Label smoothing and HXE achieve their best accuracy when set to zero, which is equivalent to a flat softmax. Notethatweuse confidence threshold inference for all loss functions, regardless of the inference function that was usedintheoriginalpublication. Algorithm 1Algorithm for finding ordered Pareto set. The inputsxandy are lists with equal length.

Since utilities can serveas target values to learn the scoring function through square loss regression, the optimality ofsorting byexpected utilities isequivalent tothe consistencyofregression.

This paper addresses the question of which of these tasks are asymptotically solved by sorting by decreasing order of expected utility, for some suitable notion of utility, or, equivalently, when is square loss regression consistent for ranking via score-and-sort?

Various Transformer-based models have been proposed for time series forecasting. These models leverage the self-attention mechanism to capture long-term temporal or variate dependencies in sequences. Existing methods can be divided into two approaches: (1) reducing computational cost of attention by making the calculations sparse, and (2) reshaping the input data to aggregate temporal features. However, existing attention mechanisms may not adequately capture inherent nonlinear dependencies present in time series data, leaving room for improvement. In this study, we propose a novel attention mechanism based on Chatterjee's rank correlation coefficient, which measures nonlinear dependencies between variables. Specifically, we replace the matrix multiplication in standard attention mechanisms with this rank coefficient to measure the query-key relationship. Since computing Chatterjee's correlation coefficient involves sorting and ranking operations, we introduce a differentiable approximation employing SoftSort and SoftRank. Our proposed mechanism, ``XicorAttention,'' integrates it into several state-of-the-art Transformer models. Experimental results on real-world datasets demonstrate that incorporating nonlinear correlation into the attention improves forecasting accuracy by up to approximately 9.1\% compared to existing models.

Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterative algorithm onto layers of a neural network, known as algorithm unrolling. However, greedy sparse recovery algorithms depend on the non-differentiable argsort operator, which hinders their integration into neural networks. In this paper, we address this challenge in Orthogonal Matching Pursuit (OMP) and Iterative Hard Thresholding (IHT), two popular representative algorithms in this class. We propose permutation-based variants of these algorithms and approximate permutation matrices using "soft" permutation matrices derived from softsort, a continuous relaxation of argsort. We demonstrate -- both theoretically and numerically -- that Soft-OMP and Soft-IHT, as differentiable counterparts of OMP and IHT and fully compatible with neural network training, effectively approximate these algorithms with a controllable degree of accuracy. This leads to the development of OMP- and IHT-Net, fully trainable network architectures based on Soft-OMP and Soft-IHT, respectively. Finally, by choosing weights as "structure-aware" trainable parameters, we connect our approach to structured sparse recovery and demonstrate its ability to extract latent sparsity patterns from data.

Large language models (LLMs) are increasingly being used to synthesize and reason about source code. However, the static nature of these models' knowledge does not reflect the fact that libraries and API functions they invoke are continuously evolving, with functionality being added or changing. While numerous benchmarks evaluate how LLMs can generate code, no prior work has studied how an LLMs' knowledge about code API functions can be updated. To fill this gap, we present CodeUpdateArena, a benchmark for knowledge editing in the code domain. An instance in our benchmark consists of a synthetic API function update paired with a program synthesis example that uses the updated functionality; our goal is to update an LLM to be able to solve this program synthesis example without providing documentation of the update at inference time. Compared to knowledge editing for facts encoded in text, success here is more challenging: a code LLM must correctly reason about the semantics of the modified function rather than just reproduce its syntax. Our dataset is constructed by first prompting GPT-4 to generate atomic and executable function updates. Then, for each update, we generate program synthesis examples whose code solutions are prone to use the update. Our benchmark covers updates of various types to 54 functions from seven diverse Python packages, with a total of 670 program synthesis examples. Our experiments show that prepending documentation of the update to open-source code LLMs (i.e., DeepSeek, CodeLlama) does not allow them to incorporate changes for problem solving, and existing knowledge editing techniques also have substantial room for improvement. We hope our benchmark will inspire new methods for knowledge updating in code LLMs.