However, these decisions may be imperfect due to limited experience, implicit biases, or faulty probabilistic reasoning.

Autoregressive (AR) decoding is a major latency bottleneck for large language models. Speculative decoding (SD) accelerates AR by letting a drafter propose multi-token blocks that a verifier accepts or rejects. However, many SD systems require heavy offline training or extra components. These choices raise data/compute cost and can yield brittle drafters under distribution drift. We introduce \emph{Draft, Verify, \& Improve (DVI)}, a training-aware self-speculative framework that combines inference with continual online learning. We partition an LLM into a drafter and a verifier, and during generation, verifier accept/reject decisions are converted into supervision signals and used to update the drafter head. A simple \emph{KL$\rightarrow$RL} schedule bootstraps calibration via online distillation and then adds reward-masked cross-entropy with a on-policy policy-gradient term, preserving lossless, single model deployment. On Spec-Bench, DVI achieves a $2.16\times$ wall-time speedup, on par with SoTA approaches like EAGLE-2, while orders of magnitude less data for training, and ablations show that DVI outperforms KL-only online distillation. DVI demonstrates that \emph{training-aware} self-speculation can deliver state-of-the-art, lossless speedups with minimal training overhead.

Previous research focused on either facet, respectively with a potential-based architecture and with degenerate variational integrators, but new issues arise when combining both. In experiments, the learnt model is sometimes numerically unstable due to the gauge dependency of the scheme, rendering long-time simulations impossible. In this paper, we identify this problem and propose two different training strategies to address it, either by directly learning the vector field or by learning a time-discrete dynamics through the scheme. Several numerical test cases assess the ability of the methods to learn complex physical dynamics, like the guiding center from gyrokinetic plasma physics. Keywords Hamiltonian dynamics, structure preserving integrator, symplectic integrators, neural models, geometric machine learning, guiding center Subject classification (MSC2020) 65P10, 68T07, 37M15 1 Introduction With the rise in machine learning research, the connection between neural networks and differential equations--particularly ordinary differential equations (ODEs)--has become an increasingly active area of study, explored through three main application domains. The first approach interprets certain neural networks, such as Residual Networks (ResNets), as discretizations of ODEs [CRBD18, DDT19, MPP + 20]. This perspective not only enables the design of novel architectures but also provides deeper insight into the internal dynamics of neural networks.

Monitoring the training of neural networks is essential for identifying potential data anomalies, enabling timely interventions and conserving significant computational resources. Apart from the commonly used metrics such as losses and validation accuracies, the hidden representation could give more insight into the model progression. To this end, we introduce SentryCam, an automated, real-time visualization tool that reveals the progression of hidden representations during training. Our results show that this visualization offers a more comprehensive view of the learning dynamics compared to basic metrics such as loss and accuracy over various datasets. Furthermore, we show that SentryCam could facilitate detailed analysis such as task transfer and catastrophic forgetting to a continual learning setting. The code is available at https://github.com/xianglinyang/SentryCam.

Understanding how the predictions of deep learning models are formed during the training process is crucial to improve model performance and fix model defects, especially when we need to investigate nontrivial training strategies such as active learning, and track the root cause of unexpected training results such as performance degeneration. In this work, we propose a time-travelling visual solution DeepVisualInsight (DVI), aiming to manifest the spatio-temporal causality while training a deep learning image classifier. The spatio-temporal causality demonstrates how the gradient-descent algorithm and various training data sampling techniques can influence and reshape the layout of learnt input representation and the classification boundaries in consecutive epochs. Such causality allows us to observe and analyze the whole learning process in the visible low dimensional space. Technically, we propose four spatial and temporal properties and design our visualization solution to satisfy them. These properties preserve the most important information when inverse-)projecting input samples between the visible low-dimensional and the invisible high-dimensional space, for causal analyses. Our extensive experiments show that, comparing to baseline approaches, we achieve the best visualization performance regarding the spatial/temporal properties and visualization efficiency. Moreover, our case study shows that our visual solution can well reflect the characteristics of various training scenarios, showing good potential of DVI as a debugging tool for analyzing deep learning training processes.