ICLR 2026 Papers

Transformers excel through content-addressable retrieval and the ability to exploit contexts of, in principle, unbounded length. We recast associative memory at the level of probability measures, treating a context as a distribution over tokens and viewing attention as an integral operator on measures. Concretely, for mixture contexts $\nu = I^{-1} \sum_{i=1}^I \mu^{(i)}$ and a query $x_{\mathrm{q}}(i^\*)$, the task decomposes into (i) recall of the relevant component $\mu^{(i^\*)}$ and (ii) prediction from $(\mu_{i^\*},x_{\mathrm{q}})$. We study learned softmax attention (not a frozen kernel) trained by empirical risk minimization and show that a shallow measure-theoretic Transformer composed with an MLP learns the recall-and-predict map under a spectral assumption on the input densities. We further establish a matching minimax lower bound with the same rate exponent (up to multiplicative constants), proving sharpness of the convergence order. The framework offers a principled recipe for designing and analyzing Transformers that recall from arbitrarily long, distributional contexts with provable generalization guarantees.

Humans rely on memory to perform tasks; our goal is to endow robot policies with the same ability. Naively conditioning on long observation histories is computationally expensive and brittle under covariate shift, while indiscriminate subsampling of history leads to irrelevant or redundant information. We propose a hierarchical policy framework, where the high-level policy is trained to select and track previous task-relevant keyframes from its experience. The high-level policy uses selected keyframes and the most recent frames when generating text instructions for a low-level policy to execute. This design is compatible with existing vision-language-action (VLA) models and enables the system to efficiently reason over long-horizon dependencies. In our experiments, we fine-tune Qwen2.5-VL-7B-Instruct and $\pi_{0.5}$ as the high-level and low-level policies respectively, using demonstrations supplemented with minimal language annotations. Our approach, MemER, outperforms prior methods on three real-world long-horizon robotic manipulation tasks that require minutes of memory. Videos and code can be found at https://memer-policy.github.io.

Modern approaches to enhancing Large Language Models' factual accuracy and knowledge utilization face a fundamental trade-off: non-parametric retrieval-augmented generation (RAG) provides flexible access to external knowledge but suffers from high inference latency and shallow integration, while parametric fine-tuning methods like LoRA risk catastrophic forgetting and degraded general capabilities. In this work, we propose MLP Memory, a lightweight parametric module that learns to internalize retrieval patterns without explicit document access. By pretraining an MLP to imitate a $k$NN retriever's behavior on the entire pretraining dataset, we create a differentiable memory component that captures the benefits of retrieval-based knowledge access in a fully parametric form. Our architecture integrates this pretrained MLP Memory with Transformer decoders through simple probability interpolation, achieving 12.3\% relative improvement on five question-answering benchmarks and 5.2 points absolute gain across nine general NLP tasks, while reducing hallucinations by up to 10 points on HaluEval. Moreover, MLP Memory delivers 2.5$\times$ faster inference than RAG with superior accuracy. Our findings show that learning retrieval patterns parametrically bridges the gap between efficient inference and effective knowledge access, offering a practical alternative to both RAG and fine-tuning approaches.

Associative memory systems face significant challenges in efficiently retrieving semantically related information from large document collections, particularly when queries require traversing complex relationships between concepts. Traditional retrieval-augmented generation (RAG) approaches often struggle to capture intricate associative patterns and relationships embedded within textual data. To address this limitation, we propose BrowseNet, a novel associative memory framework that leverages query-specific subgraph exploration within a named-entity-based graph for enhanced information retrieval. Our method transforms unstructured text into a graph-of-chunks representation, where nodes encode document chunks with semantic embeddings and edges capture lexical relationships between content segments. By dynamically traversing the graph-of-chunks based on query characteristics, BrowseNet emulates content-addressable memory systems that enable efficient pattern matching and associative recall. The framework incorporates both structural similarity derived from lexical relationships and semantic similarity based on embedding representations to optimize retrieval performance. We evaluate BrowseNet against established RAG baselines and state-of-the-art (SOTA) pipelines using publicly available datasets that require associative reasoning across multiple information sources. Experimental results demonstrate that BrowseNet achieves SOTA performance in exact match score over both the graph-based RAG approaches and the dense retrieval methods. The two-pronged approach combining structural graph traversal with semantic embeddings enables more effective associative memory retrieval, particularly for queries requiring the integration of disparate but related information. The code and datasets are open-sourced at: https://github.com/bisect-group/BrowseNet

Retrieval-Augmented Generation (RAG) improves the factuality of large language models (LLMs) by grounding outputs in retrieved evidence, but faithfulness failures, where generations contradict or extend beyond the provided sources, remain a critical challenge. Existing hallucination detection methods for RAG often rely either on large-scale detector training, which requires substantial annotated data, or on querying external LLM judges, which leads to high inference costs. Although some approaches attempt to leverage internal representations of LLMs for hallucination detection, their accuracy remains limited. Motivated by recent advances in mechanistic interpretability, we employ sparse autoencoders (SAEs) to disentangle internal activations, successfully identifying features that are specifically triggered during RAG hallucinations. Building on a systematic pipeline of information-based feature selection and additive feature modeling, we introduce RAGLens, a lightweight hallucination detector that accurately flags unfaithful RAG outputs using LLM internal representations. RAGLens not only achieves superior detection performance compared to existing methods, but also provides interpretable rationales for its decisions, enabling effective post-hoc mitigation of unfaithful RAG. Finally, we justify our design choices and reveal new insights into the distribution of hallucination-related signals within LLMs. The code is available at https://github.com/Teddy-XiongGZ/RAGLens.

Retrieval-Augmented Generation (RAG) systems often rely on information retrieved from heterogeneous sources to support generation tasks. However, existing approaches typically either aggregate all sources uniformly or statically select a single source, neglecting semantic complementarity. Moreover, they commonly employ re-ranking models to obtain Top-k documents, without accounting for actual contribution to generation objective. In this paper, we propose GRO-RAG, a training-free, gradient-aware re-ranking framework for multi-source RAG. Our method performs Top-k document selection by reading gradients from the language model, estimating each document’s contribution to the generation loss through a single backward pass. This enables re-ranking not by heuristic relevance, but by direct feedback from LLM's generation objective. At the source level, we incorporate inter-source redundancy and query relevance to select source combination prior to re-ranking. Theoretically, we prove that this gradient-based Top-k selection approximates the optimal subset minimizing the generation loss, and aligns with minimizing the leave-one-out loss upper bound. Experiments across multi-source QA and open-domain generation tasks demonstrate consistent improvements in generation quality, highlighting the importance of generation-aware retrieval selection in multi-source RAG.

Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g., undefined predicates, symbol misuse, and version incompatibility) and the semantic gap caused by ambiguous or missing premises in natural language descriptions. To address these issues, we propose CRAMF, a Concept-driven Retrieval-Augmented Mathematical Formalization framework. CRAMF enhances LLM-based autoformalization by retrieving formal definitions of core mathematical concepts, providing contextual grounding during code generation. However, applying retrieval-augmented generation (RAG) in this setting is non-trivial due to the lack of structured knowledge bases, the polymorphic nature of mathematical concepts, and the high precision required in formal retrieval. We introduce a framework for automatically constructing a concept-definition knowledge base from Mathlib4, the standard mathematical library for the Lean 4 theorem prover, indexing over 26,000 formal definitions and 1,000+ core mathematical concepts. To address conceptual polymorphism, we propose contextual query augmentation with domain- and application-level signals. In addition, we design a dual-channel hybrid retrieval strategy with reranking to ensure accurate and relevant definition retrieval. Experiments on miniF2F, ProofNet, and our newly proposed AdvancedMath benchmark show that CRAMF can be seamlessly integrated into LLM-based autoformalizers, yielding consistent improvements in translation accuracy—achieving up to 62.1% and an average of 29.9% relative improvement.

Retrieval-augmented generation (RAG) enhances the response quality of large language models (LLMs) when handling domain-specific tasks, yet raises significant privacy concerns. This is because both the user query and documents within the knowledge base often contain sensitive or confidential information. To address these concerns, we propose $\texttt{Pisces}$, the first practical cryptography-based RAG framework that supports dual-path retrieval, while protecting both the query and documents. Along the semantic retrieval path, we reduce computation and communication overhead by leveraging a coarse-to-fine strategy. Specifically, a novel oblivious filter is used to privately select a candidate set of documents to reduce the scale of subsequent cosine similarity computations. For the lexical retrieval path, to reduce the overhead of repeatedly invoking labeled PSI, we implement a multi-instance labeled PSI protocol to compute term frequencies for BM25 scoring in a single execution. $\texttt{Pisces}$ can also be integrated with existing privacy-preserving LLM inference frameworks to achieve end-to-end privacy. Experiments demonstrate that $\texttt{Pisces}$ achieves retrieval accuracy comparable to the plaintext baselines, within a 1.87% margin.

While Retrieval-Augmented Generation (RAG) has advanced knowledge-intensive tasks, we identify a fundamental vulnerability: the Correlation Trap. Existing systems cannot distinguish causally decisive evidence from overwhelmingly correlated yet misleading information, leading to systematic failures. We introduce Counterfactual RAG (CF-RAG), a new framework that operationalizes causal reasoning to overcome this limitation. CF-RAG systematically generates and evaluates counterfactual queries to identify causally relevant distinctions, and employs a parallel arbitration mechanism to reconcile conflicting evidence without interference. On challenging benchmarks, CF-RAG substantially improves robustness against the Correlation Trap, achieving state-of-the-art performance while maintaining comparable efficiency to standard RAG models.

Despite recent advances, Large Language Models (LLMs) still generate vulnerable code. Retrieval-Augmented Generation (RAG) has the potential to enhance LLMs for secure code generation by incorporating external security knowledge. However, the conventional RAG design struggles with the noise of raw security-related documents, and existing retrieval methods overlook the significant security semantics implicitly embedded in task descriptions. To address these issues, we propose \textsc{Rescue}, a new RAG framework for secure code generation with two key innovations. First, we propose a hybrid knowledge base construction method that combines LLM-assisted cluster-then-summarize distillation with program slicing, producing both high-level security guidelines and concise, security-focused code examples. Second, we design a hierarchical multi-faceted retrieval that traverses the constructed knowledge base from top to bottom and integrates multiple security-critical facts at each hierarchical level, ensuring comprehensive and accurate retrieval. We evaluated \textsc{Rescue} on four benchmarks and compared it with five state-of-the-art secure code generation methods on six LLMs. The results demonstrate that \textsc{Rescue} improves the SecurePass@1 metric by an average of 4.8 points, establishing a new state-of-the-art performance for security. Furthermore, we performed in-depth analysis and ablation studies to rigorously validate the effectiveness of individual components in \textsc{Rescue}. Our code is available at \url{https://github.com/steven1518/RESCUE}.