melo et al., 2024).

In temporal graph continual learning, the formal problem is not merely sequential task arrival but simultaneous new-class emergence and evolution of old-class distributions. At period $N$, one observes a graph $G_N = G_N^{old} \cup G_N^{new}$, with old classes following a new distribution $\mathcal{G}_N^{old}$ and new classes following $\mathcal{G}_N^{new}$. The objective is

$\mathcal{D}_t$0

This differs from static graph continual learning because the retained knowledge is not evaluated against a frozen historical distribution (Liu et al., 3 Mar 2025).

In continual neural topic modeling, each time step $\mathcal{D}_t$1 yields a corpus $\mathcal{D}_t$2, local topic parameters $\mathcal{D}_t$3, and a global topic parameter $\mathcal{D}_t$4. The continual mechanism is explicit:

$\mathcal{D}_t$5

with $\mathcal{D}_t$6, $\mathcal{D}_t$7. Here TCL takes the form of posterior-as-prior memory over a nonstationary corpus stream (James et al., 21 Aug 2025).

Human motion prediction introduces a different temporal decomposition. The future trajectory is partitioned into temporal segments $\mathcal{D}_t$8, and the full prediction objective is factorized as

$\mathcal{D}_t$9

Continuality is then defined over progressively expanding prediction horizons rather than over disjoint tasks or domains (Tang et al., 5 Jul 2025).

3. Objective design and memory updates

A major TCL design axis concerns how temporal dependence is incorporated into the learning objective. TD-VCL replaces single-step posterior anchoring with multi-posterior regularization. Its $\theta$0-step target distributes regularization across several previous posteriors and recent-task likelihoods, and its TD($\theta$1)-VCL variant geometrically discounts older terms. The paper defines the $\theta$2-step temporal-difference target

$\theta$3

and shows that TD($\theta$4)-VCL is equivalent to a discounted sum of such $\theta$5-step TD targets. The stated motivation is to dilute the influence of any single poor posterior approximation and thereby mitigate error compounding over time (Melo et al., 2024).

In human motion prediction, TCL is instantiated as a multi-stage curriculum over future horizons, augmented by a Prior Compensation Factor (PCF),

$\theta$6

The factor measures lost prior information when moving from previously learned horizons to a later segment. The resulting stage-wise objective weights segment losses by $\theta$7 and adds regularizers derived from an upper bound on the negative log-likelihood. In this formulation, temporal continuality is not a property of the data stream but of the optimization path through short-, mid-, and long-term prediction targets (Tang et al., 5 Jul 2025).

Temporal graph continual learning introduces a different mechanism: selective replay under distribution drift. The LTF framework derives an upper bound on old-class error using $\theta$8-divergence and operationalizes it through subset selection that minimizes a proxy classification error plus an MMD discrepancy between the full old-class data and its selected subset. The learning objective then combines supervised loss on new data, supervised replay on the selected subset, and an embedding-alignment term between the selected subset and a similarity subset. This makes temporal memory explicit at the level of curated data support rather than parameter regularization alone (Liu et al., 3 Mar 2025).

CoNTM uses neither replay nor multi-posterior KL penalties. Its temporal memory is a global parameter matrix updated by a decayed running average, while per-step local topic parameters are modeled as perturbations of that global memory. The continual effect is therefore concentrated in the schedule-controlled accumulation of persistent topic structure, with $\theta$9 and $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$0 governing the plasticity–stability balance (James et al., 21 Aug 2025).

Online continual learning with temporal ensembles uses a lighter mechanism. The Exponential Moving Average of parameters,

$$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$1

is maintained during training and used only at evaluation time. Training and replay buffers remain unchanged, but the evaluation model becomes a temporal ensemble over the weight trajectory. The reported effect is a large reduction in instability under continual evaluation, particularly in worst-case metrics such as WC-ACC and RAG (Soutif--Cormerais et al., 2023).

4. Structural and representational adaptation

Another TCL line treats time as a driver of structural reorganization rather than only objective design. TD-MCL models continual learning across Perception-Motor-Interaction tasks with a deep spiking neural network using PLIF neurons and a ResNet18-like four-block organization with channels $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$2–$$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$3–$$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$4–$$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$5. As tasks arrive from simple perception to motor control to interaction, the model grows new modules, evolves sparse long-range connections between tasks by an online evolutionary rule, and prunes local synapses using a threshold coefficient $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$6 that combines local Hebbian activity with a global generalization score. The method explicitly avoids replay, regularization, and freezing, and instead uses temporal development, reorganization, and pruning as the retention mechanism (Han et al., 8 Apr 2025).

Thalamus represents a distinct TCL strategy based on a latent task or event embedding $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$7 updated at inference time. The model alternates between slow weight updates $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$8 and fast latent updates $$p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T}) \propto p(\boldsymbol{\theta} \mid \mathcal{D}_{1:T-1})\,p(\mathcal{D}_{T} \mid \boldsymbol{\theta}),$$9, with a change detector triggered by an accuracy drop $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$0, where $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$1. When performance drops, the system first performs a latent-update loop with $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$2 frozen; only if performance does not recover does it update $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$3. The result is unsupervised event segmentation and a factorization in which stable computations reside in the weights while rapidly changing contextual control is offloaded into a low-dimensional latent space (Hummos, 2022).

CHEEM, or ArtiHippo, applies structural TCL to Vision Transformers. The “sweet spot” for continual memory is identified as the final linear projection in the MHSA block. That projection is organized as a per-layer mixture of experts, and each new task may reuse, adapt, create, or skip experts under a Hierarchical task-synergy Exploration-Exploitation sampling policy. Reused modules are frozen, new or adapted modules are trained, and task similarity is estimated via normalized cosine similarity of mean class tokens. In this formulation, TCL is task-incremental and exemplar-free, with temporal order expressed through streaming tasks and progressively expanding expert sets (Savadikar et al., 2023).

These structural methods share a common logic: temporal order changes not only what is learned but which parts of the model remain editable, reusable, or suppressible. Their temporal memory is embodied in routing, sparsity, latent control, or growth policies rather than solely in buffers or posterior penalties.

5. Empirical regimes and reported behavior

Empirical TCL results span markedly different modalities, but several patterns recur: temporally aware mechanisms improve retention under constrained replay or no replay, gains are strongest when approximation or drift is severe, and evaluation protocols strongly shape conclusions.

Area	Representative protocol	Reported outcome
Bayesian CL (Melo et al., 2024)	PermutedMNIST, SplitMNIST, SplitNotMNIST; single-head, constrained replay	approximately 90% average accuracy on PermutedMNIST after 10 tasks; markedly better Task 1 retention than VCL and MLE baselines
Temporal graphs (Liu et al., 3 Mar 2025)	Yelp, Reddit, Amazon with TGAT and DyGFormer	LTF improves AP and AF over OTGNet, iCaRL, ER, and URCL, with substantial time reductions relative to OTGNet
OCL with EMA (Soutif--Cormerais et al., 2023)	Split-MiniImageNet, Split-CIFAR100, Split-CIFAR10	2–10 point end-of-stream accuracy gains and 18–60 point RAG reductions across replay baselines
Video CIL (Alssum et al., 2023)	UCF101, ActivityNet, Kinetics; frame-budget replay	up to 21.49% over previous state of the art; single-frame replay outperforms multi-frame storage under tight budgets
Human motion prediction (Tang et al., 5 Jul 2025)	Human3.6M, CMU-MoCap, 3DPW, AMASS	consistent MPJPE/EAE improvements for short and long horizons across RNN, GCN, Transformer, and MLP backbones
Topic modeling (James et al., 21 Aug 2025)	NYT, UN, NIPS/NeurIPS, NASA tweets, ArXiv, DBLP	top average topic-quality rank, competitive or lowest predictive perplexity on most datasets, TTS around 0.49

The TD-VCL results are especially notable because the evaluation protocol is deliberately non-trivial: single-head classifiers, constrained replay, and per-task accuracy tracking over time. Under those conditions, TD-VCL and the $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$4-step KL objective approximately reach $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$5 average accuracy on PermutedMNIST after all 10 tasks, while early-task retention remains around $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$6–$$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$7 for Task 1 after the full sequence, compared with approximately $$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$8–$$\mathcal{L}_{VCL}^{t}(\boldsymbol{\theta}) = \mathbb{E}_{\boldsymbol{\theta} \sim q_{t}(\boldsymbol{\theta})}\!\left[\log p(\mathcal{D}_{t} \mid \boldsymbol{\theta})\right] - \mathscr{D}_{KL}\!\left(q_{t}(\boldsymbol{\theta}) \,\middle\|\, q_{t-1}(\boldsymbol{\theta})\right).$$9 for VCL and approximately $q_{t-1}$0 for MLE baselines (Melo et al., 2024).

Temporal graph continual learning shows that distribution-aware subset selection is particularly valuable when old classes drift. On Yelp, Reddit, and Amazon, LTF improves Average Precision and lowers Average Forgetting relative to replay and regularization baselines, and on TGAT it reduces time by over an order of magnitude relative to OTGNet on some reported settings (Liu et al., 3 Mar 2025). In online continual learning, EMA does not modify training yet still raises Acc, AAA, and WC-ACC while sharply shrinking RAG; on Split-MiniImageNet, for example, ER improves from $q_{t-1}$1 to $q_{t-1}$2 Acc and RAG drops from $q_{t-1}$3 to $q_{t-1}$4 (Soutif--Cormerais et al., 2023).

Two domain-specific results are particularly instructive for TCL. In video continual learning, fixing memory in frames reveals a direct diversity–temporal-resolution trade-off: on UCF101 with a budget of $q_{t-1}$5 frames, storing $q_{t-1}$6 frames per video gives $q_{t-1}$7 accuracy, whereas $q_{t-1}$8 frames per video gives $q_{t-1}$9; the single-frame SMILE strategy then improves further with a domain-gap mitigation loss (Alssum et al., 2023). In CLTSQA, sequential training over five chronological subsets of a $N$0-question dataset degrades early temporal subsets, while the combination of Temporal Memory Replay and temporal contrastive learning improves EM/F1, especially on earlier subsets; the ablation indicates that TMR is essential for retention and the contrastive component is complementary (Yang et al., 2024).

6. Evaluation issues, ambiguities, and open problems

A central recent result is that temporal partitioning itself is an evaluation variable. “Temporal Taskification in Streaming Continual Learning” argues that converting a stream into tasks through temporal boundaries is not a neutral preprocessing step. The paper introduces plasticity and stability profiles, a profile distance between taskifications, and Boundary-Profile Sensitivity (BPS), and shows on CESNET-Timeseries24 that changing only the taskification from 9-day to 30-day to 44-day windows materially changes MSE, forgetting, and backward transfer while keeping stream, model, and training budget fixed. The reported mean BPS decreases from $N$1 for 9-day splits to $N$2 for 30-day and $N$3 for 44-day splits, identifying shorter taskifications as structurally more fragile (Filat et al., 23 Apr 2026).

There is also terminological ambiguity. In the CLTSQA literature, “TCL” denotes Temporal Contrastive Learning, not Temporal Continual Learning; the continual-learning problem itself is named CLTSQA (Yang et al., 2024). More broadly, the phrase “temporal continual learning” can refer to temporally structured Bayesian regularization, logic-constrained curricula, graph distribution drift, continual horizon expansion, or simply online evaluation of non-stationary streams. Any technical discussion therefore depends on the temporal object under consideration.

Several common assumptions recur across TCL methods. TD-VCL assumes task boundaries and i.i.d. within-task data, and its memory cost grows as $N$4 because it stores the last $N$5 posteriors (Melo et al., 2024). LTF depends on representative subsets and on the quality of embeddings produced by the previous model when estimating MMD, so strong drift or rare modes can degrade selection quality (Liu et al., 3 Mar 2025). TD-MCL reports sensitivity to developmental hyperparameters and notes that scaling beyond nine Perception-Motor-Interaction tasks requires better control of module growth and long-range connectivity (Han et al., 8 Apr 2025). CoNTM is strongest on larger corpora and may underfit abrupt shifts under a slow decay schedule, motivating adaptive $N$6 schedules and topic birth/death mechanisms (James et al., 21 Aug 2025).

A frequent misconception is that TCL always requires preserving maximal temporal detail within each sample. The video evidence argues against that generalization: under extreme memory constraints, storing more unique videos with a single frame each is empirically preferable to storing fewer videos with richer temporal clips (Alssum et al., 2023). Another misconception is that evaluation conclusions are properties of methods alone. The taskification results indicate that benchmark conclusions also depend on how temporal structure is discretized before training (Filat et al., 23 Apr 2026).

Current open directions are correspondingly heterogeneous: deeper formal links between continual learning and TD or MDP formalisms, adaptive divergences and OOD-aware subset selection, temporally evolving sparse expert routing, hardware-level energy metrics for developmental models, topic birth/death in latent-variable TCL, and taskification-robust evaluation and algorithms (Melo et al., 2024, Liu et al., 3 Mar 2025, Han et al., 8 Apr 2025, James et al., 21 Aug 2025, Filat et al., 23 Apr 2026). Taken together, these works indicate that TCL is not a single method family but an organizing perspective on continual learning in which time is modeled as structure, not merely sequence.