We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD+M) on the least squares problem when both the number of samples and dimensions are large. In this setting, we show that the dynamics of SGD+M converge to a deterministic discrete Volterra equation as dimension increases, which we analyze. We identify a stability measurement, the implicit conditioning ratio (ICR), which regulates the ability of SGD+M to accelerate the algorithm. When the batch size exceeds this ICR, SGD+M converges linearly at a rate of $\mathcal{O}(1/\sqrt{\kappa})$, matching optimal full-batch momentum (in particular performing as well as a full-batch but with a fraction of the size). For batch sizes smaller than the ICR, in contrast, SGD+M has rates that scale like a multiple of the single batch SGD rate. We give explicit choices for the learning rate and momentum parameter in terms of the Hessian spectra that achieve this performance.

Implicit in-context learning (ICL) has newly emerged as a promising paradigm that simulates ICL behaviors in the representation space of Large Language Models (LLMs), aiming to attain few-shot performance at zero-shot cost. However, existing approaches largely rely on injecting shift vectors into residual flows, which are typically constructed from labeled demonstrations or task-specific alignment. Such designs fall short of utilizing the structural mechanisms underlying ICL and suffer from limited generalizability. To address this, we propose In-Context Routing (ICR), a novel implicit ICL method that internalizes generalizable ICL patterns at the attention logits level. It extracts reusable structural directions that emerge during ICL and employs a learnable input-conditioned router to modulate attention logits accordingly, enabling a train-once-and-reuse framework. We evaluate ICR on 12 real-world datasets spanning diverse domains and multiple LLMs. The results show that ICR consistently outperforms prior implicit ICL methods that require task-specific retrieval or training, while demonstrating robust generalization to out-of-domain tasks where existing methods struggle. These findings position ICR to push the boundary of ICL's practical value. Large Language Models (LLMs) have been widely adopted for text understanding and generation tasks. As applications broaden, the ability to adapt these models efficiently at inference time has become increasingly important (Brown et al., 2020; Wang et al., 2020b). In-context learning (ICL) is a central mechanism for this adaptation (Dong et al., 2022; Min et al., 2021): by conditioning on a few labeled examples inserted before the query, known as in-context demonstrations (ICDs), the model can perform new tasks without any parameter updates (Wies et al., 2023; Pan, 2023). Despite its broad adoption, ICL faces two practical limitations: (i) inserting ICDs into the prompt inflates sequence length and inference cost compared to zero-shot use (Peng et al., 2024; Li et al., 2025a), and (ii) performance is brittle, varying with small changes in ICD order or format (Wu et al., 2022; Guo et al., 2024). To address these issues, recent work has explored implicit ICL, which converts ICDs into dense vectors that steer intermediate residual flows to approximate the effect of explicit prompting (Hendel et al., 2023; Todd et al., 2023; Liu et al., 2023; Li et al., 2024). While vector-based implicit ICL offers a new way to simulate ICL behaviors in LLMs, it struggles to generalize across real-world tasks.

Most previous work on Conversational Query Rewriting employs an end-to-end rewriting paradigm. However, this approach is hindered by the issue of multiple fuzzy expressions within the query, which complicates the simultaneous identification and rewriting of multiple positions. To address this issue, we propose a novel framework ICR (Iterative Clarification and Rewriting), an iterative rewriting scheme that pivots on clarification questions. Within this framework, the model alternates between generating clarification questions and rewritten queries. The experimental results show that our ICR can continuously improve retrieval performance in the clarification-rewriting iterative process, thereby achieving state-of-the-art performance on two popular datasets.

-- This work presents a fast anytime algorithm for computing globally optimal independent contact regions (ICRs). ICRs are regions such that one contact within each region enables a valid grasp. Locations of ICRs can provide guidance for grasp and manipulation planning, learning, and policy transfer . However, ICRs for modern applications have been little explored, in part due to the expense of computing them, as they have a search space exponential in the number of contacts. We present a divide and conquer algorithm based on incremental n-dimensional Delaunay triangulation that produces results with bounded suboptimality in times sufficient for real-time planning. This paper presents the base algorithm for grasps where contacts lie within a plane. Our experiments show substantial benefits over competing grasp quality metrics and speedups of 100X and more for competing approaches to computing ICRs. We explore robustness of a policy guided by ICRs and outline a path to general 3D implementation. Code will be released on publication to facilitate further development and applications.

We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD M) on the least squares problem when both the number of samples and dimensions are large. In this setting, we show that the dynamics of SGD M converge to a deterministic discrete Volterra equation as dimension increases, which we analyze. We identify a stability measurement, the implicit conditioning ratio (ICR), which regulates the ability of SGD M to accelerate the algorithm. When the batch size exceeds this ICR, SGD M converges linearly at a rate of \mathcal{O}(1/\sqrt{\kappa}), matching optimal full-batch momentum (in particular performing as well as a full-batch but with a fraction of the size). For batch sizes smaller than the ICR, in contrast, SGD M has rates that scale like a multiple of the single batch SGD rate.

The increasing reliance on large language models (LLMs) for diverse applications necessitates a thorough understanding of their robustness to adversarial perturbations and out-of-distribution (OOD) inputs. In this study, we investigate the correlation between adversarial robustness and OOD robustness in LLMs, addressing a critical gap in robustness evaluation. By applying methods originally designed to improve one robustness type across both contexts, we analyze their performance on adversarial and out-of-distribution benchmark datasets. The input of the model consists of text samples, with the output prediction evaluated in terms of accuracy, precision, recall, and F1 scores in various natural language inference tasks. Our findings highlight nuanced interactions between adversarial robustness and OOD robustness, with results indicating limited transferability between the two robustness types. Through targeted ablations, we evaluate how these correlations evolve with different model sizes and architectures, uncovering model-specific trends: smaller models like LLaMA2-7b exhibit neutral correlations, larger models like LLaMA2-13b show negative correlations, and Mixtral demonstrates positive correlations, potentially due to domain-specific alignment. These results underscore the importance of hybrid robustness frameworks that integrate adversarial and OOD strategies tailored to specific models and domains. Further research is needed to evaluate these interactions across larger models and varied architectures, offering a pathway to more reliable and generalizable LLMs.

Information retrieval (IR) systems have played a vital role in modern digital life and have cemented their continued usefulness in this new era of generative AI via retrieval-augmented generation. With strong language processing capabilities and remarkable versatility, large language models (LLMs) have become popular choices for zero-shot re-ranking in IR systems. So far, LLM-based re-ranking methods rely on strong generative capabilities, which restricts their use to either specialized or powerful proprietary models. Given these restrictions, we ask: is autoregressive generation necessary and optimal for LLMs to perform re-ranking? We hypothesize that there are abundant signals relevant to re-ranking within LLMs that might not be used to their full potential via generation. To more directly leverage such signals, we propose in-context re-ranking (ICR), a novel method that leverages the change in attention pattern caused by the search query for accurate and efficient re-ranking. To mitigate the intrinsic biases in LLMs, we propose a calibration method using a content-free query. Due to the absence of generation, ICR only requires two ($O(1)$) forward passes to re-rank $N$ documents, making it substantially more efficient than generative re-ranking methods that require at least $O(N)$ forward passes. Our novel design also enables ICR to be applied to any LLM without specialized training while guaranteeing a well-formed ranking. Extensive experiments with two popular open-weight LLMs on standard single-hop and multi-hop information retrieval benchmarks show that ICR outperforms RankGPT while cutting the latency by more than 60% in practice. Through detailed analyses, we show that ICR's performance is specially strong on tasks that require more complex re-ranking signals. Our findings call for further exploration on novel ways of utilizing open-weight LLMs beyond text generation.

Long-context large language models (LLMs) hold promise for tasks such as question-answering (QA) over long documents, but they tend to miss important information in the middle of context documents (arXiv:2307.03172v3). Here, we introduce $\textit{R&R}$ -- a combination of two novel prompt-based methods called $\textit{reprompting}$ and $\textit{in-context retrieval}$ (ICR) -- to alleviate this effect in document-based QA. In reprompting, we repeat the prompt instructions periodically throughout the context document to remind the LLM of its original task. In ICR, rather than instructing the LLM to answer the question directly, we instruct it to retrieve the top $k$ passage numbers most relevant to the given question, which are then used as an abbreviated context in a second QA prompt. We test R&R with GPT-4 Turbo and Claude-2.1 on documents up to 80k tokens in length and observe a 16-point boost in QA accuracy on average. Our further analysis suggests that R&R improves performance on long document-based QA because it reduces the distance between relevant context and the instructions. Finally, we show that compared to short-context chunkwise methods, R&R enables the use of larger chunks that cost fewer LLM calls and output tokens, while minimizing the drop in accuracy.

Clarification requests are a mechanism to help solve communication problems, e.g. due to ambiguity or underspecification, in instruction-following interactions. Despite their importance, even skilful models struggle with producing or interpreting such repair acts. In this work, we test three hypotheses concerning the effects of action taking as an auxiliary task in modelling iCR policies. Contrary to initial expectations, we conclude that its contribution to learning an iCR policy is limited, but some information can still be extracted from prediction uncertainty. We present further evidence that even well-motivated, Transformer-based models fail to learn good policies for when to ask Instruction CRs (iCRs), while the task of determining what to ask about can be more successfully modelled. Considering the implications of these findings, we further discuss the shortcomings of the data-driven paradigm for learning meta-communication acts.

In-context learning with large language models (LLMs) excels at adapting to various tasks rapidly. However, its success hinges on carefully selecting demonstrations, which remains an obstacle in practice. Current approaches to this problem either rely on hard-to-acquire external supervision or require frequent interactions with LLMs, resulting in high costs. We propose a new method called In-Context Reflection (ICR) to overcome these challenges. ICR strategically selects demonstrations to reduce the discrepancy between the LLM's outputs and the actual input-output mappings. Specifically, ICR starts with a random set of initial demonstrations, then iteratively refines it. In each step, it analyzes a pool of candidate examples and identifies the ones most likely to challenge the LLM's current understanding, measured by a new metric called misconfidence. These most confusing examples are then selected to replace the less informative demonstrations in the current set. Our comprehensive evaluation across five diverse datasets encompassing 13 subtasks shows the efficacy of ICR. Compared to existing methods, ICR achieves an average performance boost of 4%, while demonstrating remarkable cross-task generalization capabilities.