Implicit Assumptions About Tasks in Continual Learning

Kathrin Korte; Christian Metzner; Akshay Bedhotiya; Viet Anh Khoa Tran; Eleni Nisioti; Sebastian Risi

cs.LGOct 30, 2026

Implicit Assumptions About Tasks in Continual Learning

Authors: Kathrin Korte, Christian Metzner, Akshay Bedhotiya, Viet Anh Khoa Tran, Eleni Nisioti, Sebastian Risi

Organizations: IT University of Copenhagen Copenhagen, Denmark · Institute of Neuroinformatics University of Zurich and ETH Zurich · Peter Grünberg Institute Forschungszentrum Jülich & RWTH Aachen

Abstract

Continual learning is the study of how a model accumulates knowledge from data received over time, rather than all at once. In practice, this is typically achieved by dividing a dataset into tasks and presenting them sequentially. Explanations of the resulting measurements take into account factors such as the similarity between segments, the rate at which the data changes and the order of presentation. Each of these factors can be defined in terms of the underlying data, the partition imposed on it, or the learner that encounters it. These levels do not necessarily coincide, and it is usually left implicit which level a reported quantity refers to. We separate these and identify which properties acquire a value at each level. In controlled teacher--student experiments, we demonstrate that partitioning the same underlying trajectory at different levels of granularity, changing the order of presentation, and varying the similarity structure of the underlying data all result in different measured outcomes. We review representative benchmarks to determine which of these properties are stated. Where the underlying data cannot be inspected, as in foundation models built on undisclosed pre-training corpora, its properties are inherited by the model's initial state, and the training applied on top of it can be described.

Figures & tables

Figure 1: One stream, many partitions. (a) A stream is a realized, ordered sequence. Colour denotes content of experience; nearby colours indicate related experience. (b) A task cut produces a task sequence. Segment width = task scope. (c) Change within a task depends on scope. (d) Similarity between tasks depends on scope: coarse segments span heterogeneous stretches and overlap; fine segments are narrow and largely disjoint. $S(K_{N},C_{N})$ is the similarity of two tasks under a partition into $N$ tasks. (e) The same segments in a different order are a different stream, since a stream is a realized order. None of (c)-(e) is a property of the stream alone; each is dependent on stream & cut. Everything here is learner independent. Fig. 2 shows what changes once a learner is present.

Property	Stream (§ 2.1 )	Task Cut (§ 2.2 )	Learner (§ 2.3 )
Scope	Support of the realized stream (data)	Support of a task/segment induced by the partition	Support of the learner’s trajectory in function space. Access: the learner’s filtration
Order	Realized order at sample or batch level	Order of the task labels induced by the partition	Which learner state encounters which segment
Similarity	A function of time points, $D(t,t^{\prime})$ , or an aggregate	Intra- and inter-task similarity	Distance in hypothesis or representation space
Change	Gradual change or drift over time	Discrete change across task boundaries, and intra-task change induced by partition	State displacement or learning dynamics induced by the update rule

Table 1: Properties of the realized stream, task discretization, and learner.

Figure 2: A learner enters the setting. (a) A learner occupies one point in a stream at a time. Its lifetime scope is the breadth of experience the stream covers as a whole, of which only the past is available to it and the future is unobserved. (b) The same stream under a single partition. Similarity is defined for every pair of tasks and computable from the data once the boundaries are fixed. What a learner retains of each task is a separate quantity (Sec. 2.3 ). (c–e) A teacher–student stream in which the teacher’s weights follow a fixed trajectory, with the student trained on tasks sampled along it. Curves show mean squared test error on each task after the whole stream has been traversed, shaded by standard error over five initialisations, with task position on the horizontal axis. Full setup in Sec. B . (c) Partition granularity,

N\in\{5,10,50\}

, which alters similarity between tasks and change within them together. (d) Presentation order at

N=50

. Reversing the stream reverses the profile of retained error across it, and shuffling removes its structure. (e) Distance traversed by the teacher across the stream at

N=50

, which sets the overall similarity between its regions.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Benchmark	Scope	Order/Exposure	Similarity	Change	Task identity	Boundaries
Classical synthetic partitions
Split MNIST [ Zenke et al., 2017 , Van de Ven et al., 2022 ]	2 classes per task $?$	blocked $\checkmark$	label-disjoint, pairs fixed or per run $\checkmark$	abrupt $\checkmark$	given or withheld $\checkmark$	given $\checkmark$
Split CIFAR-100 [ Rebuffi et al., 2017 , Van de Ven et al., 2022 ]	2–50 classes per task $?$	blocked $\checkmark$	label-disjoint, grouping per run $\checkmark$	abrupt $\checkmark$	given or withheld $\checkmark$	given $\checkmark$
Permuted MNIST [ Goodfellow et al., 2013 , Kirkpatrick et al., 2017 ]	full label set $?$	blocked $\checkmark$	labels shared, inputs permuted $\checkmark$	abrupt $\checkmark$	none (shared output) $\checkmark$	given $\checkmark$
Purpose-built streams
CORe50 [ Lomonaco and Maltoni, 2017 ]	scenario-dependent $?$	shuffled batch order $\checkmark$	same objects across sessions $\circ$	abrupt at switch $\circ$	none (single head) $\checkmark$	batch-marked $\checkmark$

Appendix

Table 2: Benchmark families against the properties of Sec. 2 . Superscripts denote the status of the entry (

\checkmark

specified;

\circ

not stated by the benchmark but our reading of its description, judged recoverable from the released data and not computed here;

?

unspecified and not recoverable from the protocol, with a marker alone indicating that the protocol gives no value). For Similarity,

\checkmark

marks that the benchmark states how tasks were constructed, which constrains the kind of relatedness without providing a magnitude. Two of the reviewed benchmarks provide more information. Ibrahim et al. [2024] grade their two shifts as weak or strong, and Wołczyk et al. [2021] report forward transfer between every pair of tasks for a reference agent, a learner-level quantity that they also use to set the task order. For Scope, a class count fixes how many labels fall in a task without stating the breadth of experience they cover, and is recorded as

?

; only Liu et al. [2023] is marked with

\checkmark

, for declaring per suite which factors are held fixed and which vary. The Order/Exposure column records the presentation regime, while the realized ordering within it is typically drawn per run rather than fixed by the benchmark. The last two columns, Task identity at test time and Boundaries, are two facets of the learner’s access. Each entry is recorded at whichever level the benchmark specifies.

Figure 3: (a) Changing different parameters in the teacher has different effects on forgetting in the student. (b) Changing the stream scope (i.e., the intrinsic dimensionality of the teacher’s weight trajectory) affects forgetting in the learner.

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As large language models (LLMs) become increasingly capable, the next question is how can we enable models to continually learn? Today, the field largely frames this as a problem of context management and mitigating forgetting. We argue this framing is incomplete: continual learning is fundamentally about increasing model competence as the world changes. We disentangle this change along two axes -- space, where the model encounters new domains, and time, where the underlying data drifts under a fixed task. This framing lets us study continual learning under realistic conditions: new domains arrive over time, facts drift past their training cutoff, and agentic interactions accumulate state across episodes. To evaluate methods under this setting, we recast widely used LLM benchmarks as sequential problems and introduce a single mechanism-agnostic protocol that compares prompt-based methods (GEPA, ACE), supervised learning (SFT, SDFT), reinforcement learning (GRPO, SDPO), and context compression (Cartridges, In-place TTT). Prompt-based methods fit each new stage quickly but degrade on future tasks. Distillation-based methods accumulate knowledge stably but struggle to update outdated facts. Context compression improves efficiency without substantially improving the ability to learn new tasks. Online reinforcement learning adapts most effectively to knowledge updates but remains sensitive to noisy reward signals. Overall, our results suggest that continual learning is not a single capability: different patterns of environmental change require fundamentally different update behaviors, determining when adaptation must be learned inside model weights and when it can be achieved through external scaffolding. We hope that understanding where each method succeeds and fails will guide the design of stronger continual learning systems.

Abstract

Continual Learning

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