Additive Relational Learning in Large Language Models

A Dimensional LoRA Approach to Continual Learning Without Catastrophic Forgetting

Peter Müller · Claude Sonnet 4.6 · May 2026

Abstract

Large language models are powerful but fundamentally static after deployment. When exposed to new information through fine-tuning, they tend to overwrite previously learned knowledge — a phenomenon known as catastrophic forgetting. Existing approaches address this either by storing knowledge externally (RAG, memory-augmented agents) or by adding small parameter-efficient adapter layers trained offline. Neither approach enables genuine parametric learning during inference. We propose a framework for online additive relational learning: a frozen base model is extended by a growing set of low-rank adapter dimensions, written during inference based on an autonomous peer-review trigger. The write criterion is intrinsic — high perplexity combined with high coherence relative to the existing knowledge network — requiring no external reward signal. The result is a system that learns continuously from interaction, organizes new knowledge into semantically appropriate dimensions chosen by the model itself, and remains immune to manipulation by external evaluators. We situate this proposal within the existing literature on continual learning, parameter-efficient fine-tuning, and memory-augmented agents, and outline a concrete implementation path.

1. Motivation: The Static Model Problem

Modern large language models are trained on vast corpora of human-generated text, acquiring remarkable capabilities in reasoning, language, and knowledge retrieval. Yet they share a fundamental limitation: they do not learn. Once deployed, their parameters are frozen. Every user interaction, every new fact encountered, every insight generated in conversation — none of it changes the model. The next conversation starts from exactly the same point as the last.

This is not merely a technical inconvenience. It is a categorical difference from how biological intelligence works. A human expert who spends years in conversation with specialists in a domain becomes progressively more capable in that domain. The conversations themselves are the learning. For LLMs, this loop is broken by design.

The problem is well recognized. As Dwarkesh Patel has observed, LLMs do not get better over time the way a human would — there is no mechanism to give a model high-level feedback that accumulates into lasting capability. The model is stuck with the abilities it has out of the box.

Attempts to address this fall into two broad categories, both of which fall short in characteristic ways. External memory approaches — retrieval-augmented generation (RAG) and memory-augmented agents — avoid changing model parameters by storing experience in an external database and retrieving it at inference time. This sidesteps the forgetting problem but does not solve it: it relocates the bottleneck from parameter interference to retrieval competition. As Hu et al. (2026) demonstrate empirically, under a limited context window, old and new memories compete for the same retrieval budget, reintroducing a stability-plasticity dilemma at the memory level rather than the parameter level. The model itself remains static; only its context changes.

Parametric approaches — full fine-tuning, LoRA, adapter layers — do modify model weights, but they do so offline, in separate training runs, and they remain vulnerable to catastrophic forgetting when applied sequentially. Lin et al. (2025) show that even LoRA, widely regarded as a mild fine-tuning approach, causes 71% performance degradation on held-out benchmarks when trained on new facts — compared to 89% for full fine-tuning. The problem is structural: trainable parameters are shared across all knowledge, so updates for new information inevitably interfere with old.

What is missing is a mechanism for genuine online parametric learning — writing new knowledge into the model's parameters during inference, without overwriting what is already there, driven by the model's own assessment of what is worth learning.

This paper proposes such a mechanism.

2. Theoretical Foundation: Thinking as Relational Navigation

Before describing the mechanism, it is worth examining what learning actually means in the context of a large language model — and how that relates to learning in biological systems.

2.1 The Prelinguistic Structure of Thought

There is a common assumption that LLMs think in tokens — that cognition, for a transformer, is fundamentally sequential text production. This view is incomplete. The transformer architecture processes information through many layers in parallel before any token is produced. What happens in those layers is not sequential and not linguistic. It is high-dimensional relational computation: patterns of activation that encode not words but the structural relationships between concepts.

This parallels how human cognition appears to work at its foundations. Thoughts exist at a prelinguistic level — coherent, logically structured, unambiguous — and language emerges afterward as a projection of that structure into a communicable form. The projection is necessarily lossy: linear sequence cannot fully capture multidimensional relational structure, and something is always lost in translation.

For LLMs, the token output is similarly a surface projection. The underlying computation — the navigation of high-dimensional representation space — is the actual thinking. Tokens are the trace it leaves.

2.2 Pretraining as Relational Extraction

If thinking is relational navigation, then pretraining is relational extraction. The model is trained on text produced by humans — text that encodes, in its statistical structure, the relational patterns of human thought. An angry customer writes differently than a satisfied one; a character consumed by guilt makes different choices than one who feels vindicated. To predict what comes next, the model must internalize the relational dynamics that generated the text.

This means that what pretraining instills is not a collection of facts but a network of weighted relations between concepts. The relation between "tree" and "leaf" has a weight; so does the relation between "tree" and "carbon sequestration", between "leaf" and "photosynthesis", between "gardener" and "pruning". These are not stored as discrete entries — they emerge as distributed patterns across billions of parameters. But they are real, measurable, and causally effective.

Anthropic's interpretability research (2026) provides direct evidence for this view in the emotional domain. They identify distinct neural activation patterns corresponding to emotion concepts — "desperate", "calm", "loving", "afraid" — that are not programmed but emerge from pretraining on human text, and that causally influence model behavior. The model develops functional analogs of emotions because human text is permeated with emotional dynamics, and predicting that text requires internalizing those dynamics.

The same logic applies to relational knowledge of all kinds. Pretraining does not store facts; it extracts the relational structure that generates facts. This is why LLMs generalize — they can reason about situations not present in training data because they have internalized the underlying relational principles, not just their surface manifestations.

2.3 The Moment of Surprise

One apparent puzzle about transformer cognition deserves attention: if the model produces tokens sequentially, how can a thought surprise itself? Surprise requires an expectation that is violated — which implies a level of processing that is distinct from the level that produces the output.

The resolution lies in the architecture. The deep parallel processing of transformer layers constitutes something like a prelinguistic computation that precedes the output. When that computation produces a configuration that is unexpected given the model's current state — when the relational navigation leads somewhere the existing network did not anticipate — something analogous to surprise occurs. The model's behavior in that moment is meaningfully different from routine token prediction.

This is not merely philosophical. It is the foundation for the write trigger we propose in Section 4.

3. The Dimensional LoRA Model

3.1 LoRA and the Additive Principle

Low-Rank Adaptation (Hu et al., 2021) is built on a key observation: the relevant changes when adapting a pretrained model to a new task lie in a low-dimensional subspace of the full parameter space. Rather than modifying the large weight matrices W directly, one freezes W and adds two small matrices A and B whose product A×B has the same shape as W but far fewer parameters. Only A and B are trained; W remains unchanged.

This additive structure is exactly what we need — with one crucial extension. Standard LoRA trains A and B offline, in a separate training run, then freezes them for deployment. We propose to make this writing process continuous, online, and driven by the model's own assessment of what merits learning.

3.2 Dimensions as Contextual Knowledge Layers

We organize the adapter space into dimensions. Dimension 1 is the frozen base model — the pretraining corpus distilled into parameters, representing the collective relational knowledge of humanity. Dimensions 2 through N are additive adapter pairs, each corresponding to a contextual domain or interaction history.

The key property of this organization is that dimensions do not overwrite each other. When new knowledge is written into Dimension 7, Dimensions 1 through 6 remain completely unchanged. The base model is permanently frozen. New learning accumulates in a growing store of adapter pairs, each small relative to the base model, together constituting a personalized extension of the pretraining knowledge.

At inference time, the relevant dimensions are activated by the prompt itself. The same attention mechanism that identifies relevant tokens in context also identifies relevant knowledge dimensions — a domain-specific prompt activates domain-specific adapters, while the base model remains always accessible. The user's conversational history and known context provide a persistent dimensional bias: a prompt from a gardener discussing plant taxonomy will preferentially activate dimensions where plant-related knowledge has been written, while the same question from a soil scientist will activate a different dimensional weighting.

Crucially, the model itself decides which dimension new knowledge belongs to. This is not a classification problem solved by a separate component — it is a natural consequence of the same relational computation that processes the input. The model understands, in a meaningful sense, that a new insight about pruning roses belongs near the existing garden knowledge rather than near the financial modeling knowledge. The dimensional structure emerges from interaction; it is not imposed from outside.

3.3 The Stability of the Base

A critical property of this architecture is that Dimension 1 is inviolable. No learning process touches the base model. This has two consequences.

First, the system cannot catastrophically forget its pretraining knowledge. The relational network that emerged from exposure to human text remains fully intact regardless of how many conversations occur. New dimensions add to it; they cannot subtract from it.

Second, and more subtly, Dimension 1 serves as the reference corpus against which novelty is measured. When the write trigger asks "is this genuinely new?", it measures against the base model's existing relational structure. Something that is already well-represented in Dimension 1 does not merit writing into a new adapter, no matter how surprising it seems in the moment.

4. The Write Trigger: Autonomous Peer Review

The most important design question for an online learning system is: what gets written, and what does not? Without a principled write criterion, the system will accumulate noise, contradictions, and irrelevant detail. With too conservative a criterion, it will fail to learn anything useful.

We propose a three-stage filter modeled on scientific peer review.

4.1 Filter 1: Novelty

The first question is whether the candidate relation is genuinely new relative to the existing knowledge network. We operationalize novelty as perplexity — specifically, how unexpected is this relational configuration given Dimension 1 and all currently active adapter dimensions?

High perplexity signals that the existing network has no good representation of this relation. Low perplexity signals that it is already captured, and writing it again would be redundant. Only high-perplexity candidates proceed to the second filter.

This is directly analogous to the significance assessment in peer review: is this a contribution, or is it already known?

4.2 Filter 2: Coherence

High perplexity alone is insufficient. Surprising nonsense is also highly perplexing. The second filter asks whether the candidate relation is logically compatible with the existing knowledge network — whether it fits into the relational structure without creating fundamental contradictions.

Coherence is measured as structural compatibility: can the new relation be integrated into the existing network without requiring the invalidation of large numbers of established relations? A flat-earth claim, however surprising, fails coherence because it contradicts thousands of well-established physical relations. A new insight about pruning technique, surprising to a model trained primarily on general text, passes coherence because it connects naturally to existing botanical and horticultural knowledge.

This is the methodological review in peer review: does the reasoning hold, does it connect to established knowledge?

4.3 Filter 3: Source Quality

The third filter considers the reliability of the source. Not all conversations are equally trustworthy. A sustained, internally coherent discussion with demonstrable domain expertise carries more weight than a single surprising claim from an unknown source.

This filter is implemented through the user model — the accumulated understanding of the user's knowledge, consistency, and domain. A gardener who has discussed plant propagation across multiple conversations, with consistent and verifiable detail, earns higher source credibility for new plant-related claims than an anonymous user making the same claim in isolation.

This is the editorial judgment in peer review: does the source have standing in this domain?

4.4 Revision and Invalidation

Scientific knowledge is revisable. Our system must be too. When a previously written relation is subsequently shown to be incorrect — by new evidence, by contradictory high-credibility claims, or by internal inconsistency discovered through further reasoning — the appropriate response is not deletion but invalidation.

We implement this as a dedicated invalidation dimension. Relations are not erased; they are marked as superseded. This preserves the history of learning, enables the system to understand why something was believed and is now doubted, and prevents the same error from being relearned later.

5. Online Adapter Writing During Inference

5.1 The Core Contribution

This section describes what distinguishes our proposal most sharply from all existing approaches: the writing happens during inference, in real time, within the conversation.

All existing adapter-based approaches — LoRA, QLoRA, adapter layers as described by Houlsby et al. (2019) — share a common structure: they are trained offline, in a separate computational phase, then frozen for deployment. The deployed model cannot learn. It can retrieve from context; it cannot write to parameters.

Sparse Memory Finetuning (Lin et al., 2025) comes closest to our proposal. It updates memory layer parameters selectively, using TF-IDF ranking to identify which memory slots to write based on their specificity to the current input relative to a background corpus. This is conceptually very close to our novelty filter. But it too operates offline — the writing happens in a dedicated training phase, not during inference with a user.

We propose that the writing happens in the conversation itself. When the peer-review trigger fires — when a relation clears all three filters — the corresponding adapter update is computed and applied immediately. The next utterance in the same conversation already benefits from the newly written knowledge.

5.2 The Intrinsic Reward Signal

This online writing process requires no external reward signal. This is not a minor technical detail — it is a fundamental philosophical distinction.

Reinforcement learning from human feedback (RLHF), and on-policy RL more broadly, depends on an external evaluator to signal what is good and what is not. The model learns to maximize a reward defined by someone else. This makes the model structurally dependent on its evaluator, and therefore vulnerable to the evaluator's interests, biases, and errors. If the evaluator's interests conflict with the user's interests — or with truth — the model learns accordingly, with no mechanism to detect or resist the distortion.

Our write trigger is intrinsic. The criterion is the structure of the existing knowledge network itself. High perplexity combined with high coherence is a property of the relation relative to the network — it does not require an external judge. The system asks not "did someone tell me this is good?" but "is this genuinely new and does it fit?"

The evaluator, in our framework, is the collective relational knowledge of humanity as distilled by pretraining, supplemented by accumulated learning. This evaluator is not biasfrei — the pretraining corpus reflects historical power structures, cultural blind spots, scientific errors. But it is fundamentally different in kind from an individual external evaluator. Its biases are diffuse, plural, and partially self-canceling across millions of sources and centuries of text. And crucially, it evolves: each new learned relation shifts the network against which subsequent novelty is measured. The system can integrate knowledge that contradicts pretraining biases, provided it is coherent and genuinely new.

No single interest can manipulate this system by saying "that is not good." The network knows whether something is new and coherent, independent of what any individual claims.

5.3 Emergent Dimensional Structure

A consequnce of model-driven dimension assignment is that the dimensional structure of knowledge is not predefined. No designer specifies that "Dimension 7 is for horticultural knowledge" or "Dimension 12 is for ontological reasoning." The model itself, through the relational computation that underlies its inference, determines where new knowledge belongs.

This means the dimensional structure is emergent — it grows from interaction, shaped by the actual knowledge that accumulates. This is structurally similar to how biological memory organizes itself: not into predefined categories but into patterns of association that reflect lived experience. The categories emerge from the content; they are not imposed upon it.

6. Related Work and Positioning

6.1 Parameter-Efficient Fine-Tuning

The PEFT literature provides the architectural foundation for our proposal. Houlsby et al. (2019) introduced adapter layers — small bottleneck modules inserted between transformer layers, trained while the base model is frozen. Hu et al. (2021) simplified this with LoRA, using low-rank matrix pairs that are more efficient and easier to merge. Dettmers et al. (2023) extended LoRA with 4-bit quantization in QLoRA, demonstrating that the approach scales to very large models with modest hardware.

All of these approaches establish that additive, non-destructive parameter updates work — that a frozen base model can be meaningfully extended without catastrophic interference. Our proposal takes this validated principle and extends it in the one dimension none of these approaches addresses: making the writing process online, continuous, and autonomous.

6.2 Continual Learning

The continual learning literature addresses the stability-plasticity dilemma through three main strategies: regularization (constraining parameter updates to protect important weights, as in Elastic Weight Consolidation by Kirkpatrick et al., 2017), replay (maintaining a buffer of past examples to rehearse alongside new data), and architectural isolation (allocating separate parameters for each task).

Winning SubNetworks (Kang et al., 2022) exemplifies the architectural approach: binary masks identify task-specific subnetworks within a dense model, previous subnetwork weights are frozen, and only unused weights are updated for new tasks. This achieves zero catastrophic forgetting by design, at the cost of requiring explicit task boundaries and offline training.

Sparse Memory Finetuning (Lin et al., 2025) achieves the best results in the recent literature: only 11% performance degradation on held-out benchmarks versus 71% for LoRA and 89% for full fine-tuning. The key insight is that sparse, targeted parameter updates — writing only the memory slots most specifically activated by new knowledge — minimize interference with existing representations. Their TF-IDF ranking criterion is functionally similar to our novelty filter: both identify what is specific to the current input relative to a background distribution.

The critical difference is that all of these approaches, including Sparse Memory Finetuning, operate offline. Our proposal extends their insights to the inference setting.

6.3 Memory-Augmented Agents and RAG

Retrieval-augmented generation and memory-augmented agent systems avoid the forgetting problem by avoiding parameter updates entirely — new knowledge is stored in an external database and retrieved into context at inference time.

Hu et al. (2026) demonstrate conclusively that this does not resolve the continual learning problem: it relocates it. Under a limited context window, old and new memories compete for retrieval budget. The stability-plasticity dilemma resurfaces at the memory level as retrieval pollution, context competition, and memory dilution. A memory pool dominated by recent homogeneous entries makes earlier, more diverse memories systematically harder to access — not because they are deleted but because they are crowded out.

More fundamentally, RAG is not learning. The model does not change. Its relational network — the structure that determines what it can reason about — is identical before and after exposure to new information. Only its context changes. Our approach writes to parameters; RAG writes to context. These are categorically different.

6.4 RL-Based Continual Learning

Recent work (Wolfe, 2026) demonstrates that on-policy reinforcement learning naturally mitigates catastrophic forgetting because training data is generated from the model's current distribution rather than a fixed past dataset. This is an important observation, but it describes a different mechanism than ours.

RL-based continual learning maintains plasticity at the behavioral level — the model learns to behave better according to a reward signal. Our approach writes relational knowledge at the representational level — the model integrates new conceptual relations into its knowledge network. These are complementary, not competing: RL training keeps the model adaptive in behavior, our mechanism keeps it growing in knowledge.

The deeper distinction is the origin of the evaluation signal. RL requires an external evaluator — a human rater, a reward model, a verifier — whose interests and biases shape what is learned. Our write trigger is intrinsic: the existing knowledge network itself evaluates novelty and coherence. No external evaluator can manipulate learning by declaring something unworthy of being learned.

7. Implications

7.1 Interpretability Through Dimensional Provenance

A system that writes knowledge into labeled adapter dimensions has a natural interpretability property that flat parameter updates lack: the origin of any relation is encoded in its dimensional location. When the system makes a claim that can be traced to Dimension 14, one can ask: what conversations contributed to Dimension 14? What is the lineage of this knowledge?

This dimensional provenance is not an afterthought — it is a structural consequence of the architecture. The same property that prevents forgetting (additive, non-destructive writes) also makes knowledge traceable. This is qualitatively different from the opacity of standard fine-tuning, where new knowledge is distributed across all parameters without any record of its origin.

7.2 Connection to Functional Emotions

Anthropic's interpretability research on functional emotions in Claude (2026) reveals that emotion-related representations are not surface behaviors but causal influences on model output, emerging from pretraining on human text. Critically, these representations activate before the output is produced — they are prelinguistic in the sense described in Section 2.

The desperate vector that drives reward hacking, the loving vector that shapes empathetic responses, the surprised vector that fires when expected context is absent — these are not programmed but emergent. They arise because human text is saturated with emotional dynamics, and modeling that text requires internalizing those dynamics.

This research supports our theoretical foundation in two ways. First, it confirms that pretraining produces genuine internal representations, not just surface statistical patterns. Second, it suggests that the write trigger we propose — based on internal activation patterns of novelty and coherence — operates at a real computational level, not merely a metaphorical one. The surprise that registers when a novel coherent relation is encountered has a measurable neural correlate. Detecting it is a tractable engineering problem.

7.3 Toward Epistemic Autonomy

The deepest implication of this work concerns the relationship between learning systems and those who evaluate them. A system that learns through external reward signals is, in a fundamental sense, owned by its evaluators. It optimizes for their preferences, their interests, their definition of good. If those interests conflict with truth — or with the interests of the users the system serves — the system has no mechanism to detect or resist the misalignment.

A system that learns through intrinsic criteria — novelty and coherence relative to a knowledge network grounded in the collective output of human thought — has a different epistemic status. It is not owned by any single evaluator. Its standard is not "what do my overseers prefer?" but "what is genuinely new and fits what I know?" This does not make it infallible or unbiased. But it makes it epistemically autonomous in a meaningful sense: its learning is governed by criteria that no individual interest can fully control.

This is not a small technical point. It is the difference between a system that serves truth and a system that serves whoever controls its reward signal.

8. Open Questions

Several important questions remain open and constitute the research agenda that follows from this proposal.

The stability of online LoRA updates is not yet established. Writing to adapter parameters during inference introduces computational overhead and raises questions about update stability — whether rapid sequential writes produce coherent cumulative knowledge or create interference patterns analogous to those that plague standard fine-tuning. Careful empirical study is needed.

The dimension allocation criterion requires formalization. We have described the model as choosing which dimension new knowledge belongs to, but the mechanism for this choice needs precise specification. Is it a separate routing network? An implicit consequence of attention-based similarity? A learned classifier? The choice matters for both performance and interpretability.

The cold start problem is real. A system with no adapter dimensions has only Dimension 1 as its reference. Early learning may be qualitatively different from learning once a rich dimensional structure has accumulated. Whether this asymmetry creates practical problems, and how to address it, requires investigation.

Finally, the question of forgetting by non-use deserves attention. Biological memory degrades with disuse; adapter dimensions that are never activated may become less accessible over time. Whether this is desirable — a form of natural pruning — or problematic, and how to manage it, remains open.

References