Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models. Here, each edge in the graph has a known, independent probability of existing derived from some prediction. Algorithms must probe edges to determine existence and match them irrevocably if they exist. Further, each vertex may have a patience constraint denoting how many of its neighboring edges can be probed. We present new ordered contention resolution schemes yielding improved approximation guarantees for some of the foundational problems studied in this area. For stochastic matching with patience constraints in general graphs, we provide a 0.382-approximate algorithm, significantly improving over the previous best 0.31-approximation of Baveja et al. (2018). When the vertices do not have patience constraints, we describe a 0.432-approximate random order probing algorithm with several corollaries such as an improved guarantee for the Prophet Secretary problem under Edge Arrivals. Finally, for the special case of bipartite graphs with unit patience constraints on one of the partitions, we show a 0.632-approximate algorithm that improves on the recent 1/3-guarantee of Hikima et al. (2021).

In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models.

In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models.

However,such predictions, although usually accurate, can be arbitrarily poor.

Post-training with reinforcement learning (RL) typically optimizes a single scalar objective and ignores structure in how solutions are produced. We ask whether a scalar hint toward a canonical solver ordering, used only during RL post-training, improves performance even when fine-tuned on randomized solution sequences. On Sudoku, we train a Transformer with standard fine-tuning on randomized solving orders, then post-train it with Group Relative Policy Optimization (GRPO) with two rewards: cell accuracy and an ordering reward that increases when the model's emission order aligns with the solver order. To compare signals cleanly, we combine them via fixed mixtures and use a simple bootstrapped scaling to equalize component magnitudes at initialization. Mixed rewards generally outperform cell-only optimization--the best mixture yields substantially higher test accuracy than the fine-tuned-only model trained on random-order and approaches the fine-tuned-only model trained on solver-order sequences in accuracy. These results suggest that coarse ordering signals can steer RL post-training toward solver-order trajectories without modifying supervised data or architecture.

Curriculum learning, a training technique where data is presented to the model in order of example difficulty (e.g., from simpler to more complex documents), has shown limited success for pre-training language models. In this work, we investigate whether curriculum learning becomes competitive if we replace conventional human-centered difficulty metrics with one that more closely corresponds to example difficulty as observed during model training. Specifically, we experiment with sorting training examples by their \textit{training data influence}, a score which estimates the effect of individual training examples on the model's output. Models trained on our curricula are able to outperform ones trained in random order by over 10 percentage points in benchmarks, confirming that curriculum learning is beneficial for language model pre-training, as long as a more model-centric notion of difficulty is adopted.

While eXplainable AI (XAI) has advanced significantly, few methods address interpretabil-ity in embedded vector spaces where dimensions represent complex abstractions. We introduce Distance Explainer, a novel method for generating local, post-hoc explanations of embedded spaces in machine learning models. Our approach adapts saliency-based techniques from RISE to explain the distance between two embedded data points by assigning attribution values through selective masking and distance-ranked mask filtering. We evaluate Distance Explainer on cross-modal embeddings (image-image and image-caption pairs) using established XAI metrics including Faithfulness, Sensitivity/Robustness, and Randomization. Experiments with ImageNet and CLIP models demonstrate that our method effectively identifies features contributing to similarity or dissimilarity between embedded data points while maintaining high robustness and consistency. We also explore how parameter tuning, particularly mask quantity and selection strategy, affects explanation quality. This work addresses a critical gap in XAI research and enhances transparency and trustworthiness in deep learning applications utilizing embedded spaces.