We consider the basic statistical challenge of designing an "all-purpose" mean estimation algorithm that is recommendable across a variety of settings and models.Recent work by [Lee and Valiant 2022] introduced the first 1-d mean estimator whose error in the standard finite-variance+i.i.d. setting is optimal even in its constant factors; experimental demonstration of its good performance was shown by [Gobet et al. 2022].Yet, unlike for classic (but not necessarily practical) estimators such as median-of-means and trimmed mean, this new algorithm lacked proven robustness guarantees in other settings, including the settings of adversarial data corruption and heavy-tailed distributions with infinite variance.Such robustness is important for practical use cases.This raises a research question: is it possible to have a mean estimator that is robust, *without* sacrificing provably optimal performance in the standard i.i.d. setting?In this work, we show that Lee and Valiant's estimator is in fact an "all-purpose" mean estimator by proving:(A) It is robust to an $\eta$-fraction of data corruption, even in the strong contamination model; it has optimal estimation error $O(\sigma\sqrt{\eta})$ for distributions with variance $\sigma^2$.(B) For distributions with finite $z^\text{th}$ moment, for $z \in (1,2)$, it has optimal estimation error, matching the lower bounds of [Devroye et al. 2016] up to constants.We further show (C) that outlier robustness for 1-d mean estimators in fact implies neighborhood optimality, a notion of beyond worst-case and distribution-dependent optimality recently introduced by [Dang et al. 2023].Previously, such an optimality guarantee was only known for median-of-means, but now it holds also for all estimators that are simultaneously *robust* and *sub-Gaussian*, including Lee and Valiant's, resolving a question raised by Dang et al.Lastly, we show (D) the asymptotic normality and efficiency of Lee and Valiant's estimator, as further evidence for its performance across many settings.
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Deep Learning · Large Language Models
Despite the success of distillation in large language models (LLMs), most prior work applies identical loss functions to both teacher- and student-generated data. These strategies overlook the synergy between loss formulations and data types, leading to a suboptimal performance boost in student models. To address this, we propose DistiLLM-2, a contrastive approach that simultaneously increases the likelihood of teacher responses and decreases that of student responses by harnessing this synergy. Our extensive experiments show that DistiLLM-2 not only builds high-performing student models across a wide range of tasks, including instruction-following and code generation, but also supports diverse applications, such as preference alignment and vision-language extensions. These findings highlight the potential of a contrastive approach to enhance the efficacy of LLM distillation by effectively aligning teacher and student models across varied data types.
We introduce Referring 3D Gaussian Splatting Segmentation (R3DGS), a new task that aims to segment target objects in a 3D Gaussian scene based on natural language descriptions, which often contain spatial relationships or object attributes. This task requires the model to identify newly described objects that may be occluded or not directly visible in a novel view,posing a significant challenge for 3D multi-modal understanding. Developing this capability is crucial for advancing embodied AI.To support research in this area, we construct the first R3DGS dataset, Ref-LERF.Our analysis reveals that 3D multi-modal understanding and spatial relationship modeling are key challenges for R3DGS.To address these challenges, we propose ReferSplat, a framework that explicitly models 3D Gaussian points with natural language expressions in a spatially aware paradigm. ReferSplat achieves state-of-the-art performance on both the newly proposed R3DGS task and 3D open-vocabulary segmentation benchmarks.Dataset and code are available at https://github.com/heshuting555/ReferSplat.
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.
We consider the Euclidean bi-chromatic matching problem in the dynamic setting, where the goal is to efficiently process point insertions and deletions while maintaining a high-quality solution. Computing the minimum cost bi-chromatic matching is one of the core problems in geometric optimization that has found many applications, most notably in estimating Wasserstein distance between two distributions. In this work, we present the first fully dynamic algorithm for Euclidean bi-chromatic matching with sublinear update time. For any fixed $\varepsilon > 0$, our algorithm achieves $O(1/\varepsilon)$-approximation and handles updates in $O(n^{\varepsilon})$ time. Our experiments show that our algorithm enables effective monitoring of the distributional drift in the Wasserstein distance on real and synthetic data sets, while outperforming the runtime of baseline approximations by orders of magnitudes.
Deep Learning · Large Language Models
The ability to organically reason over and with both text and images is a pillar of human intelligence, yet the ability of Multimodal Large Language Models (MLLMs) to perform such multimodal reasoning remains under-explored. Existing benchmarks often emphasize text-dominant reasoning or rely on shallow visual cues, failing to adequately assess integrated visual and textual reasoning. We introduce EMMA (Enhanced MultiModal reAsoning), a benchmark targeting organic multimodal reasoning across mathematics, physics, chemistry, and coding. EMMA tasks demand advanced cross-modal reasoning that cannot be addressed by reasoning independently in each modality, offering an enhanced test suite for MLLMs' reasoning capabilities. Our evaluation of state-of-the-art MLLMs on EMMA reveals significant limitations in handling complex multimodal and multi-step reasoning tasks, even with advanced techniques like Chain-of-Thought prompting and test-time compute scaling underperforming. These findings underscore the need for improved multimodal architectures and training paradigms to close the gap between human and model reasoning in multimodality.
A core data-centric learning challenge is the identification of training samples that are detrimental to model performance. Influence functions serve as a prominent tool for this task and offer a robust framework for assessing training data influence on model predictions. Despite their widespread use, their high computational cost associated with calculating the inverse of the Hessian matrix pose constraints, particularly when analyzing large-sized deep models. In this paper, we establish a bridge between identifying detrimental training samples via influence functions and outlier gradient detection. This transformation not only presents a straightforward and Hessian-free formulation but also provides insights into the role of the gradient in sample impact. Through systematic empirical evaluations, we first validate the hypothesis of our proposed outlier gradient analysis approach on synthetic datasets. We then demonstrate its effectiveness in detecting mislabeled samples in vision models and selecting data samples for improving performance of natural language processing transformer models. We also extend its use to influential sample identification for fine-tuning Large Language Models.
Accelerating the inference of large language models (LLMs) is a critical challenge in generative AI. Speculative decoding (SD) methods offer substantial efficiency gains by generating multiple tokens using a single target forward pass. However, existing SD approaches require the drafter and target models to share the same vocabulary, thus limiting the pool of possible drafters, often necessitating the training of a drafter from scratch. We present three new SD methods that remove this shared-vocabulary constraint. All three methods preserve the target distribution (i.e., they are lossless) and work with off-the-shelf models without requiring additional training or modifications. Empirically, on summarization, programming, and long-context tasks, our algorithms demonstrate significant speedups of up to 2.8x over standard autoregressive decoding. By enabling any off-the-shelf model to serve as a drafter and requiring no retraining, this work substantially broadens the applicability of the SD framework in practice.
Knowledge Distillation (KD) transfers knowledge from a large teacher model to a smaller student model by minimizing the divergence between their output distributions, typically using forward Kullback-Leibler divergence (FKLD) or reverse KLD (RKLD). It has become an effective training paradigm due to the broader supervision information provided by the teacher distribution compared to one-hot labels. We identify that the core challenge in KD lies in balancing two mode-concentration effects: the \textbf{\textit{Hardness-Concentration}} effect, which refers to focusing on modes with large errors, and the \textbf{\textit{Confidence-Concentration}} effect, which refers to focusing on modes with high student confidence. Through an analysis of how probabilities are reassigned during gradient updates, we observe that these two effects are entangled in FKLD and RKLD, but in extreme forms. Specifically, both are too weak in FKLD, causing the student to fail to concentrate on the target class. In contrast, both are too strong in RKLD, causing the student to overly emphasize the target class while ignoring the broader distributional information from the teacher. To address this imbalance, we propose ABKD, a generic framework with $\alpha$-$\beta$-divergence. Our theoretical results show that ABKD offers a smooth interpolation between FKLD and RKLD, achieving a better trade-off between these effects. Extensive experiments on 17 language/vision datasets with 12 teacher-student settings confirm its efficacy.
Mixture-of-Experts (MoE) activates only a subset of experts during inference, allowing the model to maintain low inference FLOPs and latency even as the parameter count scales up. However, since MoE dynamically selects the experts, all the experts need to be loaded into VRAM. Their large parameter size still limits deployment, and offloading, which load experts into VRAM only when needed, significantly increase inference latency. To address this, we propose Mixture of Lookup Experts (MoLE), a new MoE architecture that is efficient in both communication and VRAM usage. In MoLE, the experts are Feed-Forward Networks (FFNs) during training, taking the output of the embedding layer as input. Before inference, these experts can be re-parameterized as lookup tables (LUTs) that retrieves expert outputs based on input ids, and offloaded to storage devices. Therefore, we do not need to perform expert computations during inference. Instead, we directly retrieve the expert's computation results based on input ids and load them into VRAM, and thus the resulting communication overhead is negligible. Experiments show that, with the same FLOPs and VRAM usage, MoLE achieves inference speeds comparable to dense models and significantly faster than MoE with experts offloading, while maintaining performance on par with MoE. Code: https://github.com/JieShibo/MoLE.
From Weight-Based to State-Based Fine-Tuning: Further Memory Reduction on LoRA with Parallel Control
The LoRA method has achieved notable success in reducing GPU memory usage by applying low-rank updates to weight matrices. Yet, one simple question remains: can we push this reduction even further? Furthermore, is it possible to achieve this while improving performance and reducing computation time? Answering these questions requires moving beyond the conventional weight-centric approach. In this paper, we present a state-based fine-tuning framework that shifts the focus from weight adaptation to optimizing forward states, with LoRA acting as a special example. Specifically, state-based tuning introduces parameterized perturbations to the states within the computational graph, allowing us to control states across an entire residual block. A key advantage of this approach is the potential to avoid storing large intermediate states in models like transformers. Empirical results across multiple architectures—including ViT, RoBERTa, LLaMA2-7B, and LLaMA3-8B—show that our method further reduces memory consumption and computation time while simultaneously improving performance. Moreover, as a result of memory reduction, we explore the feasibility to train 7B/8B models on consumer-level GPUs like Nvidia 3090, without model quantization. The code is available at an anonymous GitHub repository
We introduce SWE-Lancer, a benchmark of over 1400 freelance software engineering tasks from Upwork, valued at \\\$1 million USD total in real-world payouts. SWE-Lancer encompasses both independent engineering tasks — ranging from \\\$50 bug fixes to \\\$32000 feature implementations — and managerial tasks, where models choose between technical implementation proposals. Independent tasks are graded with end-to-end tests triple-verified by experienced software engineers, while managerial decisions are assessed against the choices of the original hired engineering managers. We evaluate model performance and find that frontier models are still unable to solve the majority of tasks. To facilitate future research, we open-source a unified Docker image and a public evaluation split. By mapping model performance to monetary value, we hope SWE-Lancer enables greater research into the economic impact of AI model development.
Driven by steady progress in deep generative modeling, simulation-based inference (SBI) has emerged as the workhorse for inferring the parameters of stochastic simulators. However, recent work has demonstrated that model misspecification can harm SBI's reliability, preventing its adoption in important applications where only misspecified simulators are available.This work introduces robust posterior estimation (RoPE), a framework that overcomes model misspecification with a small real-world calibration set of ground truth parameter measurements.We formalize the misspecification gap as the solution of an optimal transport (OT) problem between learned representations of real-world and simulated observations, allowing RoPE to learn a model of the misspecification without placing additional assumptions on its nature. RoPE shows how the calibration set and OT together offer a controllable balance between calibrated uncertainty and informative inference even under severely misspecified simulators. Results on four synthetic tasks and two real-world problems with ground-truth labels demonstrate that RoPE outperforms baselines and consistently returns informative and calibrated credible intervals.
Position · Methodology
The AI research community plays a vital role in shaping the scientific, engineering, and societal goals of AI research. In this position paper, we argue that focusing on the highly contested topic of 'artificial general intelligence' ('AGI') undermines our ability to choose effective goals. We identify six key traps---obstacles to productive goal setting---that are aggravated by AGI discourse: Illusion of Consensus, Supercharging Bad Science, Presuming Value-Neutrality, Goal Lottery, Generality Debt, and Normalized Exclusion. To avoid these traps, we argue that the AI research community needs to (1) prioritize specificity in scientific, engineering, and societal goals, (2) center pluralism about multiple worthwhile approaches to multiple valuable goals, and (3) foster innovation through greater inclusion of disciplines and communities. Therefore, the AI research community needs to stop treating ``AGI'' as the north-star goal of AI research.
Theory · Probabilistic Methods
The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free"' embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) algorithms for time series and sequential data. The convergence results proved in this paper bridge the gap between the expected signature's empirical discrete-time estimator and its theoretical continuous-time value, allowing for a more complete probabilistic interpretation of expected signature-based ML methods. Moreover, when the data generating process is a martingale, we suggest a simple modification of the expected signature estimator with significantly lower mean squared error and empirically demonstrate how it can be effectively applied to improve predictive performance.
Deep Learning · Generative Models and Autoencoders
Despite tremendous recent progress, generative video models still struggle to capture real-world motion, dynamics, and physics. We show that this limitation arises from the conventional pixel reconstruction objective, which biases models toward appearance fidelity at the expense of motion coherence.To address this, we introduce **VideoJAM**, a novel framework that instills an effective motion prior to video generators, by encouraging the model to learn *a joint appearance-motion representation*. VideoJAM is composed of two complementary units. During training, we extend the objective to predict both the generated pixels and their corresponding motion from a single learned representation. During inference, we introduce **Inner-Guidance**, a mechanism that steers the generation toward coherent motion by leveraging the model's own evolving motion prediction as a dynamic guidance signal.Notably, our framework can be applied to any video model with minimal adaptations, requiring no modifications to the training data or scaling of the model.VideoJAM achieves state-of-the-art performance in motion coherence, surpassing highly competitive proprietary models while also enhancing the perceived visual quality of the generations.These findings emphasize that appearance and motion can be complementary and, when effectively integrated, enhance both the visual quality and the coherence of video generation.
We study the Gaussian process (GP) bandit problem, whose goal is to minimize regret under an unknown reward function lying in some reproducing kernel Hilbert space (RKHS). The maximum posterior variance analysis is vital in analyzing near-optimal GP bandit algorithms such as maximum variance reduction (MVR) and phased elimination (PE).Therefore, we first show the new upper bound of the maximum posterior variance, which improves the dependence of the noise variance parameters of the GP. By leveraging this result, we refine the MVR and PE to obtain (i) a nearly optimal regret upper bound in the noiseless setting and (ii) regret upper bounds that are optimal with respect to the RKHS norm of the reward function. Furthermore, as another application of our proposed bound, we analyze the GP bandit under the time-varying noise variance setting, which is the kernelized extension of the linear bandit with heteroscedastic noise. For this problem, we show that MVR and PE-based algorithms achieve noise variance-dependent regret upper bounds, which matches our regret lower bound.
General Machine Learning · Representation Learning
Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive embedding lengths, but it requires full model retraining and suffers from noticeable performance degradations at short lengths. In this paper, we show that *sparse coding* offers a compelling alternative for achieving adaptive representation with minimal overhead and higher fidelity. We propose **Contrastive Sparse Representation** (**CSR**), a method that specifies pre-trained embeddings into a high-dimensional but *selectively activated* feature space. By leveraging lightweight autoencoding and task-aware contrastive objectives, CSR preserves semantic quality while allowing flexible, cost-effective inference at different sparsity levels. Extensive experiments on image, text, and multimodal benchmarks demonstrate that CSR consistently outperforms MRL in terms of both accuracy and retrieval speed—often by large margins—while also cutting training time to a fraction of that required by MRL. Our results establish sparse coding as a powerful paradigm for adaptive representation learning in real-world applications where efficiency and fidelity are both paramount. Code is available at [this URL.](https://github.com/neilwen987/CSR_Adaptive_Rep)
Zero-shot coordination (ZSC), the ability to adapt to a new partner in a cooperative task, is a critical component of human-compatible AI. While prior work has focused on training agents to cooperate on a single task, these specialized models do not generalize to new tasks, even if they are highly similar. Here, we study how reinforcement learning on a **distribution of environments with a single partner** enables learning general cooperative skills that support ZSC with **many new partners on many new problems**. We introduce *two* Jax-based, procedural generators that create billions of solvable coordination challenges. We develop a new paradigm called **Cross-Environment Cooperation (CEC)**, and show that it outperforms competitive baselines quantitatively and qualitatively when collaborating with real people. Our findings suggest that learning to collaborate across many unique scenarios encourages agents to develop general norms, which prove effective for collaboration with different partners. Together, our results suggest a new route toward designing generalist cooperative agents capable of interacting with humans without requiring human data.
General Machine Learning · Causality
Generalizing causal effects from Randomized Controlled Trials (RCTs) to target populations across diverse environments is of significant practical importance, as RCTs are often costly and logistically complex to conduct. A key challenge is environmental shift, defined as changes in the distribution and availability of covariates between source and target environments. A common approach addressing this challenge is to identify a separating set--covariates that govern both treatment effect heterogeneity and environmental differences--and combine RCT samples with target populations matched on this set. However, this approach assumes that the separating set is fully observed and shared across datasets, an assumption often violated in practice. We propose a novel Two-Stage Doubly Robust (2SDR) method that relaxes this assumption by allowing the separating set to be observed in only one of the two datasets. 2SDR leverages shadow variables to impute missing components of the separating set and generalize treatment effects across environments in a two-stage procedure. We show the identification of causal effects in target environments under 2SDR and demonstrate its effectiveness through extensive experiments on both synthetic and real-world datasets.