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Memory in Deep Time-Series Models

Minh Hoang Nguyen, Huu Hiep Nguyen, Manh Nguyen, Van Dai Do, Dung Nguyen, Hung Le

arXiv:2609.06006v1cs.LGcs.AI

TL;DR

Time-series predictions may depend on information beyond feasible input windows, while fixed-size states can discard history that becomes useful later. This survey organizes time-series methods around memory, develops a taxonomy and task-centered analysis, and finds that long-term retrieval, memory-specific evaluation, and agentic memory remain limited or emerging.

  • Problem

    Time-series predictions may depend on distant history that feasible input windows miss, while compressing history into fixed-size states can discard information needed later.

    Source: §1 · p. 1, §5.3 · pp. 16–17

  • Method

    The survey organizes time-series methods along a memory spectrum and reviews external-memory classes through a shared framework for what is retained, accessed, and persisted.

    Source: §1 · p. 3, §4.1 · p. 12

  • Results

    The survey finds that long-term retrieval remains concentrated in forecasting, memory-specific evaluation is limited, and agentic time-series memory remains at an early stage.

    Source: §12 · p. 49

  • Takeaways & Limitations

    The unified memory perspective connects methods across backbones and makes gaps in time-series memory research more visible.

    Source: §1 · p. 3, §12 · p. 49

    Internal memory has fixed-dimensional capacity and limited persistence, requiring compression or overwriting as the data horizon expands.

    Source: §5.3 · pp. 16–17

Abstract

from arXiv · show

Deep learning for time series has progressed through successive architectural paradigms, from recurrent networks and transformers to structured state-space models, retrieval-augmented predictors, foundation models, and tool-using agents. These developments are typically studied in isolation, organized by architecture or modeling era. We argue that they can instead be viewed through a common question of \emph{how does a time-series model retain and access information beyond its immediate input?} This question is motivated by a fundamental limitation of conventional time-series modeling: information relevant to a prediction may lie far beyond a feasible input window, while compressing history into a fixed-size state can discard information that may become useful later. We formulate this challenge as a \emph{memory} problem and organize existing time-series methods along a spectrum from internal memory, encoded in parameters and fixed-size states, to external memory that is addressable, retrievable, and increasingly maintained by agents. We then develop a unified taxonomy of memory mechanisms and review three classes of external memory, including explicit modules, retrieval augmentation, and agentic stores, under a common framework for what is retained, how it is written and accessed, and how it persists. A cross-cutting analysis maps these mechanisms to time-series tasks and identifies gaps in both methods and evaluation. We conclude by outlining open problems in building memory systems that can selectively retain, retrieve, revise, and forget information as temporal environments evolve. The result is a framework for studying memory as a first-class dimension of time series modeling, independent of the underlying backbone.

1 Introduction

The survey reframes time-series modeling as a question of how information is retained and accessed, connecting architectural families along a spectrum from internal states to external and agent-maintained memory. It develops a shared framework for comparing these mechanisms and examining their tasks, evaluation, and open challenges.

1 Introduction

  • The survey connects time-series methods through a memory spectrum, from compressed internal states to explicit, retrievable, and actively maintained external stores.It compares mechanisms by what they retain and how information is written, accessed, and persisted.Source: §1 · pp. 1–2
  • Existing surveys cover parametric and architectural approaches more substantially than explicit, retrieval-based, and agentic memory, which remain fragmented.The survey positions its memory-centered account as complementary to architecture- and agent-centered reviews.Source: §1 · p. 3
  • The framework characterizes memory by retained information, access, persistence, representation, and capacity.It introduces representation, capacity, access mechanism, and persistence as four comparison dimensions.Source: §1 · p. 3
  • The review examines three external-memory classes through their mechanisms, subclasses, writing and integration strategies, limitations, and a shared read/write lifecycle.Source: §1 · p. 4
  • The task-centric analysis maps memory mechanisms across forecasting, classification, anomaly detection, imputation, reasoning, and decision-making, identifying well-studied and underexplored areas.Source: §1 · p. 4
  • The survey argues that current evaluations emphasize downstream accuracy over memory operations and identifies four measures: retention, retrieval quality, temporal validity, and memory management.Source: §1 · p. 4
  • The survey identifies seven challenges for building time-series memory systems that remain useful, efficient, and trustworthy as data and environments evolve.Source: §1 · p. 4

2 Preliminaries

The preliminaries define memory by information available beyond the current prediction context and formalize how models read, use, and retain it. They apply this framework across tasks and characterize mechanisms by representation, capacity, persistence, and access.

2.1 A Generic Memory-Augmented Model

  • A memory-augmented model reads retained information alongside the current observation, then uses the retrieved representation to produce a task output.The formulation separates writing to memory, reading from it, and producing the task output.Source: §2.1 · pp. 4–5

2.2 What is memory? A working definition

  • Time-series memory is historical information made available beyond the current prediction target through a context window, dynamic state, or separately maintained store.Static trained parameters are excluded, while dynamically updated parameter stores can count as memory.Source: §2.2 · p. 5

2.3 Task Instantiations

  • The framework instantiates memory for forecasting, classification, anomaly detection, and imputation using task-specific outputs.Source: §2.3 · p. 6
  • For reasoning, retrieved information supports an inference; for decision-making, it informs an action that shapes subsequent interaction.Source: §2.3 · p. 6

2.4 Four Axes of Memory

  • Memory mechanisms are compared along representation, capacity, persistence, and access, which characterize the memory state and its lifecycle rather than the downstream task.Access includes how information is written, read, updated, and forgotten.Source: §2.4 · pp. 7–8
  • Capacity may be architecturally bounded, scale with accumulated data, or grow subject to a retention policy.Persistence is separately classified as per-sequence, per-dataset, or online, so capacity and persistence need not coincide.Source: §2.4 · p. 7

2.5 Internal versus External Memory

  • Internal memory uses fixed-size implicit latent states, whereas external memory uses discrete stores with distinct access mechanisms and may scale with data or retention policy.The survey centers on explicit, retrieval, and agentic external memory, while using internal memory as a contrast.Source: §2.5 · p. 8

3 Why Time Series Need Memory

The section explains why time-series models need information beyond recent input: relevant events may be distant, recurring, misleading after regime changes, or available only in related series. It connects these needs to memory designs and shared practical concerns.

3 Why Time Series Need Memory

  • A winter-demand forecast can stall with a 90-day window until context reaches the prior winter peak, illustrating why some predictions need distant history.The figure reports flat error under about 90 days, a sharp drop when context crosses the prior winter peak, and a plateau beyond 450 days.Source: §3 · p. 8, Figure 2 · p. 9

3.1 P1: Long-horizon dependence

  • Long-horizon signals can lie beyond practical windows, while extending history is costly and fixed-state compression can lose faint, distant information.The section describes periodic dependencies as well as slower exogenous drivers such as climate trends and regime changes.Source: §3.1 · pp. 9–10

3.2 P2: Recurring Patterns

  • Recurring events support prediction when current conditions resemble past episodes, but compressed internal states can blend the local dynamics needed for direct matching.Explicit memory can retain addressable historical windows or learned prototypes, and retrieval can make predictions traceable to examples.Source: §3.2 · p. 10

3.3 P3: Non-stationarity and regime shift

  • After a distribution shift, historical observations may become misleading, creating tension between adapting a dynamic store and trusting similarity-based retrieval.The section motivates active policies to overwrite, discard, or ignore records from outdated regimes.Source: §3.3 · p. 10

3.4 P4: Sparse and hierarchical data

  • Sparse series may need information from related series or higher aggregation levels, unlike long-horizon dependence within a single series.Shared repositories can let data-scarce nodes draw on cross-series patterns.Source: §3.4 · pp. 10–11

3.5 Concerns shared across problems

  • Memory systems must also store and index exogenous covariates, including weather, news, or macroeconomic indicators beyond the target series.Source: §3.5 · p. 11
  • External memory can support auditability by identifying the past episodes or prototypes that triggered a prediction.Source: §3.5 · p. 11

4 Taxonomy of Time-series Memory

The taxonomy organizes time-series memory into four architectural classes according to where history is stored and how models interact with it. These classes offer different ways to address temporal problems, with suitability depending on the data and the historical information required.

4 Taxonomy of Time-series Memory

  • The taxonomy distinguishes internal, explicit, retrieval, and agentic memory by where historical information is stored and how the model interacts with it.It describes how memory is implemented, complementing the preceding section's account of why memory is needed.Source: §4 · p. 11

4.1 Four memory architectures

  • Internal memory accumulates history in a fixed-size state, providing a simple baseline but potentially weakening distant or infrequent events.It is less suitable when particular historical episodes must remain individually accessible.Source: §4.1 · p. 12
  • Explicit memory keeps observations or learned representations as addressable entries, with capacity limited by context length, slot count, or learned-memory size.Its forms include verbatim, slot, and learned memory.Source: §4.1 · p. 12
  • Retrieval memory searches a larger external collection for instances, latent representations, or knowledge, but must find information that is relevant rather than merely similar.The collection can include long archives, other series, or external knowledge.Source: §4.1 · p. 12
  • Agentic memory stores episodic, semantic, or procedural information and can update it using new observations and outcomes.That flexibility suits changing data or tasks, while requiring decisions about what to keep, update, or remove.Source: §4.1 · p. 12

4.2 Connecting problems and memory architectures

  • Architecture–problem pairings are common choices, not fixed assignments: several memory types may address one problem, depending on the data and information needed.Internal memory is used for long horizons, explicit or retrieval memory for recurring patterns, and retrieval or agentic memory for non-stationarity; internal sharing and explicit cross-series memory are used in sparse or hierarchical settings.Source: §4.2 · pp. 12–13

5 Internal Memory

Internal memory compresses observed history into a fixed-dimensional state that evolves as new observations arrive. Recurrent and structured state approaches implement this compression differently, but share limits in capacity, persistence, and explicit access.

5.1 Mechanism

  • Internal memory encodes historical observations in recurrently updated, fixed-dimensional latent states, allowing the model to incorporate long histories through continuous compression.The memory is carried by the hidden state and updated as observations arrive.Source: §5 · p. 13, §5.1 · p. 13
  • The internal-memory mechanism uses the hidden state as its memory and local observation context as input to the predictor, with retrieval implicit in the state.Repeated updates let the state depend on the full history, but its fixed dimension bounds capacity and makes individual events difficult to inspect, address, or revise.Source: §5.1 · pp. 13–14, Figure 5 · p. 14

5.2.1 Recurrent state

  • Recurrent models carry history in an evolving state; LSTMs add gated updates to address long-horizon gradient difficulties, while GRUs offer a simpler gated alternative.The hidden state, rather than learned parameters, carries information from observed history.Source: §5.2.1 · pp. 14–15
  • Recurrent memory has been used for forecasting, classification, anomaly detection [45, 46], and imputation.Examples include shared temporal patterns, selective attention, local temporal features, and decay mechanisms for missing intervals.Source: §5.2.1 · p. 15
  • Recurrent methods also combine memory with attention or spatial operators, and P-sLSTM shows recurrent models can remain competitive with appropriate architectural and training choices.Examples include clinical time series and spatiotemporal point-cloud streams.Source: §5.2.1 · p. 15

5.2.2 Structured state

  • Structured state-space models replace nonlinear gating with parameterized state transitions; their linear form provides a closed-form compression map, and FiLM combines structured states with frequency-domain information.In the linear formulation, the state transition and input projection are matrices A and B, with readout C h_t.Source: §5.2.2 · pp. 15–16
  • Selective state spaces use input-dependent transitions for efficient linear-time processing, and time-series variants span forecasting, classification, and anomaly detection; evidence also suggests selective compression is not universally optimal.Extensions include multi-scale sampling, bidirectional processing, and combining state-space components with attention or Transformer experts.Source: §5.2.2 · p. 16

5.3 Coverage and Limitations

  • Across recurrent and structured forms, internal memory remains a fixed-dimensional implicit state: capacity cannot grow with the data horizon, individual observations may be diluted, and past events cannot be directly retrieved or selectively revised.Its compactness and computational efficiency motivate external mechanisms for persistent storage, retrieval, and management.Source: §5.3 · pp. 16–17

6 Explicit Memory

Explicit memory separates individually addressable entries from model weights or dense states, making stored content selectively readable and individually writable. The section distinguishes verbatim, slot, and learned stores by what they retain, how they are updated, and the tasks and constraints associated with them.

6 Explicit Memory

  • Explicit memory stores individually addressable entries that can be read or revised separately, rather than entangled in weights or a dense state.Separating storage from computation makes entries inspectable, editable, or expandable without changing the model that reads them.Source: §6 · p. 17

6.1 Mechanism

  • A lookback query retrieves a similarity-weighted mixture from the store; writes append observations or revise slots, with verbatim state per-sequence and slot or learned capacity fixed.Slot and learned entries are parameters frozen after training, whereas verbatim entries encode and append new observations.Source: §6.1 · pp. 17–18

6.2.1 Verbatim Memory

  • Verbatim memory keeps timesteps or patches separately addressable, from Transformer contexts to patch caches, but finite contexts bound capacity and attention reads grow quadratically.Time-series and language tokens can share the same attention context as a joint store.Source: §6.2.1 · pp. 18, 20

6.2.2 Slot Memory

  • Slot memory uses fixed locations for stored states, supporting pattern-based forecasting, graph generation, and anomaly prototypes; STanHop also evaluates capacity and pattern-recovery reliability.All these designs fix the number of slots before training.Source: §6.2.2 · p. 20

6.2.3 Learned Memory

  • Learned stores summarize recurring structure in compact prototypes, serving anomaly detection, classification, cross-series forecasting, foundation-model adaptation, and increasingly imputation.Classification stores class prototypes or discriminative shapelets; forecasting stores can index operating regimes rather than individual episodes.Source: §6.2.3 · pp. 20–21

6.3 Memory Writing and Integration

  • Writes range from task-loss-trained entries frozen after training to input-dependent or gated updates; retrieved content can replace encodings, fuse with predictions, or parameterize components.MEMTO learns a gate controlling how much new information each entry admits.Source: §6.3 · pp. 21–22
  • Explicit stores risk slot collapse, where entries become similar, and addressing diffusion, where weights spread broadly, making diversity and sparse addressing design concerns.Clustering initialization and diversity losses target collapse, while sparse addressing is a natural response to diffusion.Source: §6.3 · p. 22

6.4 Coverage and Limitations

  • Explicit memory is strongest in anomaly detection and classification, while its predeployment-fixed capacity and content cannot accommodate unseen regimes.Its known cost and auditable, traceable reads trade off against unstable writes and stores that usually remain static after deployment unless designed to update online.Source: §6.4 · pp. 22–23

7 Retrieval-Augmented Memory

Retrieval-augmented memory keeps information in an external store and recalls query-relevant records rather than compressing all useful history into a bounded representation. The section organizes these systems by what they retain, how they retrieve and integrate it, and where coverage remains limited.

7.1 Mechanism

  • A query retrieves top-K key-matched entries, but memory type depends on the persistently returned value; keys and continuations must be available at query time to avoid leakage.Stores, retrievers, and integration mechanisms can operate over different representations.Source: §7 · p. 23, §7.1 · pp. 23–24, Figure 7 · p. 24

7.2.1 Instance Retrieval Memory

  • Instance retrieval retains addressable historical cases; ReTime [91] retrieves related series, while RAFT retrieves analogous observed patterns and their realized futures.Retrieved precedents can supply inference-time evidence complementary to parametric learning.Source: §7.2.1 · p. 25

7.2.2 Latent Retrieval Memory

  • Latent retrieval makes individually addressable embeddings, tokens, or priors the persistent recalled content, gaining compactness while risking loss of details that may later predict.The category depends on whether the encoded object itself is retrieved, rather than serving only as a key for returning an original episode.Source: §7.2.2 · p. 26

7.2.3 Knowledge Retrieval Memory

  • Knowledge retrieval stores external context such as text, events, metadata, or structured knowledge, but relevance requires temporal and semantic alignment to avoid stale context.It can complement a retrieved trajectory with information that helps assess whether the analogy remains valid.Source: §7.2.3 · p. 27

7.3 Memory Access and Integration

  • Query-dependent reads use fixed similarities or learned and time-series-specific relevance functions, then integrate retrieved content through augmentation, attention, generative conditioning, or prompts.Similarity alone may select a highly similar but obsolete example under non-stationarity; the same store can serve different predictor backbones.Source: §7.3 · pp. 27–28

7.4 Coverage and Limitations

  • Retrieval memory is concentrated in forecasting, while anomaly detection has a strong recent example and imputation, classification, reasoning, and decision-making remain sparse.The surveyed stores are largely passive; stale records under non-stationarity motivate active writing, updating, and forgetting.Source: §7.4 · pp. 28–29
  • Instance, latent, and knowledge retrieval respectively provide concrete precedents, compact reusable representations, and information absent from the numerical series, with data-scaled external capacity.Their limitations include retrieval and index costs, relevance-function dependence, loss of latent detail, knowledge provenance and timing, and no benefit when the store lacks informative precedents.Source: §7.4 · p. 28

8 Agentic Memory

Agentic memory places an external store under controller-issued write, read, and forget policies that can evolve across interactions. The surveyed time-series systems are mostly offline or frozen at deployment, leaving fully online memory and memory-decision evaluation underexplored.

8 Agentic Memory

  • Earlier explicit modules and retrieval indices use policies fixed before deployment, whereas agentic memory delegates decisions about what to keep, revise, and remove to a controller.This distinction matters under non-stationarity, when a once-useful episode may become misleading.Source: §8 · p. 29

8.1 Mechanism

  • An agentic controller governs what interaction artifacts are persisted, what is recalled and when, and what is revised, demoted, or discarded as the store evolves.The write lifecycle can filter and consolidate artifacts, while the read operation returns the signal used by the predictor.Source: §8.1 · pp. 29–30

8.2 Type of Agentic Memory

  • Time-series agentic systems are organized by the store they populate, including episodic, semantic, procedural, and within-episode working memory.The review compares store operations rather than the surrounding agent architecture.Source: §8.1 · p. 30, Table 4 · p. 31, §8.2 · p. 32

8.2.1 Episodic and working stores.

  • Episodic stores refine prediction experience or calibration guidance, while working memory carries evidence and tool outputs within one run but does not persist across episodes.MemCast updates per-entry confidence without test-data leakage; Cast-R1 is a boundary case for episode-confined state.Source: §8.2.1 · pp. 32–33

8.2.2 Semantic stores.

  • Semantic stores provide reusable laws, anomaly descriptions, or prototypes for verification and grounding, while Argos turns validated knowledge into inspectable executable rules.Argos reviews candidate rules against validation data and can revise performance regressions rather than simply discard a rule.Source: §8.2.2 · p. 33

8.2.3 Procedural stores.

  • Procedural stores retain strategies or skills for acting: CastFlow retrieves tool schedules associated with similar windows, while Agentic-RAG organizes reusable skills by task.CastFlow reports that too many recalled trajectories can inject redundant context and degrade reasoning; success-only skill stores lack records of failure conditions.Source: §8.2.3 · pp. 33–34

8.3 Memory Management and Integration

  • Memory design must address abstraction, inference-time integration, policy control, and when stores change; most systems freeze offline-built stores, and type-specific decay remains limited.The fully online regime—where a deployed forecaster writes and forgets as it goes—is largely underexplored.Source: §8.3 · p. 34

8.4 Coverage and Limitations

  • Only one surveyed method revises its store after deployment, while another updates confidence without removing entries; agentic memory remains concentrated in forecasting.Potential benefits include adaptation under drift and auditability, but costs, hand-designed policies, spurious abstractions, error amplification, and missing memory-decision benchmarks constrain evidence of benefit.Source: §8.4 · pp. 34–35

9 Cross-Cutting View: Memory by Task

The task view reorganizes memory methods around applications, because different tasks draw on different forms of stored information. The reviewed literature spans several tasks but remains concentrated in forecasting, leaving task–mechanism combinations underexplored.

Forecasting

  • Forecasting is the only task where all four memory types are well represented, and retrieval is particularly strong when a few relevant past episodes matter.Agentic memory is newer and can decide what historical evidence to retain or revise as conditions change.Source: §9 · p. 35

Classification

  • Classification naturally favors explicit prototypes or discriminative subsequences, while retrieval of similar labeled series is almost absent.The review identifies retrieval as a possible source of evidence and explanation, especially for rare or heterogeneous classes.Source: §9 · p. 35

Anomaly detection

  • Anomaly detection uses explicit normal-pattern references, with retrieval offering historical comparisons and agentic memory potentially updating stale notions of normal under drift.Source: §9 · p. 37

Imputation

  • Imputation methods mostly propagate nearby context through internal or explicit memory, although retrieval could exploit analogous missing segments in other series.The reviewed literature suggests broader historical analogues remain less explored than local context.Source: §9 · p. 37

Reasoning and Decision-making

  • Reasoning uses retrieval to extend evidence beyond the current window and agentic memory to retain intermediate findings, tool outputs, and conclusions.Decision-making instead needs memory of prior observations, actions, and outcomes; explicit and retrieval approaches there remain largely open.Source: §9 · p. 37

Cross-task overview

  • Memory requirements are task-dependent: explicit memory fits stored-pattern tasks, retrieval fits forecasting analogues, and agentic memory offers a broader workflow across tasks.The open task–mechanism cells indicate combinations that the reviewed literature has barely addressed.Source: Table 5 · p. 36, §9 · p. 37

10 Benchmarks, Evaluation, and Resources

The section surveys benchmark families that test memory across conventional tasks, multivariate and spatial structure, and hierarchical sharing. Existing results suggest memory helps when history contains reusable evidence, but coverage remains fragmented and several larger-scale or memory-specific evaluations are still missing.

10 Benchmarks, Evaluation, and Resources

  • The benchmark landscape spans conventional numerical, foundation-model, multimodal, reasoning, and agentic settings, whose evaluation needs expand along the memory spectrum.These benchmark families can overlap; Table 6 presents representative families and marks emerging non-archival or workshop resources with †.Source: §10 · p. 37, Table 6 · p. 38

10.1.1 General Time Series

  • General archives provide complementary coverage, while memory-specific imputation benchmarking remains absent despite the relevance of realistic MCAR, MAR, and NMAR missingness.Monash covers heterogeneous frequencies, lengths, and missing values; UCR is used for classification, and TSB-AD curates 1,070 series from 40 datasets.Source: §10.1.1 · pp. 38–39
  • Memory helps across conventional time-series tasks when stores contain reusable evidence, but findings remain fragmented across task-specific benchmarks.A broader evaluation is needed to determine whether mechanisms generalize across heterogeneous regimes.Source: §10.1.1 · p. 39

10.1.2 Multivariate Time Series

  • BasicTS+ exposes how multivariate-memory usefulness depends on temporal and cross-variable structure; a controlled comparison under its exact protocol remains missing.Retrieval gains can shrink or become detrimental when similar observed histories do not imply similar future dynamics.Source: §10.1.2 · p. 39

10.1.3 Spatiotemporal Time Series

  • Traffic is a favorable memory regime because recurring patterns and related sensors provide reusable evidence, but its advantage at LargeST scale remains unestablished.LargeST extends traffic forecasting to five years and up to 8,600 sensors, beyond smaller controlled PeMS benchmarks.Source: §10.1.3 · pp. 39–40

10.1.4 Hierarchical Time Series

  • Hierarchical memory can help sparse lower-level series draw on richer aggregate histories, but this benefit has not been established at M5 scale.HAMN improves forecasting across multiple hierarchical datasets by allowing lower-level series to use aggregate-series memory.Source: §10.1.4 · p. 40

10.2 Foundation-Model Benchmarks

Foundation-model benchmarks test generalization across datasets, frequencies, and domains, while raising the question of whether external memory adds evidence beyond pretraining. Current approaches indicate that parametric pretraining and additional memory can complement one another, with provenance needed to interpret gains.

10.2 Foundation-Model Benchmarks

  • Foundation-model evaluation tests generalization across datasets, frequencies, and domains, including zero-shot targets not used for task-specific fitting.Chronos helped establish this setting through pretraining on public and synthetic data and evaluation across a broad dataset collection.Source: §10.2 · p. 40
  • Pretraining overlap can confound apparent external-memory gains, making provenance increasingly important.Some information supplied by external memory may already have been encoded parametrically during pretraining.Source: §10.2 · pp. 40–41
  • Retrieval-based methods show query-specific historical evidence can improve strong pretrained forecasters, while compact memory modules offer an alternative to datastore retrieval at inference.The useful form depends on the trade-off between adaptable external evidence and bounded inference cost.Source: §10.2 · p. 40

10.3 Multimodal Time-Series Benchmarks

Multimodal benchmarks test whether models retrieve external information that complements numerical histories, while reasoning benchmarks examine evidence use across tasks and steps. Current evaluations indicate that memory can help when it supplies missing evidence, but memory operations and persistent-memory effects remain difficult to isolate.

10.3 Multimodal Time-Series Benchmarks

  • CiK pairs numerical histories with textual context necessary to solve each instance, testing whether contextual evidence changes the forecast rather than merely being fused.TRACE separately measures text-to-series and series-to-text retrieval, while Time-MMD and Time-IMM broaden evaluation to multiple domains and irregular modalities.Source: §10.3 · p. 41
  • Multimodal memory is most useful when recalled evidence supplies information absent from numerical history, and should be judged by whether retrieval finds temporally and semantically aligned evidence.Robustness to asynchronous, missing, or misaligned modalities remains less characterized.Source: §10.3 · p. 41

10.4 Reasoning Benchmarks

  • Reasoning benchmarks span controlled categories and real-world domains, but often score answers rather than the underlying memory operations.TimeSeriesExamAgent covers pattern recognition, noise understanding, similarity, anomaly detection, and causality.Source: §10.4 · p. 41
  • Longer context and retained intermediate reasoning do not guarantee recovery of distant evidence; most reasoning benchmarks lack matched with-memory and without-memory variants.TS-Haystack finds access deteriorates as informative events are buried in longer histories, while explicit retrieval is more reliable.Source: §10.4 · p. 42

10.5 Agentic Evaluation

Agentic evaluations often measure final outcomes without isolating persistent memory, while memory-specific evaluation should directly test retention, retrieval, temporal validity, and management. Existing software ecosystems and the survey’s organized method collection support reproducible benchmarking and resource discovery.

10.5 Agentic Evaluation

  • TimeSeriesGym evaluates practical time-series engineering challenges, but agentic benchmarks do not explicitly measure writing, updating, recalling, or forgetting persistent experience.The absence of a standardized archival benchmark for these operations is identified as a survey finding.Source: §10.5 · p. 42
  • Memory-enabled forecasting agents suggest accumulated experience can improve workflows, but current evaluations do not isolate the causal contribution of persistent-memory operations.MAFS reports gains from specialization and inter-agent information exchange without isolating persistent memory.Source: §10.5 · p. 42

10.6 Memory-Specific Evaluation

  • Memory evaluation should separately measure retention, retrieval quality, temporal validity, and write/update/forget decisions under a fixed storage budget.These measures are intended to be reported separately from final task error.Source: §10.6 · pp. 42–43

10.7 Open-Source Resources

  • The survey’s method collection records stored representation, read/write semantics, target task, venue, and code alongside mature general-purpose and specialized time-series software resources.Named ecosystems include GluonTS, aeon, and Merlion.Source: §10.7 · p. 43

11 Open Challenges and Future Directions

The section frames the central challenge as deciding which history to retain, in what form, and at what cost. It develops seven research questions spanning memory allocation, retrieval, validity, multimodality, agents, privileged information, and causal reasoning.

11.1 Memory Allocation and Effective Temporal Capacity

  • Time-series memory must prioritize rare predictive precursors over routine observations, motivating event-driven writes and separate compressed-state and permanent-store tracks.The section proposes evaluating effective temporal memory capacity by testing whether task-relevant information remains recoverable as its distance from the prediction target increases.Source: §11.1 · pp. 44–45

11.2 From information retrieval to temporal retrieval.

  • Retrieval should match historical precursors by future relevance, not only past morphology, and fuse retrieved evidence without erasing distinctive temporal patterns.The section also identifies phase and frequency mismatch and absent recency weighting as vulnerabilities, and proposes asymmetric similarity with uncertainty-aware gating.Source: §11.2 · pp. 45–46

11.3 Memory Validity under Distribution Shift

  • Stored patterns can remain retrievable but become unreliable as conditions change, so memory should continuously assess validity and distinguish transient shifts from structural breaks.The proposed lifecycle allows memories to remain active, be suppressed and reactivated, or be retired as evidence changes.Source: §11.3 · pp. 46–47

11.4 Hierarchical Multimodal Memory

  • Multimodal memory should organize information across shared and modality-specific representations, preserving complementary details while limiting redundant storage and cost.The section presents adaptive choices about joint encoding, separate preservation, and promotion to richer representations as open problems.Source: §11.4 · p. 47

11.5 Beyond LLM-Centric Agentic Systems

  • Time-series agents remain concentrated around LLM-centric designs, although converting continuous numerical streams into text may lose information.The section proposes heterogeneous agents in which specialized models jointly govern perception, memory, and control.Source: §11.5 · pp. 47–48

11.6 Memory from Privileged Information

  • Privileged temporal context could train causal students to retain or discard history by revealing which observations matter for subsequent dynamics.The surveyed privileged-information methods mainly target prediction, leaving direct supervision of memory formation largely unexplored.Source: §11.6 · p. 48

11.7 Causal Memory for Temporal Reasoning

  • Predictive states may capture event associations without preserving mechanisms, limiting their support for explanations and intervention-based counterfactual reasoning.The proposed direction is to retain and update causal structure, including delayed effects, regime-specific mechanisms, and intervention outcomes.Source: §11.7 · p. 49

12 Conclusion

The conclusion unifies time-series methods as a spectrum of memory mechanisms, from implicit states to agent-curated stores. It identifies gaps in retrieval, evaluation, and agentic memory, and emphasizes deciding what history to retain and trust.

12 Conclusion

  • The survey recasts time-series methods as a unified memory spectrum spanning implicit parametric states, explicit and compressed representations, persistent retrieval, and agent-curated stores.The framework compares how historical information is represented, accessed, updated, and forgotten.Source: §12 · p. 49
  • The survey identifies long-term retrieval as concentrated in forecasting, memory-specific evaluation as limited, and agentic time-series memory as early-stage.Source: §12 · p. 49
  • The central challenge is determining which historical information is worth retaining, how to represent and place it, and when it remains trustworthy.The authors present the memory spectrum, taxonomy, and online repository as a framework for organizing the literature beyond architectural eras.Source: §12 · p. 49

S1 Supplementary Material: Glossary

The glossary standardizes the survey’s memory categories, operating dimensions, evaluation terms, and recurring problem settings.

S1 Supplementary Material: Glossary

  • Effective temporal memory capacity measures whether distant information remains recoverable and usable, while memory management evaluates write, update, and forget decisions under a fixed budget.Source: S1 Supplementary Material: Glossary · pp. 64–65
  • Explicit memory uses separately addressable entries, retrieval memory recalls query-dependent subsets, and curated retrieval stores agent-chosen content that remains read-only at deployment.Source: S1 Supplementary Material: Glossary · pp. 64, 66
  • Internal memory stores history in fixed-dimensional latent states, whereas external memory keeps it in a separately addressable store that can be read and sometimes written.The survey defines model memory as any mechanism making history available beyond the current prediction target.Source: S1 Supplementary Material: Glossary · pp. 64–65
  • The glossary distinguishes long-horizon dependence, recurring patterns, sparse or hierarchical data, and regime shifts as settings that pose different historical-memory demands.It also names causal memory as retaining dependencies and intervention outcomes to support counterfactual reasoning.Source: S1 Supplementary Material: Glossary · pp. 64–66
  • Memory mechanisms are compared by representation, capacity, read/write mechanism, and persistence, from implicit states and bounded stores to growing retrieval indexes.Source: S1 Supplementary Material: Glossary · pp. 64–66
  • Retrieval quality tests whether a relevant record is retrieved, temporal validity tests rejection of obsolete-regime memories, and slot collapse means learned slots converge on similar content.Source: S1 Supplementary Material: Glossary · p. 66

S2 Supplementary Material: Search and Selection Protocol

The supplement documents how the surveyed corpus was assembled and how inclusion, exclusion, and classification decisions were made. It also notes search and classification limitations that qualify the resulting coverage.

S2 Supplementary Material: Search and Selection Protocol

S2.1 Scope and Time Window

  • The primary search window is 2015–2026, with four earlier foundational works retained because reviewed mechanisms descend from them.Source: S2.1 Scope and Time Window · p. 67

S2.2 Sources and Search Terms

  • The search covered arXiv, Google Scholar, major conference proceedings, and relevant journals, using backward and forward snowballing alongside keyword searches.Mechanism terms were paired with at least one time-series term.Source: S2.2 Sources and Search Terms · p. 67

S2.3 Inclusion and Exclusion Criteria

  • Screening proceeded from title and abstract to full text, retaining works whose memory could be characterized by retained information, writing, retrieval, and persistence.A work was kept only if it met every inclusion criterion and triggered no exclusion criterion.Source: S2.3 Inclusion and Exclusion Criteria · p. 67, Table 9 · p. 69

S2.4 Threats to Validity

  • The authors flag terminology gaps, unsettled archival status among recent preprints, and judgment calls near taxonomy boundaries as threats to validity.Snowballing reduces but may not eliminate missed slot-memory or prototype-based work; the collection records classifications for inspection.Source: S2.4 Threats to Validity · p. 67

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