Xuechen Li

Xinquan Yang, Jinheng Xie, Xuechen Li et al.

In implant prosthesis treatment, the surgical guide of implant is used to ensure accurate implantation. However, such design heavily relies on the manual location of the implant position. When deep neural network has been proposed to assist the dentist in locating the implant position, most of them take a single slice as input, which do not fully explore 3D contextual information and ignoring the influence of implant slope. In this paper, we design a Text Guided 3D Context and Slope Aware Triple Network (TCSloT) which enables the perception of contextual information from multiple adjacent slices and awareness of variation of implant slopes. A Texture Variation Perception (TVP) module is correspondingly elaborated to process the multiple slices and capture the texture variation among slices and a Slope-Aware Loss (SAL) is proposed to dynamically assign varying weights for the regression head. Additionally, we design a conditional text guidance (CTG) module to integrate the text condition (i.e., left, middle and right) from the CLIP for assisting the implant position prediction. Extensive experiments on a dental implant dataset through five-fold cross-validation demonstrated that the proposed TCSloT achieves superior performance than existing methods.

Ahmed M. Ahmed, Rafael Rafailov, Stepan Sharkov et al.

Reinforcement Learning from Human Feedback (RLHF) has enabled significant advancements within language modeling for powerful, instruction-following models. However, the alignment of these models remains a pressing challenge as the policy tends to overfit the learned ``proxy" reward model past an inflection point of utility as measured by a ``gold" reward model that is more performant -- a phenomenon known as overoptimisation. Prior work has mitigated this issue by computing a pessimistic statistic over an ensemble of reward models, which is common in Offline Reinforcement Learning but incredibly costly for language models with high memory requirements, making such approaches infeasible for sufficiently large models. To this end, we propose using a shared encoder but separate linear heads. We find this leads to similar performance as the full ensemble while allowing tremendous savings in memory and time required for training for models of similar size.

Xinquan Yang, Xuguang Li, Xuechen Li et al.

In implant prosthesis treatment, the design of the surgical guide heavily relies on the manual location of the implant position, which is subjective and prone to doctor's experiences. When deep learning based methods has started to be applied to address this problem, the space between teeth are various and some of them might present similar texture characteristic with the actual implant region. Both problems make a big challenge for the implant position prediction. In this paper, we develop a two-stream implant position regression framework (TSIPR), which consists of an implant region detector (IRD) and a multi-scale patch embedding regression network (MSPENet), to address this issue. For the training of IRD, we extend the original annotation to provide additional supervisory information, which contains much more rich characteristic and do not introduce extra labeling costs. A multi-scale patch embedding module is designed for the MSPENet to adaptively extract features from the images with various tooth spacing. The global-local feature interaction block is designed to build the encoder of MSPENet, which combines the transformer and convolution for enriched feature representation. During inference, the RoI mask extracted from the IRD is used to refine the prediction results of the MSPENet. Extensive experiments on a dental implant dataset through five-fold cross-validation demonstrated that the proposed TSIPR achieves superior performance than existing methods.

Patrick Kidger, James Foster, Xuechen Li et al.

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing Neural SDEs has sought to solve. Here, we show that the current classical approach to fitting SDEs may be approached as a special case of (Wasserstein) GANs, and in doing so the neural and classical regimes may be brought together. The input noise is Brownian motion, the output samples are time-evolving paths produced by a numerical solver, and by parameterising a discriminator as a Neural Controlled Differential Equation (CDE), we obtain Neural SDEs as (in modern machine learning parlance) continuous-time generative time series models. Unlike previous work on this problem, this is a direct extension of the classical approach without reference to either prespecified statistics or density functions. Arbitrary drift and diffusions are admissible, so as the Wasserstein loss has a unique global minima, in the infinite data limit any SDE may be learnt. Example code has been made available as part of the \texttt{torchsde} repository.

Shun-ichi Amari, Jimmy Ba, Roger Grosse et al.

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced view on how the \textit{implicit bias} of first- and second-order methods affects the comparison of generalization properties. We provide an exact asymptotic bias-variance decomposition of the generalization error of overparameterized ridgeless regression under a general class of preconditioner $\boldsymbol{P}$, and consider the inverse population Fisher information matrix (used in NGD) as a particular example. We determine the optimal $\boldsymbol{P}$ for both the bias and variance, and find that the relative generalization performance of different optimizers depends on the label noise and the "shape" of the signal (true parameters): when the labels are noisy, the model is misspecified, or the signal is misaligned with the features, NGD can achieve lower risk; conversely, GD generalizes better than NGD under clean labels, a well-specified model, or aligned signal. Based on this analysis, we discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between GD and NGD. We then extend our analysis to regression in the reproducing kernel Hilbert space and demonstrate that preconditioned GD can decrease the population risk faster than GD. Lastly, we empirically compare the generalization error of first- and second-order optimizers in neural network experiments, and observe robust trends matching our theoretical analysis.

Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen et al.

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differential equation whose solution is the gradient, a memory-efficient algorithm for caching noise, and conditions under which numerical solutions converge. In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations. We use our method to fit stochastic dynamics defined by neural networks, achieving competitive performance on a 50-dimensional motion capture dataset.