We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers.

A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w.r.t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof, and often fail to scale to real-world applications. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continuous, temperature-controlled relaxation to the sorting operator based on NeuralSort [1]. We show that PiRank exactly recovers the desired metrics in the limit of zero temperature and further propose a divide-and-conquer extension that scales favorably to large list sizes, both in theory and practice. Empirically, we demonstrate the role of larger list sizes during training and show that PiRank significantly improves over comparable approaches on publicly available Internet-scale learning-to-rank benchmarks.

Large language models (LLMs) are increasingly used in finance and economics, where prompt-based attempts against look-ahead bias implicitly assume that models understand chronology. We test this fundamental question with a series of chronological ordering tasks with increasing complexities over facts the model already knows from pre-training. Our tasks cover (1) chronological ordering, (2) conditional sorting (filter, then order), and (3) anachronism detection. We evaluate GPT-4.1, Claude-3.7 Sonnet, with and without Extended Thinking (ET), and GPT-5 across multiple reasoning-effort settings. Across models, Exact match rate drops sharply as sequences lengthen even while rank correlations stay high as LLMs largely preserve local order but struggle to maintain a single globally consistent timeline. In conditional sorting, most failures stem from the filtering step rather than the ordering step, but GPT-5 and Claude-3.7 Sonnet with Extended Thinking outshine normal models significantly. Lastly, anachronism detection is found to be the easiest task for the LLMs but performance still declines with increasingly overlapping timelines or entities. Overall, our main contribution is showing that allocating explicit reasoning budget helps with chronological ordering with GPT-5 at medium/high reasoning effort achieving flawless ordering at all lengths and perfect conditional sorting (both self-filtered and given-subset), whereas low/minimal effort degrades with longer lists, mirroring earlier models. Our findings delineate limits of current LLMs on chronological tasks, providing insights into task complexity, and demonstrate scenarios in which reasoning helps. These patterns are important for the real-time application of LLMs in finance. We release all code and evaluation templates to support full reproducibility.

The preference over items is specified via relevance labels for each candidate.

Aligning large VLMs with human preferences is a challenging task, as methods like RLHF and DPO often overfit to textual information or exacerbate hallucinations. Although augmenting negative image samples partially addresses these pitfalls, no prior work has employed listwise preference optimization for VLMs, due to the complexity and cost of constructing listwise image samples. In this work, we propose LPOI, the first object-aware listwise preference optimization developed for reducing hallucinations in VLMs. LPOI identifies and masks a critical object in the image, and then interpolates the masked region between the positive and negative images to form a sequence of incrementally more complete images. The model is trained to rank these images in ascending order of object visibility, effectively reducing hallucinations while retaining visual fidelity. LPOI requires no extra annotations beyond standard pairwise preference data, as it automatically constructs the ranked lists through object masking and interpolation. Comprehensive experiments on MMHalBench, AMBER, and Object HalBench confirm that LPOI outperforms existing preference optimization methods in reducing hallucinations and enhancing VLM performance. We make the code available at https://github.com/fatemehpesaran310/lpoi.

A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w.r.t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof, and often fail to scale to real-world applications. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continuous, temperature-controlled relaxation to the sorting operator based on NeuralSort [1]. We show that PiRank exactly recovers the desired metrics in the limit of zero temperature and further propose a divide-and-conquer extension that scales favorably to large list sizes, both in theory and practice.

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight, much less is known when outliers may crowd out low-weight clusters - a setting we refer to as list-decodable mixture learning (LD-ML). In this case, adversarial outliers can simulate additional spurious mixture components. Hence, if all means of the mixture must be recovered up to a small error in the output list, the list size needs to be larger than the number of (true) components. We propose an algorithm that obtains order-optimal error guarantees for each mixture mean with a minimal list-size overhead, significantly improving upon list-decodable mean estimation, the only existing method that is applicable for LD-ML. Although improvements are observed even when the mixture is non-separated, our algorithm achieves particularly strong guarantees when the mixture is separated: it can leverage the mixture structure to partially cluster the samples before carefully iterating a base learner for list-decodable mean estimation at different scales.

Heuristic search is often used for motion planning and pathfinding problems, for finding the shortest path in a graph while also promising completeness and optimal efficiency. The drawback is it's space complexity, specifically storing all expanded child nodes in memory and sorting large lists of active nodes, which can be a problem in real-time scenarios with limited on-board computation. To combat this, we present the Search with Learned Optimal Pruning-based Expansion (SLOPE), which, learns the distance of a node from a possible optimal path, unlike other approaches that learn a cost-to-go value. The unfavored nodes are then pruned according to the said distance, which in turn reduces the size of the open list. This ensures that the search explores only the region close to optimal paths while lowering memory and computational costs. Unlike traditional learning methods, our approach is orthogonal to estimating cost-to-go heuristics, offering a complementary strategy for improving search efficiency. We demonstrate the effectiveness of our approach evaluating it as a standalone search method and in conjunction with learned heuristic functions, achieving comparable-or-better node expansion metrics, while lowering the number of child nodes in the open list. Our code is available at https://github.com/dbokan1/SLOPE.