Retrievable Gradients: Continual Post-Training Without Cumulative Weight Drift

In-context learning has recently been linked to implicit gradient descent in linear self-attention models, suggesting that context can induce a forward-pass update. Retrieval-augmented generation (RAG) also relies on context, but retrieved documents are usually treated as static evidence rather than signals for adaptation. We study RAG as an in-context optimization process. First, we show that one linear self-attention layer can implement one gradient-descent step on a unified linearized RAG objective covering both projection-based and dot-product retrieval interfaces. This gives an exact regime where retrieval-augmented prediction and in-context optimization coincide. We use this result not as a literal model of LLM computation, but as a guide for adapting the interaction between queries and retrieved evidence. We then test the boundary of this correspondence: it remains stable under controlled linear extensions, but becomes feature-distribution dependent under nonlinear architectures. Finally, we turn this view into a lightweight method for frozen RAG LLMs. The method keeps the retriever and backbone fixed, and predicts a context-conditioned update to a generator-side evidence-use interface. Across seven QA benchmarks, two retrievers, and two frozen LLM backbones, this forward-only update improves a shared-interface baseline, transfers to held-out tasks, and approaches test-time gradient adaptation at much lower per-query cost.

Generative information retrieval (GenIR) consolidates retrieval into a single neural model that decodes document identifiers (docids) directly from queries. While this model-as-index paradigm offers architectural simplicity, it is poorly suited to dynamic document collections. Unlike modular systems, where indexes are easily updated, GenIR's knowledge is parametrically encoded in its weights; consequently, standard adaptation methods such as full and parameter-efficient fine-tuning can induce catastrophic forgetting. We show that sequential adaptation improves retrieval on newly added documents but substantially degrades performance on earlier slices, exposing a pronounced stability-plasticity trade-off. To address this, we propose post-adaptation memory tuning (PAMT), a memory-only stabilization stage that augments an adapted model with a modular parametric memory head (PMH). PAMT freezes the backbone and attaches a product-key memory with fixed addressing. During prefix-trie constrained decoding, decoder hidden states sparsely query PMH to produce residual corrections in hidden space; these corrections are mapped to score adjustments via the frozen output embedding matrix, computed only over trie-valid tokens. This guides docid generation while keeping routing and backbone parameters fixed. To limit cross-slice interference, PAMT updates only a fixed budget of memory values selected using decoding-time access statistics, prioritizing entries frequently activated by the current slice and rarely used in prior sessions. Experiments on MS MARCO and Natural Questions under sequential, disjoint corpus increments show that PAMT substantially improves retention on earlier slices with minimal impact on retrieval performance for newly added documents, while modifying only a sparse subset of memory values per session.

Machine unlearning for large language models (LLMs) aims to remove targeted knowledge while preserving general capability. In this paper, we recast LLM unlearning as an asymmetric two-task problem: retention is the primary objective and forgetting is an auxiliary. From this perspective, we propose a retention-prioritized gradient synthesis framework that decouples task-specific gradient extraction from conflict-aware combination. Instantiating the framework, we adapt established PCGrad to resolve gradient conflicts, and introduce SAGO, a novel retention-prioritized gradient synthesis method. Theoretically, both variants ensure non-negative cosine similarity with the retain gradient, while SAGO achieves strictly tighter alignment through constructive sign-constrained synthesis. Empirically, on WMDP Bio/Cyber and RWKU benchmarks, SAGO consistently pushes the Pareto frontier: e.g., on WMDP Bio (SimNPO+GD), recovery of target model MMLU performance progresses from 44.6% (naive) to 94.0% (+PCGrad) and further to 96.0% (+SAGO), while maintaining comparable forgetting strength. Our results show that re-shaping gradient geometry, rather than re-balancing losses, is the key to mitigating unlearning-retention trade-offs.