Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one can optimally solve any center-based clustering objective over it (such as k-means). Moreover, these solutions can be found exceedingly quickly and are themselves necessarily hierarchical. Thus, given a cluster tree, we show that one can quickly access a plethora of new, equally meaningful hierarchies. Just as in standard hierarchical clustering, one can then choose any desired partition from these new hierarchies. We conclude by verifying the utility of our proposed techniques across datasets, hierarchies, and partitioning schemes.

We consider the Tree Alternating Optimization (TAO) algorithm to train regression trees with linear predictors in the leaves. Unlike the traditional, greedy recursive partitioning algorithms such as CART, TAO guarantees a monotonic decrease of the objective function and results in smaller trees of much better accuracy. We modify the TAO algorithm so that it produces exactly the same result but is much faster, particularly for high input dimensionality or deep trees. The idea is based on the fact that, at each iteration of TAO, each leaf receives only a subset of the training instances. Thus, the optimization of the leaf model can be done exactly but faster by using the Sherman-Morrison-Woodbury formula. This has the unexpected advantage that, once a tree exceeds a critical depth, then making it deeper makes it faster to train, even though the tree is larger and has more parameters. Indeed, this can make learning a nonlinear model (the tree) asymptotically faster than a regular linear regression model. We analyze the corresponding computational complexity and verify the speedups experimentally in various datasets. The argument can be applied to other types of trees, whenever the optimization of a node can be computed in superlinear time of the number of instances.

Our evaluation and analysis are conducted mainly on the group of models listed in Table 2 in the13 main paper. We have chosen models such that they cover most of the popular and best-performing14 methods used by recent multimodal understanding work. In this part, we discuss all the models we15 have used in our experiments and explain their evaluation details, the public checkpoints we have16 chosen, and display the prompts we used to adapt the model to our datasets.17 During evaluation, we chose to follow the standard prompt provided by the authors whenever possi-18 ble for multiple-choice and short-answer questions. When the prompt is not provided for the model,19 we select a custom prompt that is created through several iterations of prompt engineering to select20 the one that produces the most effective results. The images are always included as the prefix.21 We used three proprietary models in our evaluation: GPT-o4-mini [1], Gem-22 ini 1.5 Pro [9], and Claude 3 Haiku [10]. Below we note the model API version used for evaluation.23 GPT-o4-mini: May 13-15, 2025.24 Cambrian-1 is a recent state-of-the-art model that excels at visual-centric tasks.27 This model explores combinations of vision encoders, text and image integration techniques, and28 instruction tuning strategies. We use the official implementation and checkpoint1 with a LLaMA3-29 8B-Instruct LLM backbone model in our evaluation.30 InternVL scales up the vision foundation model while aligning it with the back-31 bone LLM, and is trained on web-scale image-text data to achieve strong performance across a vari-32 ety of vision-centric tasks. We use the official implementation and checkpoint2 with the InternViT-33 300M-448px vision backbone and Internlm2.5-7B-chat LLaMA-3.2 is the first collection of multimodal large language model from the35 LLaMA family that was previously text-only. The integration of vision involves utilizing cross-36 attention layers and a pre-trained vision encoder that feeds directly into the text-processor. The37 model follows a commonly used training recipe that includes pretraining on noisy image-text pairs38 and then high-quality knowledge enhanced pairs. Notably, the language-model parameters were39 frozen during the training of alignment of image and text to retain strong text-only capabilities. We40 use the official implementation and checkpoint3 that uses a LLaMA-3.1 text-only language backbone41 in our evaluation. When evaluating the model, we choose to use a custom prompt since no standard42 prompt is provided.43

Unlike prior datasets that rely on crowdsourced prompts, AGMMU is distilled from 116,231 authentic dialogues between everyday growers and USDAauthorized Cooperative Extension experts. Through a three-stage pipeline: automated knowledge extraction, QA generation, and human verification, we construct (i) AGMMU, an evaluation set of 746 multiple-choice questions (MCQs) and 746 open-ended questions (OEQs), and (ii) AGBASE, a development corpus of 57,079 multimodal facts covering five high-stakes agricultural topics: insect identification, species identification, disease categorization, symptom description, and management instruction. AGMMU has three key advantages: Authentic & Expert-Verified: All facts, images, and answers originate from real farmer and gardener inquiries answered by credentialed specialists, ensuring high-fidelity agricultural knowledge. Complete Development Suite: AGMMU uniquely couples a dual-format evaluation benchmark (MCQ and OEQ) with AGBASE, a large-scale training set, enabling both rigorous assessment and targeted improvement of VLMs. Knowledge-intensive Challenge: Our tasks demand the synergy of nuanced visual perception and domain expertise, exposing fundamental limitations of current general-purpose models and charting a path toward robust, application-ready agricultural AI. Benchmarking 12 leading VLMs reveals pronounced gaps in fine-grained perception and factual grounding. Open-sourced models trail after proprietary ones by a wide margin. Simple fine-tuning on AGBASE boosts open-sourced model performance on challenging OEQs for up to 11.6% on average, narrowing this gap and also motivating future research to propose better strategies in knowledge extraction and distillation from AGBASE. We hope AGMMU stimulates research on domain-specific knowledge integration and trustworthy decision support in agriculture AI development.

We consider the problem of testing properties of graphs underlying high-dimensional graphical models. We adopt the model of covariance queries introduced by Lugosi, Truszkowski, Velona, and Zwiernik (2021). We study the case when the underlying graph is a tree. The main results of the paper show that, while reconstructing the entire tree may be costly, certain global structural properties can be tested efficiently. In particular, we design randomized tests for global structural properties that use a sub-quadratic number of queries. We develop testing procedures for several fundamental properties, including the number of leaves, the maximum degree, the typical distance, and the diameter of the tree. For each property, we obtain explicit query complexity bounds that depend on the target threshold and tolerance parameters.

We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact $k$-gram ansatz} in place of transformers with context length $k$, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the \emph{Ising broadcast process} (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian -- both deviating from the true language for any sublinear context. For the \emph{coloring broadcast process} (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with \emph{any} valid coloring of the underlying tree. Together these results imply an $Ω(n)$ lower bound on the context length required to faithfully sample length-$n$ sequences. In contrast, we prove that an autoregressive \emph{reasoning} model with only $Θ(\log n)$ working memory can sample exactly from the true language -- an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

We study the fixed-budget max-min action identification problem in depth-2 max-min trees, an important special case of Monte Carlo Tree Search. A learner sequentially allocates $T$ samples to leaves and then recommends a subtree whose minimum leaf value is largest. Motivated by approximate planning, we focus on $\varepsilon$-good subtree identification, where any subtree whose min value is within $\varepsilon$ of the optimal maximin value is acceptable. Our main contribution is an $\varepsilon$-agnostic algorithm: it does not require $\varepsilon$ as input, but achieves instance-dependent error bounds for every meaningful $\varepsilon$. We show that the misidentification probability decays as $\exp(-\widetildeΘ(T/H_2(\varepsilon)))$, where $H_2(\varepsilon)$ captures both cross-subtree and within-subtree gaps. When each subtree has a single leaf, the problem reduces to standard fixed-budget best-arm identification, and our analysis recovers, up to accelerating factors, known $\varepsilon$-good guarantees for halving-style methods while giving a new $\varepsilon$-good guarantee for Successive Rejects. On the lower-bound side, we provide complementary positive and negative results showing that max-min identification has a different hardness structure from standard $K$-armed bandits. To our knowledge, this is the first provable fixed-budget algorithmic guarantee for max-min action identification.

As a result of this analysis, we are able to pinpoint possible future paths to improvement forscalability andcomputational speed.

Neural Information Processing Systems http://nips.cc/