We study the problem of combining neural networks with symbolic reasoning.

Is texting behind the wheel of a self-driving Tesla crazy? As self-driving cars get closer to reality, Tesla is striving to remain a big player. But is it sacrificing safety to stay in the game? For the past few weeks, Geoff Perlman, a 61-year-old technology executive from Texas, has been testing a free trial of Tesla's latest self-driving software as he travels around Austin. He's impressed: it can handle confusing lane adjustments and park itself in busy lots better, he thinks, than the average human.

With the rise of AI-generated content (AIGC), generating perceptually natural and feeling-aligned music from multimodal inputs has become a central challenge. Existing approaches often rely on explicit emotion labels that require costly annotation, underscoring the need for more flexible feeling-aligned methods. To support multimodal music generation, we construct ArtiCaps, a pseudo feeling-aligned image-music-text dataset created by semantically matching descriptions from ArtEmis and MusicCaps. We further propose Art2Music, a lightweight cross-modal framework that synthesizes music from artistic images and user comments. In the first stage, images and text are encoded with OpenCLIP and fused using a gated residual module; the fused representation is decoded by a bidirectional LSTM into Mel-spectrograms with a frequency-weighted L1 loss to enhance high-frequency fidelity. In the second stage, a fine-tuned HiFi-GAN vocoder reconstructs high-quality audio waveforms. Experiments on ArtiCaps show clear improvements in Mel-Cepstral Distortion, Frechet Audio Distance, Log-Spectral Distance, and cosine similarity. A small LLM-based rating study further verifies consistent cross-modal feeling alignment and offers interpretable explanations of matches and mismatches across modalities. These results demonstrate improved perceptual naturalness, spectral fidelity, and semantic consistency. Art2Music also maintains robust performance with only 50k training samples, providing a scalable solution for feeling-aligned creative audio generation in interactive art, personalized soundscapes, and digital art exhibitions.

We present a probabilistic data-driven weather model capable of providing an ensemble of high spatial resolution realizations of 87 variables at arbitrary forecast length and ensemble size. The model uses a stretched grid, dedicating 2.5 km resolution to a region of interest, and 31 km resolution elsewhere. Based on a stochastic encoder-decoder architecture, the model is trained using a loss function based on the Continuous Ranked Probability Score (CRPS) evaluated point-wise in real and spectral space. The spectral loss components is shown to be necessary to create fields that are spatially coherent. The model is compared to high-resolution operational numerical weather prediction forecasts from the MetCoOp Ensemble Prediction System (MEPS), showing competitive forecasts when evaluated against observations from surface weather stations. The model produced fields that are more spatially coherent than mean squared error based models and CRPS based models without the spectral component in the loss.

Self-assessment is a key aspect of reliable intelligence, yet evaluations of large language models (LLMs) focus mainly on task accuracy. We adapted the 10-item General Self-Efficacy Scale (GSES) to elicit simulated self-assessments from ten LLMs across four conditions: no task, computational reasoning, social reasoning, and summarization. GSES responses were highly stable across repeated administrations and randomized item orders. However, models showed significantly different self-efficacy levels across conditions, with aggregate scores lower than human norms. All models achieved perfect accuracy on computational and social questions, whereas summarization performance varied widely. Self-assessment did not reliably reflect ability: several low-scoring models performed accurately, while some high-scoring models produced weaker summaries. Follow-up confidence prompts yielded modest, mostly downward revisions, suggesting mild overestimation in first-pass assessments. Qualitative analysis showed that higher self-efficacy corresponded to more assertive, anthropomorphic reasoning styles, whereas lower scores reflected cautious, de-anthropomorphized explanations. Psychometric prompting provides structured insight into LLM communication behavior but not calibrated performance estimates.

Chain of Thought (CoT) reasoning has demonstrated remarkable deep reasoning capabilities in both large language models (LLMs) and multimodal large language models (MLLMs). However, its reliability is often undermined by the accumulation of errors in intermediate steps. This paper introduces an novel approach to calibrate the CoT reasoning accuracy by leveraging the model's intrinsic veracity encoding. We discover that specific attention head activations reliably reflect the truthfulness of reasoning steps in CoT. Based on this insight, we train a confidence predictor to evaluate the correctness of each reasoning step using these truthfulness-sensitive activations, dynamically selecting the most plausible reasoning path via beam search. Experimental results demonstrate that our method significantly outperforms the state-of-the-art baselines (e.g., Few-Shot CoT, Self-Consistency, and Self-Evaluation Guided Beam Search) across the mathematical, symbolic, and commonsense reasoning tasks, exhibiting superior accuracy and reliability in both unimodal and multimodal settings. We further validate the approach on large reasoning models, confirming its applicability to specialized reasoning models. Additionally, we explore the role of the model's self-correction ability in CoT reasoning. This work provides a novel reliability improvement path for CoT reasoning with broad application potential.

Anomaly detection in time series data is fundamental to the design, deployment, and evaluation of industrial control systems.

In this work, we benchmark two recently developed deep density methods for nonlinear filtering. Starting from the Fokker--Planck equation with Bayes updates, we model the filtering density of a discretely observed SDE. The two filters: the deep splitting filter and the deep BSDE filter, are both based on Feynman--Kac formulas, Euler--Maruyama discretizations and neural networks. The two methods are extended to logarithmic formulations providing sound and robust implementations in increasing state dimension. Comparing to the classical particle filters and ensemble Kalman filters, we benchmark the methods on numerous examples. In the low-dimensional examples the particle filters work well, but when we scale up to a partially observed 100-dimensional Lorenz-96 model the particle-based methods fail and the logarithmic deep density method prevails. In terms of computational efficiency, the deep density methods reduce inference time by roughly two to five orders of magnitude relative to the particle-based filters.