We introduce a temperature into the exponential function and replace the softmax output layer of the neural networks by a high-temperature generalization. Similarly, the logarithm in the loss we use for training is replaced by a low-temperature logarithm. By tuning the two temperatures, we create loss functions that are non-convex already in the single layer case. When replacing the last layer of the neural networks by our bi-temperature generalization of the logistic loss, the training becomes more robust to noise. We visualize the effect of tuning the two temperatures in a simple setting and show the efficacy of our method on large datasets. Our methodology is based on Bregman divergences and is superior to a related two-temperature method that uses the Tsallis divergence.

We draw the data points by random sampling from the full data according to their gradient values.

In this paper we introduce a natural image prior that directly represents a Gaussian-smoothed version of the natural image distribution.

Foundation models have shown promise across various financial applications, yet their effectiveness for corporate bankruptcy prediction remains systematically unevaluated against established methods. We study bankruptcy forecasting using Llama-3.3-70B-Instruct and TabPFN, evaluated on large, highly imbalanced datasets of over one million company records from the Visegrád Group. We provide the first systematic comparison of foundation models against classical machine learning baselines for this task. Our results show that models such as XGBoost and CatBoost consistently outperform foundation models across all prediction horizons. LLM-based approaches suffer from unreliable probability estimates, undermining their use in risk-sensitive financial settings. TabPFN, while competitive with simpler baselines, requires substantial computational resources with costs not justified by performance gains. These findings suggest that, despite their generality, current foundation models remain less effective than specialized methods for bankruptcy forecasting.

With tangent space optimization, we can use standard Euclidean optimization techniques, and respect the geometry of the manifold. All experiments were run on Intel Cascade Lake CPUs, with microprocessors Intel Xeon Gold 6230 (20 Cores, 40 Threads, 2.1 GHz, 28MB Cache, 125W TDP). The red dot corresponds to the relation addition R . Datasets: Stats about the datasets used in Knowledge graph experiments can be found in Table 4. Results: In addition to the results provided in 6.1, in Table 5 we provide a comparison with other We include ComplEx [77], Tucker [9], and Quaternion [92]. In Figure 6 we add equivalent plots to the ones explained in 6.4 for other relations from Same grid search is applied to baselines.

Prior to recent successes using neural networks, term frequency-inverse document frequency (tf-idf) was clearly regarded as the best choice for identifying documents related to a query. We provide a different score, aver, and observe, on a dataset with ground truth marking for association, that aver does do better at finding assciated pairs than tf-idf. This example involves finding associated vertices in a large graph and that may be an area where neural networks are not currently an obvious best choice. Beyond this one anecdote, we observe that (1) aver has a natural threshold for declaring pairs as unassociated while tf-idf does not, (2) aver can distinguish between pairs of documents for which tf-idf gives a score of 1.0, (3) aver can be applied to larger collections of documents than pairs while tf-idf cannot, and (4) that aver is derived from entropy under a simple statistical model while tf-idf is a construction designed to achieve a certain goal and hence aver may be more "natural." To be fair, we also observe that (1) writing down and computing the aver score for a pair is more complex than for tf-idf and (2) that the fact that the aver score is naturally scale-free makes it more complicated to interpret aver scores.

Large Reasoning Models (LRMs) achieve superior performance by extending the thought length. However, a lengthy thinking trajectory leads to reduced efficiency. Most of the existing methods are stuck in the assumption of overthinking and attempt to reason efficiently by compressing the Chain-of-Thought, but this often leads to performance degradation. To address this problem, we introduce A*-Thought, an efficient tree search-based unified framework designed to identify and isolate the most essential thoughts from the extensive reasoning chains produced by these models. It formulates the reasoning process of LRMs as a search tree, where each node represents a reasoning span in the giant reasoning space. By combining the A* search algorithm with a cost function specific to the reasoning path, it can efficiently compress the chain of thought and determine a reasoning path with high information density and low cost. In addition, we also propose a bidirectional importance estimation mechanism, which further refines this search process and enhances its efficiency beyond uniform sampling. Extensive experiments on several advanced math tasks show that A*-Thought effectively balances performance and efficiency over a huge search space. Specifically, A*-Thought can improve the performance of QwQ-32B by 2.39$\times$ with low-budget and reduce the length of the output token by nearly 50% with high-budget. The proposed method is also compatible with several other LRMs, demonstrating its generalization capability. The code can be accessed at: https://github.com/AI9Stars/AStar-Thought.

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning.