Daily Papers

While large language models based on the transformer architecture have demonstrated remarkable in-context learning (ICL) capabilities, understandings of such capabilities are still in an early stage, where existing theory and mechanistic understanding focus mostly on simple scenarios such as learning simple function classes. This paper takes initial steps on understanding ICL in more complex scenarios, by studying learning with representations. Concretely, we construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function, composed with a linear function that differs in each instance. By construction, the optimal ICL algorithm first transforms the inputs by the representation function, and then performs linear ICL on top of the transformed dataset. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size. Empirically, we find trained transformers consistently achieve near-optimal ICL performance in this setting, and exhibit the desired dissection where lower layers transforms the dataset and upper layers perform linear ICL. Through extensive probing and a new pasting experiment, we further reveal several mechanisms within the trained transformers, such as concrete copying behaviors on both the inputs and the representations, linear ICL capability of the upper layers alone, and a post-ICL representation selection mechanism in a harder mixture setting. These observed mechanisms align well with our theory and may shed light on how transformers perform ICL in more realistic scenarios.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

In-context learning (ICL) allows LLMs to learn from examples without changing their weights, which is a particularly promising capability for long-context LLMs that can potentially learn from many examples. Recently, Lin et al. (2024) proposed URIAL, a method using only three in-context examples to align base LLMs, achieving non-trivial instruction following performance. In this work, we show that, while effective, ICL alignment with URIAL still underperforms compared to instruction fine-tuning on established benchmarks such as MT-Bench and AlpacaEval 2.0 (LC), especially with more capable base LMs. Unlike for tasks such as classification, translation, or summarization, adding more ICL demonstrations for long-context LLMs does not systematically improve instruction following performance. To address this limitation, we derive a greedy selection approach for ICL examples that noticeably improves performance, yet without bridging the gap to instruction fine-tuning. Finally, we provide a series of ablation studies to better understand the reasons behind the remaining gap, and we show how some aspects of ICL depart from the existing knowledge and are specific to the instruction tuning setting. Overall, our work advances the understanding of ICL as an alignment technique. We provide our code at https://github.com/tml-epfl/icl-alignment.

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a O(1/T) regret bound for perfectly pretrained ICL, where T is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

In-Context Learning (ICL) enables Large Language Models (LLMs) to perform new tasks by conditioning on prompts with relevant information. Retrieval-Augmented Generation (RAG) enhances ICL by incorporating retrieved documents into the LLM's context at query time. However, traditional retrieval methods focus on semantic relevance, treating retrieval as a search problem. In this paper, we propose reframing retrieval for ICL as a recommendation problem, aiming to select documents that maximize utility in ICL tasks. We introduce the In-Context Learning Embedding and Reranker Benchmark (ICLERB), a novel evaluation framework that compares retrievers based on their ability to enhance LLM accuracy in ICL settings. Additionally, we propose a novel Reinforcement Learning-to-Rank from AI Feedback (RLRAIF) algorithm, designed to fine-tune retrieval models using minimal feedback from the LLM. Our experimental results reveal notable differences between ICLERB and existing benchmarks, and demonstrate that small models fine-tuned with our RLRAIF algorithm outperform large state-of-the-art retrieval models. These findings highlight the limitations of existing evaluation methods and the need for specialized benchmarks and training strategies adapted to ICL.

Few-shot in-context learning (ICL) enables pre-trained language models to perform a previously-unseen task without any gradient-based training by feeding a small number of training examples as part of the input. ICL incurs substantial computational, memory, and storage costs because it involves processing all of the training examples every time a prediction is made. Parameter-efficient fine-tuning (PEFT) (e.g. adapter modules, prompt tuning, sparse update methods, etc.) offers an alternative paradigm where a small set of parameters are trained to enable a model to perform the new task. In this paper, we rigorously compare few-shot ICL and PEFT and demonstrate that the latter offers better accuracy as well as dramatically lower computational costs. Along the way, we introduce a new PEFT method called (IA)^3 that scales activations by learned vectors, attaining stronger performance while only introducing a relatively tiny amount of new parameters. We also propose a simple recipe based on the T0 model called T-Few that can be applied to new tasks without task-specific tuning or modifications. We validate the effectiveness of T-Few on completely unseen tasks by applying it to the RAFT benchmark, attaining super-human performance for the first time and outperforming the state-of-the-art by 6% absolute. All of the code used in our experiments is publicly available.

Can Large language models (LLMs) learn to reason without any weight update and only through in-context learning (ICL)? ICL is strikingly sample-efficient, often learning from only a handful of demonstrations, but complex reasoning tasks typically demand many training examples to learn from. However, naively scaling ICL by adding more demonstrations breaks down at this scale: attention costs grow quadratically, performance saturates or degrades with longer contexts, and the approach remains a shallow form of learning. Due to these limitations, practitioners predominantly rely on in-weight learning (IWL) to induce reasoning. In this work, we show that by using Prefix Tuning, LLMs can learn to reason without overloading the context window and without any weight updates. We introduce ReasonCACHE, an instantiation of this mechanism that distills demonstrations into a fixed key-value cache. Empirically, across challenging reasoning benchmarks, including GPQA-Diamond, ReasonCACHE outperforms standard ICL and matches or surpasses IWL approaches. Further, it achieves this all while being more efficient across three key axes: data, inference cost, and trainable parameters. We also theoretically prove that ReasonCACHE can be strictly more expressive than low-rank weight update since the latter ties expressivity to input rank, whereas ReasonCACHE bypasses this constraint by directly injecting key-values into the attention mechanism. Together, our findings identify ReasonCACHE as a middle path between in-context and in-weight learning, providing a scalable algorithm for learning reasoning skills beyond the context window without modifying parameters. Our project page: https://reasoncache.github.io/

In-context learning (ICL) has shown impressive results in few-shot learning tasks, yet its underlying mechanism is still not fully understood. A recent line of work suggests that ICL performs gradient descent (GD)-based optimization implicitly. While appealing, much of the research focuses on simplified settings, where the parameters of a shallow model are optimized. In this work, we revisit evidence for ICL-GD correspondence on realistic NLP tasks and models. We find gaps in evaluation, both in terms of problematic metrics and insufficient baselines. We show that surprisingly, even untrained models achieve comparable ICL-GD similarity scores despite not exhibiting ICL. Next, we explore a major discrepancy in the flow of information throughout the model between ICL and GD, which we term Layer Causality. We propose a simple GD-based optimization procedure that respects layer causality, and show it improves similarity scores significantly.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

Large language models are well-known to be effective at few-shot in-context learning (ICL). Recent advancements in multimodal foundation models have enabled unprecedentedly long context windows, presenting an opportunity to explore their capability to perform ICL with many more demonstrating examples. In this work, we evaluate the performance of multimodal foundation models scaling from few-shot to many-shot ICL. We benchmark GPT-4o and Gemini 1.5 Pro across 10 datasets spanning multiple domains (natural imagery, medical imagery, remote sensing, and molecular imagery) and tasks (multi-class, multi-label, and fine-grained classification). We observe that many-shot ICL, including up to almost 2,000 multimodal demonstrating examples, leads to substantial improvements compared to few-shot (<100 examples) ICL across all of the datasets. Further, Gemini 1.5 Pro performance continues to improve log-linearly up to the maximum number of tested examples on many datasets. Given the high inference costs associated with the long prompts required for many-shot ICL, we also explore the impact of batching multiple queries in a single API call. We show that batching up to 50 queries can lead to performance improvements under zero-shot and many-shot ICL, with substantial gains in the zero-shot setting on multiple datasets, while drastically reducing per-query cost and latency. Finally, we measure ICL data efficiency of the models, or the rate at which the models learn from more demonstrating examples. We find that while GPT-4o and Gemini 1.5 Pro achieve similar zero-shot performance across the datasets, Gemini 1.5 Pro exhibits higher ICL data efficiency than GPT-4o on most datasets. Our results suggest that many-shot ICL could enable users to efficiently adapt multimodal foundation models to new applications and domains. Our codebase is publicly available at https://github.com/stanfordmlgroup/ManyICL .

Large Language Models (LLMs) have exhibited an impressive ability to perform In-Context Learning (ICL) from only a few examples. Recent works have indicated that the functions learned by ICL can be represented through compressed vectors derived from the transformer. However, the working mechanisms and optimization of these vectors are yet to be thoroughly explored. In this paper, we address this gap by presenting a comprehensive analysis of these compressed vectors, drawing parallels to the parameters trained with gradient descent, and introduce the concept of state vector. Inspired by the works on model soup and momentum-based gradient descent, we propose inner and momentum optimization methods that are applied to refine the state vector progressively as test-time adaptation. Moreover, we simulate state vector aggregation in the multiple example setting, where demonstrations comprising numerous examples are usually too lengthy for regular ICL, and further propose a divide-and-conquer aggregation method to address this challenge. We conduct extensive experiments using Llama-2 and GPT-J in both zero-shot setting and few-shot setting. The experimental results show that our optimization method effectively enhances the state vector and achieves the state-of-the-art performance on diverse tasks. Code is available at https://github.com/HITsz-TMG/ICL-State-Vector

Supervised Fine-Tuning (SFT) is used to specialize model behavior by training weights to produce intended target responses for queries. In contrast, In-Context Learning (ICL) adapts models during inference with instructions or demonstrations in the prompt. ICL can offer better generalizability and more calibrated responses compared to SFT in data scarce settings, at the cost of more inference compute. In this work, we ask the question: Can ICL's internal computations be used to improve the qualities of SFT? We first show that ICL and SFT produce distinct activation patterns, indicating that the two methods achieve adaptation through different functional mechanisms. Motivated by this observation and to use ICL's rich functionality, we introduce ICL Activation Alignment (IA2), a self-distillation technique which aims to replicate ICL's activation patterns in SFT models and incentivizes ICL-like internal reasoning. Performing IA2 as a priming step before SFT significantly improves the accuracy and calibration of model outputs, as shown by our extensive empirical results on 12 popular benchmarks and 2 model families. This finding is not only practically useful, but also offers a conceptual window into the inner mechanics of model adaptation.

Recent works have suggested that In-Context Learning (ICL) operates in dual modes, i.e. task retrieval (remember learned patterns from pre-training) and task learning (inference-time ``learning'' from demonstrations). However, disentangling these the two modes remains a challenging goal. We introduce ICL CIPHERS, a class of task reformulations based on substitution ciphers borrowed from classic cryptography. In this approach, a subset of tokens in the in-context inputs are substituted with other (irrelevant) tokens, rendering English sentences less comprehensible to human eye. However, by design, there is a latent, fixed pattern to this substitution, making it reversible. This bijective (reversible) cipher ensures that the task remains a well-defined task in some abstract sense, despite the transformations. It is a curious question if LLMs can solve ICL CIPHERS with a BIJECTIVE mapping, which requires deciphering the latent cipher. We show that LLMs are better at solving ICL CIPHERS with BIJECTIVE mappings than the NON-BIJECTIVE (irreversible) baseline, providing a novel approach to quantify ``learning'' in ICL. While this gap is small, it is consistent across the board on four datasets and six models. Finally, we examine LLMs' internal representations and identify evidence in their ability to decode the ciphered inputs.

In-context Learning (ICL) is an emerging few-shot learning paradigm on Language Models (LMs) with inner mechanisms un-explored. There are already existing works describing the inner processing of ICL, while they struggle to capture all the inference phenomena in large language models. Therefore, this paper proposes a comprehensive circuit to model the inference dynamics and try to explain the observed phenomena of ICL. In detail, we divide ICL inference into 3 major operations: (1) Summarize: LMs encode every input text (demonstrations and queries) into linear representation in the hidden states with sufficient information to solve ICL tasks. (2) Semantics Merge: LMs merge the encoded representations of demonstrations with their corresponding label tokens to produce joint representations of labels and demonstrations. (3) Feature Retrieval and Copy: LMs search the joint representations similar to the query representation on a task subspace, and copy the searched representations into the query. Then, language model heads capture these copied label representations to a certain extent and decode them into predicted labels. The proposed inference circuit successfully captured many phenomena observed during the ICL process, making it a comprehensive and practical explanation of the ICL inference process. Moreover, ablation analysis by disabling the proposed steps seriously damages the ICL performance, suggesting the proposed inference circuit is a dominating mechanism. Additionally, we confirm and list some bypass mechanisms that solve ICL tasks in parallel with the proposed circuit.

With the increasing ability of large language models (LLMs), in-context learning (ICL) has become a new paradigm for natural language processing (NLP), where LLMs make predictions only based on contexts augmented with a few examples. It has been a new trend to explore ICL to evaluate and extrapolate the ability of LLMs. In this paper, we aim to survey and summarize the progress and challenges of ICL. We first present a formal definition of ICL and clarify its correlation to related studies. Then, we organize and discuss advanced techniques, including training strategies, demonstration designing strategies, as well as related analysis. Finally, we discuss the challenges of ICL and provide potential directions for further research. We hope that our work can encourage more research on uncovering how ICL works and improving ICL.

Many-shot in-context learning has recently shown promise as an alternative to finetuning, with the major advantage that the same model can be served for multiple tasks. However, this shifts the computational burden from training-time to inference-time, making deployment of many-shot ICL challenging to justify in-practice. This cost is further increased if a custom demonstration set is retrieved for each inference example. We present Dynamic Block-Sparse Attention, a training-free framework for retrieval-based many-shot in-context learning. By combining carefully designed block-sparse attention and retrieval of cached groups of demonstrations, we achieve comparable per-example latency to finetuning while maintaining on average >95% of the best method's accuracy across strong ICL and finetuning baselines. We hope that this will further enable the deployment of many-shot ICL at scale.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

Large Language Models (LLMs) have the impressive ability to perform in-context learning (ICL) from only a few examples, but the success of ICL varies widely from task to task. Thus, it is important to quickly determine whether ICL is applicable to a new task, but directly evaluating ICL accuracy can be expensive in situations where test data is expensive to annotate -- the exact situations where ICL is most appealing. In this paper, we propose the task of ICL accuracy estimation, in which we predict the accuracy of an LLM when doing in-context learning on a new task given only unlabeled test data for that task. To perform ICL accuracy estimation, we propose a method that trains a meta-model using LLM confidence scores as features. We compare our method to several strong accuracy estimation baselines on a new benchmark that covers 4 LLMs and 3 task collections. The meta-model improves over all baselines across 8 out of 12 settings and achieves the same estimation performance as directly evaluating on 40 collected labeled test examples per task. At the same time, no existing approach provides an accurate and reliable ICL accuracy estimation in every setting, highlighting the need for better ways to measure the uncertainty of LLM predictions.

Large Language Models(LLMs) have been attracting attention due to a ability called in-context learning(ICL). ICL, without updating the parameters of a LLM, it is possible to achieve highly accurate inference based on rules ``in the context'' by merely inputting a training data into the prompt. Although ICL is a developing field with many unanswered questions, LLMs themselves serves as a inference model, seemingly realizing inference without explicitly indicate ``inductive bias''. On the other hand, a code generation is also a highlighted application of LLMs. The accuracy of code generation has dramatically improved, enabling even non-engineers to generate code to perform the desired tasks by crafting appropriate prompts. In this paper, we propose a novel ``learning'' method called an ``Inductive-Bias Learning (IBL)'', which combines the techniques of ICL and code generation. An idea of IBL is straightforward. Like ICL, IBL inputs a training data into the prompt and outputs a code with a necessary structure for inference (we referred to as ``Code Model'') from a ``contextual understanding''. Despite being a seemingly simple approach, IBL encompasses both a ``property of inference without explicit inductive bias'' inherent in ICL and a ``readability and explainability'' of the code generation. Surprisingly, generated Code Models have been found to achieve predictive accuracy comparable to, and in some cases surpassing, ICL and representative machine learning models. Our IBL code is open source: https://github.com/fuyu-quant/IBLM

RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new algorithms in the field, many of which build upon RRT* itself. In this paper, we first identify a logical gap in the optimality proof of RRT*, which was developed in Karaman and Frazzoli (2011). Then, we present an alternative and mathematically-rigorous proof for asymptotic optimality. Our proof suggests that the connection radius used by RRT* should be increased from γleft(log n{n}right)^{1/d} to γ' left(log n{n}right)^{1/(d+1)} in order to account for the additional dimension of time that dictates the samples' ordering. Here γ, γ', are constants, and n, d, are the number of samples and the dimension of the problem, respectively.

In-context Learning (ICL) enables large language models (LLMs) to tackle downstream tasks through sophisticated prompting and high-quality demonstrations. However, this traditional ICL paradigm shows limitations when facing complex mathematical reasoning tasks, primarily due to its heavy dependence on example quality and the necessity for human intervention in challenging scenarios. To address these limitations, this paper presents HiAR-ICL, a High-level Automated Reasoning paradigm in ICL that shifts focus from specific examples to abstract thinking patterns, extending the conventional concept of context in ICL. HiAR-ICL introduces five atomic reasoning actions as fundamental components for constructing chain-structured patterns. Using Monte Carlo Tree Search, we explore reasoning paths and construct thought cards to guide subsequent inference. We then develop a cognitive complexity framework that dynamically matches problems with appropriate thought cards. Experimental results demonstrate HiAR-ICL's effectiveness, achieving state-of-the-art accuracy (79.6%) on the MATH benchmark with Qwen2.5-7B-Instruct, surpassing GPT-4o (76.6%) and Claude 3.5 (71.1%).

Reward-free exploration is a reinforcement learning setting studied by Jin et al. (2020), who address it by running several algorithms with regret guarantees in parallel. In our work, we instead give a more natural adaptive approach for reward-free exploration which directly reduces upper bounds on the maximum MDP estimation error. We show that, interestingly, our reward-free UCRL algorithm can be seen as a variant of an algorithm of Fiechter from 1994, originally proposed for a different objective that we call best-policy identification. We prove that RF-UCRL needs of order ({SAH^4}/{varepsilon^2})(log(1/δ) + S) episodes to output, with probability 1-δ, an varepsilon-approximation of the optimal policy for any reward function. This bound improves over existing sample-complexity bounds in both the small varepsilon and the small δ regimes. We further investigate the relative complexities of reward-free exploration and best-policy identification.

Fine-tuning Large Language Models (LLMs) typically involves updating at least a few billions of parameters. A more parameter-efficient approach is Prompt Tuning (PT), which updates only a few learnable tokens, and differently, In-Context Learning (ICL) adapts the model to a new task by simply including examples in the input without any training. When applying optimization-based methods, such as fine-tuning and PT for few-shot learning, the model is specifically adapted to the small set of training examples, whereas ICL leaves the model unchanged. This distinction makes traditional learning methods more prone to overfitting; in contrast, ICL is less sensitive to the few-shot scenario. While ICL is not prone to overfitting, it does not fully extract the information that exists in the training examples. This work introduces Context-aware Prompt Tuning (CPT), a method inspired by ICL, PT, and adversarial attacks. We build on the ICL strategy of concatenating examples before the input, but we extend this by PT-like learning, refining the context embedding through iterative optimization to extract deeper insights from the training examples. We carefully modify specific context tokens, considering the unique structure of input and output formats. Inspired by adversarial attacks, we adjust the input based on the labels present in the context, focusing on minimizing, rather than maximizing, the loss. Moreover, we apply a projected gradient descent algorithm to keep token embeddings close to their original values, under the assumption that the user-provided data is inherently valuable. Our method has been shown to achieve superior accuracy across multiple classification tasks using various LLM models.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

Cutting-edge large language models (LLMs) demonstrate promising performance in solving complex math problems with a divide-and-conquer pipeline and the assistance of in-context learning (ICL) examples. However, their potential for improvement is limited by two critical problems within their ICL examples: granularity-mismatch and the ensuing negative-effect noise problem. Specifically, the LLMs are capable of the dividing process yet mostly failed by inaccurate reasoning within a few conquer steps, while the ICL examples retrieved in question-grained sometimes lack relevant steps for a specific challenging reasoning step. Further, this disconnect may hinder the correct reasoning due to its irrelevance. To this end, we focus on improving the reasoning quality within each step and present BoostStep. BoostStep aligns the granularity between the retrieving and reasoning on step grained, and provides highly related ICL examples for each reasoning step with a novel `first-try' strategy. BoostStep provides more relevant examples than the coarse question-grained strategy, enhancing the model reasoning quality within each step steadily. BoostStep is a general and robust reasoning-enhancing method that not only improves standalone reasoning performance but also integrates seamlessly with Monte Carlo Tree Search methods (MCTS) to refine both candidate generation and decision-making. Quantitatively, it improves GPT-4o and Qwen2.5-Math-72B by 3.6\% and 2.0\% respectively on various mathematical benchmarks, and 7.5\% gain combined with MCTS.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

The predictions of Large Language Models (LLMs) on downstream tasks often improve significantly when including examples of the input--label relationship in the context. However, there is currently no consensus about how this in-context learning (ICL) ability of LLMs works. For example, while Xie et al. (2021) liken ICL to a general-purpose learning algorithm, Min et al. (2022) argue ICL does not even learn label relationships from in-context examples. In this paper, we provide novel insights into how ICL leverages label information, revealing both capabilities and limitations. To ensure we obtain a comprehensive picture of ICL behavior, we study probabilistic aspects of ICL predictions and thoroughly examine the dynamics of ICL as more examples are provided. Our experiments show that ICL predictions almost always depend on in-context labels and that ICL can learn truly novel tasks in-context. However, we also find that ICL struggles to fully overcome prediction preferences acquired from pre-training data and, further, that ICL does not consider all in-context information equally.

Many-shot in-context learning (ICL) has emerged as a unique setup to both utilize and test the ability of large language models to handle long context. This paper delves into long-context language model (LCLM) evaluation through many-shot ICL. We first ask: what types of ICL tasks benefit from additional demonstrations, and how effective are they in evaluating LCLMs? We find that classification and summarization tasks show performance improvements with additional demonstrations, while translation and reasoning tasks do not exhibit clear trends. Next, we investigate the extent to which different tasks necessitate retrieval versus global context understanding. We develop metrics to categorize ICL tasks into two groups: (i) similar-sample learning (SSL): tasks where retrieval of the most similar examples is sufficient for good performance, and (ii) all-sample learning (ASL): tasks that necessitate a deeper comprehension of all examples in the prompt. Lastly, we introduce a new many-shot ICL benchmark, MANYICLBENCH, to characterize model's ability on both fronts and benchmark 12 LCLMs using MANYICLBENCH. We find that while state-of-the-art models demonstrate good performance up to 64k tokens in SSL tasks, many models experience significant performance drops at only 16k tokens in ASL tasks.

Large language models (LLMs) have shown impressive in-context learning (ICL) ability in code generation. LLMs take a prompt consisting of requirement-code examples and a new requirement as input, and output new programs. Existing studies have found that ICL is highly dominated by the examples and thus arises research on example selection. However, existing approaches randomly select examples or only consider the textual similarity of requirements to retrieve, leading to sub-optimal performance. In this paper, we propose a novel learning-based selection approach named LAIL (LLM-Aware In-context Learning) for code generation. Given a candidate example, we exploit LLMs themselves to estimate it by considering the generation probabilities of ground-truth programs given a requirement and the example. We then label candidate examples as positive or negative through the probability feedback. Based on the labeled data, we import a contrastive learning objective to train an effective retriever that acquires the preference of LLMs in code generation. We apply LAIL to three LLMs and evaluate it on three representative datasets (e.g., MBJP, MBPP, and MBCPP). LATA outperforms the state-of-the-art baselines by 11.58%, 6.89%, and 5.07% on CodeGen, and 4.38%, 2.85%, and 2.74% on GPT-3.5 in terms of Pass@1, respectively.

The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may forget how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based, and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called Ideal Continual Learner (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify how rehearsal affects generalization. Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.

Large Language Models (LLMs) have demonstrated their In-Context Learning (ICL) capabilities which provides an opportunity to perform few shot learning without any gradient update. Despite its multiple benefits, ICL generalization performance is sensitive to the selected demonstrations. Selecting effective demonstrations for ICL is still an open research challenge. To address this challenge, we propose a demonstration selection method called InfICL which analyzes influences of training samples through influence functions. Identifying highly influential training samples can potentially aid in uplifting the ICL generalization performance. To limit the running cost of InfICL, we only employ the LLM to generate sample embeddings, and don't perform any costly fine tuning. We perform empirical study on multiple real-world datasets and show merits of our InfICL against state-of-the-art baselines.

Active learning (AL) algorithms may achieve better performance with fewer data because the model guides the data selection process. While many algorithms have been proposed, there is little study on what the optimal AL algorithm looks like, which would help researchers understand where their models fall short and iterate on the design. In this paper, we present a simulated annealing algorithm to search for this optimal oracle and analyze it for several tasks. We present qualitative and quantitative insights into the behaviors of this oracle, comparing and contrasting them with those of various heuristics. Moreover, we are able to consistently improve the heuristics using one particular insight. We hope that our findings can better inform future active learning research. The code is available at https://github.com/YilunZhou/optimal-active-learning.

Recent advances in long-context large language models (LLMs) have led to the emerging paradigm of many-shot in-context learning (ICL), where it is observed that scaling many more demonstrating examples beyond the conventional few-shot setup in the context can lead to performance benefits. However, despite its promise, it is unclear what aspects dominate the benefits and whether simply scaling to more examples is the most effective way of improving many-shot ICL. In this work, we first provide an analysis of the factors driving many-shot ICL, and we find that 1) many-shot performance can still be attributed to often a few disproportionately influential examples and 2) identifying such influential examples ("optimize") and using them as demonstrations to regenerate new examples ("generate") can lead to further improvements. Inspired by the findings, we propose BRIDGE, an algorithm that alternates between the optimize step with Bayesian optimization to discover the influential sets of examples and the generate step to reuse this set to expand the reasoning paths of the examples back to the many-shot regime automatically. On Gemini, Claude, and Mistral LLMs of different sizes, we show that BRIDGE to significant improvements across a diverse set of tasks, including symbolic reasoning, numerical reasoning, and code generation.

Following the success of Large Language Models (LLMs), Large Multimodal Models (LMMs), such as the Flamingo model and its subsequent competitors, have started to emerge as natural steps towards generalist agents. However, interacting with recent LMMs reveals major limitations that are hardly captured by the current evaluation benchmarks. Indeed, task performances (e.g., VQA accuracy) alone do not provide enough clues to understand their real capabilities, limitations, and to which extent such models are aligned to human expectations. To refine our understanding of those flaws, we deviate from the current evaluation paradigm, and (1) evaluate 10 recent open-source LMMs from 3B up to 80B parameter scale, on 5 different axes; hallucinations, abstention, compositionality, explainability and instruction following. Our evaluation on these axes reveals major flaws in LMMs. While the current go-to solution to align these models is based on training, such as instruction tuning or RLHF, we rather (2) explore the training-free in-context learning (ICL) as a solution, and study how it affects these limitations. Based on our ICL study, (3) we push ICL further and propose new multimodal ICL variants such as; Multitask-ICL, Chain-of-Hindsight-ICL, and Self-Correcting-ICL. Our findings are as follows. (1) Despite their success, LMMs have flaws that remain unsolved with scaling alone. (2) The effect of ICL on LMMs flaws is nuanced; despite its effectiveness for improved explainability, answer abstention, ICL only slightly improves instruction following, does not improve compositional abilities, and actually even amplifies hallucinations. (3) The proposed ICL variants are promising as post-hoc approaches to efficiently tackle some of those flaws. The code is available here: https://github.com/mshukor/EvALign-ICL.

The emergence of In-Context Learning (ICL) in LLMs remains a significant phenomenon with little understanding. To explain ICL, recent studies try to theoretically connect it to Gradient Descent (GD). We ask, does this connection hold up in actual pre-trained models? We highlight the limiting assumptions in prior works that make their context considerably different from the practical context in which language models are trained. For example, the theoretical hand-constructed weights used in these studies have properties that don't match those of real LLMs. Furthermore, their experimental verification uses ICL objective (training models explicitly for ICL), which differs from the emergent ICL in the wild. We also look for evidence in real models. We observe that ICL and GD have different sensitivity to the order in which they observe demonstrations. Finally, we probe and compare the ICL vs. GD hypothesis in a natural setting. We conduct comprehensive empirical analyses on language models pre-trained on natural data (LLaMa-7B). Our comparisons of three performance metrics highlight the inconsistent behavior of ICL and GD as a function of various factors such as datasets, models, and the number of demonstrations. We observe that ICL and GD modify the output distribution of language models differently. These results indicate that the equivalence between ICL and GD remains an open hypothesis and calls for further studies.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

Improving the performance of motion planning algorithms for high-degree-of-freedom robots usually requires reducing the cost or frequency of computationally expensive operations. Traditionally, and especially for asymptotically optimal sampling-based motion planners, the most expensive operations are local motion validation and querying the nearest neighbours of a configuration. Recent advances have significantly reduced the cost of motion validation by using single instruction/multiple data (SIMD) parallelism to improve solution times for satisficing motion planning problems. These advances have not yet been applied to asymptotically optimal motion planning. This paper presents Fully Connected Informed Trees (FCIT*), the first fully connected, informed, anytime almost-surely asymptotically optimal (ASAO) algorithm. FCIT* exploits the radically reduced cost of edge evaluation via SIMD parallelism to build and search fully connected graphs. This removes the need for nearest-neighbours structures, which are a dominant cost for many sampling-based motion planners, and allows it to find initial solutions faster than state-of-the-art ASAO (VAMP, OMPL) and satisficing (OMPL) algorithms on the MotionBenchMaker dataset while converging towards optimal plans in an anytime manner.

Large Language Models (LLMs) can learn new tasks through in-context supervised learning (i.e., ICL). This work studies if this ability extends to in-context reinforcement learning (ICRL), where models are not given gold labels in context, but only their past predictions and rewards. We show that a naive application of ICRL fails miserably, and identify the root cause as a fundamental deficiency at exploration, which leads to quick model degeneration. We propose an algorithm to address this deficiency by increasing test-time compute, as well as a compute-bound approximation. We use several challenging classification tasks to empirically show that our ICRL algorithms lead to effective learning from rewards alone, and analyze the characteristics of this ability and our methods. Overall, our results reveal remarkable ICRL abilities in LLMs.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T^{2/3}-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~li2022permutation showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that Omega(2^N) evaluations are typically required in TNLS for reaching the objective reduction in the neighborhood, while ideally O(N^2R) evaluations are sufficient in TnALE, where N denotes the tensor order and R reflects the ``low-rankness'' of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

In-context learning (ICL, also known as few-shot prompting) has been the standard method of adapting LLMs to downstream tasks, by learning from a few input-output examples. Nonetheless, all ICL-based approaches only learn from correct input-output pairs. In this paper, we revisit this paradigm, by learning more from the few given input-output examples. We introduce Learning Principles (LEAP): First, we intentionally induce the model to make mistakes on these few examples; then we reflect on these mistakes, and learn explicit task-specific "principles" from them, which help solve similar problems and avoid common mistakes; finally, we prompt the model to answer unseen test questions using the original few-shot examples and these learned general principles. We evaluate LEAP on a wide range of benchmarks, including multi-hop question answering (Hotpot QA), textual QA (DROP), Big-Bench Hard reasoning, and math problems (GSM8K and MATH); in all these benchmarks, LEAP improves the strongest available LLMs such as GPT-3.5-turbo, GPT-4, GPT-4 turbo and Claude-2.1. For example, LEAP improves over the standard few-shot prompting using GPT-4 by 7.5% in DROP, and by 3.3% in HotpotQA. Importantly, LEAP does not require any more input or examples than the standard few-shot prompting settings.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

The remarkable capability of large language models (LLMs) for in-context learning (ICL) needs to be activated by demonstration examples. Prior work has extensively explored the selection of examples for ICL, predominantly following the "select then organize" paradigm, such approaches often neglect the internal relationships between examples and exist an inconsistency between the training and inference. In this paper, we formulate the problem as a sequential selection problem and introduce Se^2, a sequential-aware method that leverages the LLM's feedback on varying context, aiding in capturing inter-relationships and sequential information among examples, significantly enriching the contextuality and relevance of ICL prompts. Meanwhile, we utilize beam search to seek and construct example sequences, enhancing both quality and diversity. Extensive experiments across 23 NLP tasks from 8 distinct categories illustrate that Se^2 markedly surpasses competitive baselines and achieves 42% relative improvement over random selection. Further in-depth analysis show the effectiveness of proposed strategies, highlighting Se^2's exceptional stability and adaptability across various scenarios. Our code will be released to facilitate future research.

This paper proposes a novel admission and routing scheme which takes into account arbitrarily assigned priorities for network flows. The presented approach leverages the centralized Software Defined Networking (SDN) capabilities in order to do so. Exact and heuristic approaches to the stated Priority Flow Admission and Routing (PFAR) problem are provided. The exact approach which provides an optimal solution is based on Integer Linear Programming (ILP). Given the potentially long running time required to find an exact and optimal solution, a heuristic approach is proposed; this approach is based on Genetic Algorithms (GAs). In order to effectively estimate the performance of the proposed approaches, a simulator that is capable of generating semi-random network topologies and flows has been developed. Experimental results for large problem instances (up 50 network nodes and thousands of network flows), show that: i) an optimal solution can be often found in few seconds (even milliseconds), and ii) the heuristic approach yields close-to-optimal solutions (approximately 95\% of the optimal) in a fixed amount of time; these experimental results demonstrate the pertinence of the proposed approaches.

In-context learning (ICL) adapts LLMs by providing demonstrations without fine-tuning the model parameters; however, it does not differentiate between demonstrations and quadratically increases the complexity of Transformer LLMs, exhausting the memory. As a solution, we propose Mixtures of In-Context Learners (MoICL), a novel approach to treat subsets of demonstrations as experts and learn a weighting function to merge their output distributions based on a training set. In our experiments, we show performance improvements on 5 out of 7 classification datasets compared to a set of strong baselines (up to +13\% compared to ICL and LENS). Moreover, we enhance the Pareto frontier of ICL by reducing the inference time needed to achieve the same performance with fewer demonstrations. Finally, MoICL is more robust to out-of-domain (up to +11\%), imbalanced (up to +49\%), or noisy demonstrations (up to +38\%) or can filter these out from datasets. Overall, MoICL is a more expressive approach to learning from demonstrations without exhausting the context window or memory.

Like generic multi-task learning, continual learning has the nature of multi-objective optimization, and therefore faces a trade-off between the performance of different tasks. That is, to optimize for the current task distribution, it may need to compromise performance on some previous tasks. This means that there exist multiple models that are Pareto-optimal at different times, each addressing a distinct task performance trade-off. Researchers have discussed how to train particular models to address specific trade-off preferences. However, existing algorithms require training overheads proportional to the number of preferences -- a large burden when there are multiple, possibly infinitely many, preferences. As a response, we propose Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base in the form of a convex hull of model parameter distributions and (2) obtains particular models to address task trade-off preferences with zero-shot. That is, IBCL does not require any additional training overhead to generate preference-addressing models from its knowledge base. We show that models obtained by IBCL have guarantees in identifying the Pareto optimal parameters. Moreover, experiments on standard image classification and NLP tasks support this guarantee. Statistically, IBCL improves average per-task accuracy by at most 23% and peak per-task accuracy by at most 15% with respect to the baseline methods, with steadily near-zero or positive backward transfer. Most importantly, IBCL significantly reduces the training overhead from training 1 model per preference to at most 3 models for all preferences.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

Verilog's design cycle is inherently labor-intensive and necessitates extensive domain expertise. Although Large Language Models (LLMs) offer a promising pathway toward automation, their limited training data and intrinsic sequential reasoning fail to capture the strict formal logic and concurrency inherent in hardware systems. To overcome these barriers, we present EvolVE, the first framework to analyze multiple evolution strategies on chip design tasks, revealing that Monte Carlo Tree Search (MCTS) excels at maximizing functional correctness, while Idea-Guided Refinement (IGR) proves superior for optimization. We further leverage Structured Testbench Generation (STG) to accelerate the evolutionary process. To address the lack of complex optimization benchmarks, we introduce IC-RTL, targeting industry-scale problems derived from the National Integrated Circuit Contest. Evaluations establish EvolVE as the new state-of-the-art, achieving 98.1% on VerilogEval v2 and 92% on RTLLM v2. Furthermore, on the industry-scale IC-RTL suite, our framework surpasses reference implementations authored by contest participants, reducing the Power, Performance, Area (PPA) product by up to 66% in Huffman Coding and 17% in the geometric mean across all problems. The source code of the IC-RTL benchmark is available at https://github.com/weiber2002/ICRTL.

When verifying computer systems we sometimes want to study their asymptotic behaviors, i.e., how they behave in the long run. In such cases, we need real analysis, the area of mathematics that deals with limits and the foundations of calculus. In a prior work, we used real analysis in ACL2s to study the asymptotic behavior of the RTO computation, commonly used in congestion control algorithms across the Internet. One key component in our RTO computation analysis was proving in ACL2s that for all alpha in [0, 1), the limit as n approaches infinity of alpha raised to n is zero. Whereas the most obvious proof strategy involves the logarithm, whose codomain includes irrationals, by default ACL2 only supports rationals, which forced us to take a non-standard approach. In this paper, we explore different approaches to proving the above result in ACL2(r) and ACL2s, from the perspective of a relatively new user to each. We also contextualize the theorem by showing how it allowed us to prove important asymptotic properties of the RTO computation. Finally, we discuss tradeoffs between the various proof strategies and directions for future research.

In this work, we explore the mechanism of in-context learning (ICL) on out-of-distribution (OOD) tasks that were not encountered during training. To achieve this, we conduct synthetic experiments where the objective is to learn OOD mathematical functions through ICL using a GPT-2 model. We reveal that Transformers may struggle to learn OOD task functions through ICL. Specifically, ICL performance resembles implementing a function within the pretraining hypothesis space and optimizing it with gradient descent based on the in-context examples. Additionally, we investigate ICL's well-documented ability to learn unseen abstract labels in context. We demonstrate that such ability only manifests in the scenarios without distributional shifts and, therefore, may not serve as evidence of new-task-learning ability. Furthermore, we assess ICL's performance on OOD tasks when the model is pretrained on multiple tasks. Both empirical and theoretical analyses demonstrate the existence of the low-test-error preference of ICL, where it tends to implement the pretraining function that yields low test error in the testing context. We validate this through numerical experiments. This new theoretical result, combined with our empirical findings, elucidates the mechanism of ICL in addressing OOD tasks.

We introduce iterative retrieval, a novel framework that empowers retrievers to make iterative decisions through policy optimization. Finding an optimal portfolio of retrieved items is a combinatorial optimization problem, generally considered NP-hard. This approach provides a learned approximation to such a solution, meeting specific task requirements under a given family of large language models (LLMs). We propose a training procedure based on reinforcement learning, incorporating feedback from LLMs. We instantiate an iterative retriever for composing in-context learning (ICL) exemplars and apply it to various semantic parsing tasks that demand synthesized programs as outputs. By adding only 4M additional parameters for state encoding, we convert an off-the-shelf dense retriever into a stateful iterative retriever, outperforming previous methods in selecting ICL exemplars on semantic parsing datasets such as CalFlow, TreeDST, and MTOP. Additionally, the trained iterative retriever generalizes across different inference LLMs beyond the one used during training.

Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a linearly parameterized single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

In-context learning (ICL) is a powerful paradigm emerged from large language models (LLMs). Despite its promises, ICL performance is known to be highly sensitive to input examples. In this work, we use in-context influences to analyze few-shot ICL performance directly from the in-context examples. Our proposed influence-based example selection method can identify both positive and negative examples, outperforming several baselines when evaluated on 9 SuperGLUE tasks. Our analysis uncovers up to a 16.3% performance gap between using the most negative in-context examples compared to the most positive. In a case study, we apply our influence-based framework to quantify the phenomena of recency bias in example ordering for few-shot ICL.

Real-world applications of large language models (LLMs) in computational social science (CSS) tasks primarily depend on the effectiveness of instruction tuning (IT) or in-context learning (ICL). While IT has shown highly effective at fine-tuning LLMs for various tasks, ICL offers a rapid alternative for task adaptation by learning from examples without explicit gradient updates. In this paper, we evaluate the classification performance of LLMs using IT versus ICL in few-shot CSS tasks. The experimental results indicate that ICL consistently outperforms IT in most CSS tasks. Additionally, we investigate the relationship between the increasing number of training samples and LLM performance. Our findings show that simply increasing the number of samples without considering their quality does not consistently enhance the performance of LLMs with either ICL or IT and can sometimes even result in a performance decline. Finally, we compare three prompting strategies, demonstrating that ICL is more effective than zero-shot and Chain-of-Thought (CoT). Our research highlights the significant advantages of ICL in handling CSS tasks in few-shot settings and emphasizes the importance of optimizing sample quality and prompting strategies to improve LLM classification performance. The code will be made available.

This paper presents a novel approach, named the Group Marching Tree (GMT*) algorithm, to planning on GPUs at rates amenable to application within control loops, allowing planning in real-world settings via repeated computation of near-optimal plans. GMT*, like the Fast Marching Tree (FMT) algorithm, explores the state space with a "lazy" dynamic programming recursion on a set of samples to grow a tree of near-optimal paths. GMT*, however, alters the approach of FMT with approximate dynamic programming by expanding, in parallel, the group of all active samples with cost below an increasing threshold, rather than only the minimum cost sample. This group approximation enables low-level parallelism over the sample set and removes the need for sequential data structures, while the "lazy" collision checking limits thread divergence---all contributing to a very efficient GPU implementation. While this approach incurs some suboptimality, we prove that GMT* remains asymptotically optimal up to a constant multiplicative factor. We show solutions for complex planning problems under differential constraints can be found in ~10 ms on a desktop GPU and ~30 ms on an embedded GPU, representing a significant speed up over the state of the art, with only small losses in performance. Finally, we present a scenario demonstrating the efficacy of planning within the control loop (~100 Hz) towards operating in dynamic, uncertain settings.

We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying {\it funsearch} to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of {\it funsearch} to new problems. Our results demonstrate that {\it funsearch} successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.

Adapting Large Language Models (LLMs) to specific tasks introduces concerns about computational efficiency, prompting an exploration of efficient methods such as In-Context Learning (ICL). However, the vulnerability of ICL to privacy attacks under realistic assumptions remains largely unexplored. In this work, we present the first membership inference attack tailored for ICL, relying solely on generated texts without their associated probabilities. We propose four attack strategies tailored to various constrained scenarios and conduct extensive experiments on four popular large language models. Empirical results show that our attacks can accurately determine membership status in most cases, e.g., 95\% accuracy advantage against LLaMA, indicating that the associated risks are much higher than those shown by existing probability-based attacks. Additionally, we propose a hybrid attack that synthesizes the strengths of the aforementioned strategies, achieving an accuracy advantage of over 95\% in most cases. Furthermore, we investigate three potential defenses targeting data, instruction, and output. Results demonstrate combining defenses from orthogonal dimensions significantly reduces privacy leakage and offers enhanced privacy assurances.

Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), and the Probabilistic Road Maps (PRMs) have become very popular recently, owing to their implementation simplicity and their advantages in handling high-dimensional problems. Although these algorithms work very well in practice, the quality of the computed solution is often not good, i.e., the solution can be far from the optimal one. A recent variation of RRT, namely the RRT* algorithm, bypasses this drawback of the traditional RRT algorithm, by ensuring asymptotic optimality as the number of samples tends to infinity. Nonetheless, the convergence rate to the optimal solution may still be slow. This paper presents a new incremental sampling-based motion planning algorithm based on Rapidly-exploring Random Graphs (RRG), denoted RRT# (RRT "sharp") which also guarantees asymptotic optimality but, in addition, it also ensures that the constructed spanning tree of the geometric graph is consistent after each iteration. In consistent trees, the vertices which have the potential to be part of the optimal solution have the minimum cost-come-value. This implies that the best possible solution is readily computed if there are some vertices in the current graph that are already in the goal region. Numerical results compare with the RRT* algorithm.

Let p denote a generative language model. Let r denote a reward model that returns a scalar that captures the degree at which a draw from p is preferred. The goal of language model alignment is to alter p to a new distribution phi that results in a higher expected reward while keeping phi close to p. A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution phi_Delta that maximizes E_{phi_{Delta}} r(y) subject to a relative entropy constraint KL(phi_Delta || p) leq Delta. Another simple alignment method is best-of-N, where N samples are drawn from p and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-N alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-N is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

In-context learning (ICL) i.e. showing LLMs only a few task-specific demonstrations has led to downstream gains with no task-specific fine-tuning required. However, LLMs are sensitive to the choice of prompts, and therefore a crucial research question is how to select good demonstrations for ICL. One effective strategy is leveraging semantic similarity between the ICL demonstrations and test inputs by using a text retriever, which however is sub-optimal as that does not consider the LLM's existing knowledge about that task. From prior work (Min et al., 2022), we already know that labels paired with the demonstrations bias the model predictions. This leads us to our hypothesis whether considering LLM's existing knowledge about the task, especially with respect to the output label space can help in a better demonstration selection strategy. Through extensive experimentation on three text classification tasks, we find that it is beneficial to not only choose semantically similar ICL demonstrations but also to choose those demonstrations that help resolve the inherent label ambiguity surrounding the test example. Interestingly, we find that including demonstrations that the LLM previously mis-classified and also fall on the test example's decision boundary, brings the most performance gain.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

In-Context Learning (ICL) is a technique by which language models make predictions based on examples provided in their input context. Previously, their context window size imposed a limit on the number of examples that can be shown, making example selection techniques crucial for identifying the maximally effective set of examples. However, the recent advent of Long Context Language Models (LCLMs) has significantly increased the number of examples that can be included in context, raising an important question of whether ICL performance in a many-shot regime is still sensitive to the method of sample selection. To answer this, we revisit these approaches in the context of LCLMs through extensive experiments on 18 datasets spanning 4 tasks. Surprisingly, we observe that sophisticated example selection techniques do not yield significant improvements over a simple random sample selection method. Instead, we find that the advent of LCLMs has fundamentally shifted the challenge of ICL from that of selecting the most effective examples to that of collecting sufficient examples to fill the context window. Specifically, in certain datasets, including all available examples does not fully utilize the context window; however, by augmenting the examples in context with a simple data augmentation approach, we substantially improve ICL performance by 5%.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Recently, rapid advancements in Multi-Modal In-Context Learning (MM-ICL) have achieved notable success, which is capable of achieving superior performance across various tasks without requiring additional parameter tuning. However, the underlying rules for the effectiveness of MM-ICL remain under-explored. To fill this gap, this work aims to investigate the research question: "What factors affect the performance of MM-ICL?'' To this end, we investigate extensive experiments on the three core steps of MM-ICL including demonstration retrieval, demonstration ordering, and prompt construction using 6 vision large language models and 20 strategies. Our findings highlight (1) the necessity of a multi-modal retriever for demonstration retrieval, (2) the importance of intra-demonstration ordering over inter-demonstration ordering, and (3) the enhancement of task comprehension through introductory instructions in prompts. We hope this study can serve as a foundational guide for optimizing MM-ICL strategies in future research.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

Large pretrained language models (LMs) have shown impressive In-Context Learning (ICL) ability, where the model learns to do an unseen task via a prompt consisting of input-output examples as the demonstration, without any parameter updates. The performance of ICL is highly dominated by the quality of the selected in-context examples. However, previous selection methods are mostly based on simple heuristics, leading to sub-optimal performance. In this work, we formulate in-context example selection as a subset selection problem. We propose CEIL (Compositional Exemplars for In-context Learning), which is instantiated by Determinantal Point Processes (DPPs) to model the interaction between the given input and in-context examples, and optimized through a carefully-designed contrastive learning objective to obtain preference from LMs. We validate CEIL on 12 classification and generation datasets from 7 distinct NLP tasks, including sentiment analysis, paraphrase detection, natural language inference, commonsense reasoning, open-domain question answering, code generation, and semantic parsing. Extensive experiments demonstrate not only the state-of-the-art performance but also the transferability and compositionality of CEIL, shedding new light on effective and efficient in-context learning. Our code is released at https://github.com/HKUNLP/icl-ceil.

In-context learning (ICL) in Large Language Models (LLMs) has emerged as a powerful new learning paradigm. However, its underlying mechanism is still not well understood. In particular, it is challenging to map it to the "standard" machine learning framework, where one uses a training set S to find a best-fitting function f(x) in some hypothesis class. Here we make progress on this problem by showing that the functions learned by ICL often have a very simple structure: they correspond to the transformer LLM whose only inputs are the query x and a single "task vector" calculated from the training set. Thus, ICL can be seen as compressing S into a single task vector theta(S) and then using this task vector to modulate the transformer to produce the output. We support the above claim via comprehensive experiments across a range of models and tasks.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

Recent interest has surged in employing Large Language Models (LLMs) for machine translation (MT) via in-context learning (ICL) (Vilar et al., 2023). Most prior studies primarily focus on optimizing translation quality, with limited attention to understanding the specific aspects of ICL that influence the said quality. To this end, we perform the first of its kind, an exhaustive study of in-context learning for machine translation. We first establish that ICL is primarily example-driven and not instruction-driven. Following this, we conduct an extensive exploration of various aspects of the examples to understand their influence on downstream performance. Our analysis includes factors such as quality and quantity of demonstrations, spatial proximity, and source versus target originality. Further, we also investigate challenging scenarios involving indirectness and misalignment of examples to understand the limits of ICL. While we establish the significance of the quality of the target distribution over the source distribution of demonstrations, we further observe that perturbations sometimes act as regularizers, resulting in performance improvements. Surprisingly, ICL does not necessitate examples from the same task, and a related task with the same target distribution proves sufficient. We hope that our study acts as a guiding resource for considerations in utilizing ICL for MT. Our code is available on https://github.com/PranjalChitale/in-context-mt-analysis.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension n=8, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions 4-16, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Learning paradigms for large language models (LLMs) currently tend to fall within either in-context learning (ICL) or full fine-tuning. Each of these comes with their own trade-offs based on available data, model size, compute cost, ease-of-use, and final quality with neither solution performing well across-the-board. In this article, we first describe ICL and fine-tuning paradigms in a way that highlights their natural connections. Based on these connections, we propose a new learning paradigm called FIAT that fuses the best of these paradigms together, enabling prompt-engineered instructions and chain-of-thought reasoning with the very largest models while also using similar methods to perform parameter updates on a modestly-sized LLM with parameter-efficient tuning. We evaluate FIAT's effectiveness on a variety of multilingual tasks and observe that FIAT performs better than both ICL and fine-tuning at scales ranging from 100-10,000 training examples. We hope that FIAT provides a practical way of harnessing the full potential of LLMs without needing to make a hard choice between learning paradigms.

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and safety-critical decision-making tasks demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly.

In this paper, we consider the minimum submodular cost allocation (MSCA) problem. The input of MSCA is k non-negative submodular functions f_1,ldots,f_k on the ground set N given by evaluation oracles, and the goal is to partition N into k (possibly empty) sets X_1,ldots,X_k so that sum_{i=1}^k f_i(X_i) is minimized. In this paper, we focus on the case when f_1,ldots,f_k are monotone (denoted by Mono-MSCA). We provide a natural LP-relaxation for Mono-MSCA, which is equivalent to the convex program relaxation introduced by Chekuri and Ene. We show that the integrality gap of the LP-relaxation is at most k/2, which yields a k/2-approximation algorithm for Mono-MSCA. We also show that the integrality gap of the LP-relaxation is at least k/2-epsilon for any constant epsilon>0 when k is fixed.

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, we first design a counter-example to illustrate the invalidation of such LLS condition. Then by formulating BLPs from the view point of optimistic bi-level and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for generic bi-level optimization. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules. Additionally, as an interesting byproduct, we also improve these conventional first-order bi-level schemes (under the LLS simplification). Particularly, we establish their convergences with weaker assumptions. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

In-context Learning (ICL) empowers large language models (LLMs) to adapt to unseen tasks during inference by prefixing a few demonstration examples prior to test queries. Despite its versatility, ICL incurs substantial computational and memory overheads compared to zero-shot learning and is susceptible to the selection and order of demonstration examples. In this work, we introduce Implicit In-context Learning (I2CL), an innovative paradigm that addresses the challenges associated with traditional ICL by absorbing demonstration examples within the activation space. I2CL first generates a condensed vector representation, namely a context vector, from the demonstration examples. It then integrates the context vector during inference by injecting a linear combination of the context vector and query activations into the model's residual streams. Empirical evaluation on nine real-world tasks across three model architectures demonstrates that I2CL achieves few-shot performance with zero-shot cost and exhibits robustness against the variation of demonstration examples. Furthermore, I2CL facilitates a novel representation of "task-ids", enhancing task similarity detection and enabling effective transfer learning. We provide a comprehensive analysis of I2CL, offering deeper insights into its mechanisms and broader implications for ICL. The source code is available at: https://github.com/LzVv123456/I2CL.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. The system's behavior is primarily driven by parameters such as instructions or tool definitions. Recent advancements enable end-to-end optimization of these parameters using an LLM. Notably, leveraging an LLM as an optimizer is particularly efficient because it avoids gradient computation and can generate complex code and instructions. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems. It covers archetypes of compound AI systems, approaches to LLM-based end-to-end optimization, and insights into future directions and broader impacts. Importantly, this survey uses concepts from program analysis to provide a unified view of how an LLM optimizer is prompted to optimize a compound AI system. The exhaustive list of paper is provided at https://github.com/linyuhongg/LLM-based-Optimization-of-Compound-AI-Systems.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

Large language models (LLMs) excel at few-shot in-context learning (ICL) -- learning from a few examples provided in context at inference, without any weight updates. Newly expanded context windows allow us to investigate ICL with hundreds or thousands of examples -- the many-shot regime. Going from few-shot to many-shot, we observe significant performance gains across a wide variety of generative and discriminative tasks. While promising, many-shot ICL can be bottlenecked by the available amount of human-generated examples. To mitigate this limitation, we explore two new settings: Reinforced and Unsupervised ICL. Reinforced ICL uses model-generated chain-of-thought rationales in place of human examples. Unsupervised ICL removes rationales from the prompt altogether, and prompts the model only with domain-specific questions. We find that both Reinforced and Unsupervised ICL can be quite effective in the many-shot regime, particularly on complex reasoning tasks. Finally, we demonstrate that, unlike few-shot learning, many-shot learning is effective at overriding pretraining biases and can learn high-dimensional functions with numerical inputs. Our analysis also reveals the limitations of next-token prediction loss as an indicator of downstream ICL performance.

We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4 iterations), we demonstrate significant token reduction (29.8%, t(10)=6.36, p < 0.001, Cohen's d = 2.01) with corresponding cost savings. UCL's structural overhead function O_s(A) explains version-specific performance differences through the Over-Specification Paradox: beyond threshold S* = 0.509, additional specification degrades performance quadratically. Core mechanisms -- indicator functions (I_i in {0,1}), structural overhead (O_s = gamma * sum(ln C_k)), early binding -- are validated. Notably, optimal UCL configuration varies by model architecture -- certain models (e.g., Llama 4 Scout) require version-specific adaptations (V4.1). This work establishes UCL as a calibratable framework for efficient LLM interaction, with model-family-specific optimization as a key research direction.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

We study the problem of in-context learning (ICL) with large language models (LLMs) on private datasets. This scenario poses privacy risks, as LLMs may leak or regurgitate the private examples demonstrated in the prompt. We propose a novel algorithm that generates synthetic few-shot demonstrations from the private dataset with formal differential privacy (DP) guarantees, and show empirically that it can achieve effective ICL. We conduct extensive experiments on standard benchmarks and compare our algorithm with non-private ICL and zero-shot solutions. Our results demonstrate that our algorithm can achieve competitive performance with strong privacy levels. These results open up new possibilities for ICL with privacy protection for a broad range of applications.

Existing continual learning (CL) methods mainly rely on fine-tuning or adapting large language models (LLMs). They still suffer from catastrophic forgetting (CF). Little work has been done to exploit in-context learning (ICL) to leverage the extensive knowledge within LLMs for CL without updating any parameters. However, incrementally learning each new task in ICL necessitates adding training examples from each class of the task to the prompt, which hampers scalability as the prompt length increases. This issue not only leads to excessively long prompts that exceed the input token limit of the underlying LLM but also degrades the model's performance due to the overextended context. To address this, we introduce InCA, a novel approach that integrates an external continual learner (ECL) with ICL to enable scalable CL without CF. The ECL is built incrementally to pre-select a small subset of likely classes for each test instance. By restricting the ICL prompt to only these selected classes, InCA prevents prompt lengths from becoming excessively long, while maintaining high performance. Experimental results demonstrate that InCA significantly outperforms existing CL baselines, achieving substantial performance gains.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

Pre-trained models of source code have gained widespread popularity in many code intelligence tasks. Recently, with the scaling of the model and corpus size, large language models have shown the ability of in-context learning (ICL). ICL employs task instructions and a few examples as demonstrations, and then inputs the demonstrations to the language models for making predictions. This new learning paradigm is training-free and has shown impressive performance in various natural language processing and code intelligence tasks. However, the performance of ICL heavily relies on the quality of demonstrations, e.g., the selected examples. It is important to systematically investigate how to construct a good demonstration for code-related tasks. In this paper, we empirically explore the impact of three key factors on the performance of ICL in code intelligence tasks: the selection, order, and number of demonstration examples. We conduct extensive experiments on three code intelligence tasks including code summarization, bug fixing, and program synthesis. Our experimental results demonstrate that all the above three factors dramatically impact the performance of ICL in code intelligence tasks. Additionally, we summarize our findings and provide takeaway suggestions on how to construct effective demonstrations, taking into account these three perspectives. We also show that a carefully-designed demonstration based on our findings can lead to substantial improvements over widely-used demonstration construction methods, e.g., improving BLEU-4, EM, and EM by at least 9.90%, 175.96%, and 50.81% on code summarization, bug fixing, and program synthesis, respectively

The long-standing dominance of gradient-boosted decision trees on tabular data is currently challenged by tabular foundation models using In-Context Learning (ICL): setting the training data as context for the test data and predicting in a single forward pass without parameter updates. While the very recent TabPFNv2 foundation model (2025) excels on tables with up to 10K samples, its alternating column- and row-wise attentions make handling large training sets computationally prohibitive. So, can ICL be effectively scaled and deliver a benefit for larger tables? We introduce TabICL, a tabular foundation model for classification, pretrained on synthetic datasets with up to 60K samples and capable of handling 500K samples on affordable resources. This is enabled by a novel two-stage architecture: a column-then-row attention mechanism to build fixed-dimensional embeddings of rows, followed by a transformer for efficient ICL. Across 200 classification datasets from the TALENT benchmark, TabICL is on par with TabPFNv2 while being systematically faster (up to 10 times), and significantly outperforms all other approaches. On 56 datasets with over 10K samples, TabICL surpasses both TabPFNv2 and CatBoost, demonstrating the potential of ICL for large data.

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance tau. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision Processes (MDPs) setting. To extend CVaR RL to settings where state space is large, function approximation must be deployed. We study CVaR RL in low-rank MDPs with nonlinear function approximation. Low-rank MDPs assume the underlying transition kernel admits a low-rank decomposition, but unlike prior linear models, low-rank MDPs do not assume the feature or state-action representation is known. We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to carefully balance the interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of Oleft(H^7 A^2 d^4{tau^2 epsilon^2}right) to yield an epsilon-optimal CVaR, where H is the length of each episode, A is the capacity of action space, and d is the dimension of representations. Computational-wise, we design a novel discretized Least-Squares Value Iteration (LSVI) algorithm for the CVaR objective as the planning oracle and show that we can find the near-optimal policy in a polynomial running time with a Maximum Likelihood Estimation oracle. To our knowledge, this is the first provably efficient CVaR RL algorithm in low-rank MDPs.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

In-context learning (ICL) facilitates large language models (LLMs) exhibiting spectacular emergent capabilities in various scenarios. Unfortunately, introducing demonstrations easily makes the prompt length explode, bringing a significant burden to hardware. In addition, random demonstrations usually achieve limited improvements in ICL, necessitating demonstration selection among accessible candidates. Previous studies introduce extra modules to perform demonstration compression or selection independently. In this paper, we propose an ICL framework UniICL, which Unifies demonstration selection and compression, and final response generation via a single frozen LLM. Specifically, UniICL first projects actual demonstrations and inference text inputs into short virtual tokens, respectively. Then, virtual tokens are applied to select suitable demonstrations by measuring semantic similarity within latent space among candidate demonstrations and inference input. Finally, inference text inputs together with selected virtual demonstrations are fed into the same frozen LLM for response generation. Notably, UniICL is a parameter-efficient framework that only contains 17M trainable parameters originating from the projection layer. We conduct experiments and analysis over in- and out-domain datasets of both generative and understanding tasks, encompassing ICL scenarios with plentiful and limited demonstration candidates. Results show that UniICL effectively unifies 12 times compression, demonstration selection, and response generation, efficiently scaling up the baseline from 4-shot to 64-shot ICL in IMDb with 24 GB CUDA allocation

Chain-of-thought (CoT) prompting is a popular in-context learning (ICL) approach for large language models (LLMs), especially when tackling complex reasoning tasks. Traditional ICL approaches construct prompts using examples that contain questions similar to the input question. However, CoT prompting, which includes crucial intermediate reasoning steps (rationales) within its examples, necessitates selecting examples based on these rationales rather than the questions themselves. Existing methods require human experts or pre-trained LLMs to describe the skill, a high-level abstraction of rationales, to guide the selection. These methods, however, are often costly and difficult to scale. Instead, this paper introduces a new approach named Latent Reasoning Skills (LaRS) that employs unsupervised learning to create a latent space representation of rationales, with a latent variable called a reasoning skill. Concurrently, LaRS learns a reasoning policy to determine the required reasoning skill for a given question. Then the ICL examples are selected by aligning the reasoning skills between past examples and the question. This approach is theoretically grounded and compute-efficient, eliminating the need for auxiliary LLM inference or manual prompt design. Empirical results demonstrate that LaRS consistently outperforms SOTA skill-based selection methods, processing example banks four times faster, reducing LLM inferences during the selection stage by half, and showing greater robustness to sub-optimal example banks.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

In-context learning (ICL) in large language models (LLMs) is a striking phenomenon, yet its underlying mechanisms remain only partially understood. Previous work connects linear self-attention (LSA) to gradient descent (GD), this connection has primarily been established under simplified conditions with zero-mean Gaussian priors and zero initialization for GD. However, subsequent studies have challenged this simplified view by highlighting its overly restrictive assumptions, demonstrating instead that under conditions such as multi-layer or nonlinear attention, self-attention performs optimization-like inference, akin to but distinct from GD. We investigate how multi-head LSA approximates GD under more realistic conditions specifically when incorporating non-zero Gaussian prior means in linear regression formulations of ICL. We first extend multi-head LSA embedding matrix by introducing an initial estimation of the query, referred to as the initial guess. We prove an upper bound on the number of heads needed for ICL linear regression setup. Our experiments confirm this result and further observe that a performance gap between one-step GD and multi-head LSA persists. To address this gap, we introduce yq-LSA, a simple generalization of single-head LSA with a trainable initial guess yq. We theoretically establish the capabilities of yq-LSA and provide experimental validation on linear regression tasks, thereby extending the theory that bridges ICL and GD. Finally, inspired by our findings in the case of linear regression, we consider widespread LLMs augmented with initial guess capabilities, and show that their performance is improved on a semantic similarity task.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

In-context learning (ICL) emerges as a promising capability of large language models (LLMs) by providing them with demonstration examples to perform diverse tasks. However, the underlying mechanism of how LLMs learn from the provided context remains under-explored. In this paper, we investigate the working mechanism of ICL through an information flow lens. Our findings reveal that label words in the demonstration examples function as anchors: (1) semantic information aggregates into label word representations during the shallow computation layers' processing; (2) the consolidated information in label words serves as a reference for LLMs' final predictions. Based on these insights, we introduce an anchor re-weighting method to improve ICL performance, a demonstration compression technique to expedite inference, and an analysis framework for diagnosing ICL errors in GPT2-XL. The promising applications of our findings again validate the uncovered ICL working mechanism and pave the way for future studies.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

The emergence of Large Language Models (LLMs) with capabilities like In-Context Learning (ICL) has ushered in new possibilities for data generation across various domains while minimizing the need for extensive data collection and modeling techniques. Researchers have explored ways to use this generated synthetic data to optimize smaller student models for reduced deployment costs and lower latency in downstream tasks. However, ICL-generated data often suffers from low quality as the task specificity is limited with few examples used in ICL. In this paper, we propose GeMQuAD - a semi-supervised learning approach, extending the WeakDAP framework, applied to a dataset generated through ICL with just one example in the target language using AlexaTM 20B Seq2Seq LLM. Through our approach, we iteratively identify high-quality data to enhance model performance, especially for low-resource multilingual setting in the context of Extractive Question Answering task. Our framework outperforms the machine translation-augmented model by 0.22/1.68 F1/EM (Exact Match) points for Hindi and 0.82/1.37 F1/EM points for Spanish on the MLQA dataset, and it surpasses the performance of model trained on an English-only dataset by 5.05/6.50 F1/EM points for Hindi and 3.81/3.69 points F1/EM for Spanish on the same dataset. Notably, our approach uses a pre-trained LLM for generation with no fine-tuning (FT), utilizing just a single annotated example in ICL to generate data, providing a cost-effective development process.

Large Language Models have demonstrated remarkable performance across various tasks, exhibiting the capacity to swiftly acquire new skills, such as through In-Context Learning (ICL) with minimal demonstration examples. In this work, we present a comprehensive framework for investigating Multimodal ICL (M-ICL) in the context of Large Multimodal Models. We consider the best open-source multimodal models (e.g., IDEFICS, OpenFlamingo) and a wide range of multimodal tasks. Our study unveils several noteworthy findings: (1) M-ICL primarily relies on text-driven mechanisms, showing little to no influence from the image modality. (2) When used with advanced-ICL strategy (like RICES), M-ICL is not better than a simple strategy based on majority voting over context examples. Moreover, we identify several biases and limitations of M-ICL that warrant consideration prior to deployment. Code available at https://gitlab.com/folbaeni/multimodal-icl

Recent studies have demonstrated that large language models (LLMs) excel in diverse tasks through in-context learning (ICL) facilitated by task-specific prompts and examples. However, the existing literature shows that ICL encounters performance deterioration when exposed to adversarial inputs. Enhanced performance has been observed when ICL is augmented with natural language explanations (NLEs) (we refer to it as X-ICL). Thus, this work investigates whether X-ICL can improve the robustness of LLMs on a suite of seven adversarial and challenging natural language inference datasets. Moreover, we introduce a new approach to X-ICL by prompting an LLM (ChatGPT in our case) with few human-generated NLEs to produce further NLEs (we call it ChatGPT few-shot), which we show superior to both ChatGPT zero-shot and human-generated NLEs alone. We evaluate five popular LLMs (GPT3.5-turbo, LLaMa2, Vicuna, Zephyr, Mistral) and show that X-ICL with ChatGPT few-shot yields over 6% improvement over ICL. Furthermore, while prompt selection strategies were previously shown to significantly improve ICL on in-distribution test sets, we show that these strategies do not match the efficacy of the X-ICL paradigm in robustness-oriented evaluations.