SearcharxivSearch

arXiv subjects

Benjamin Jiang

Publications and source records attributed to Benjamin Jiang.

3 recordsLinked to original sources

Diffusion Transformer World-Action Model for AV Scene Prediction

Action-conditioned world models let an autonomous vehicle predict future camera scenes from its own planned controls, enabling planning and simulation without real-world rollouts, but at compact, trainable scale the futures are ambiguous and the field's standard distortion metrics actively mislead: they reward a blurry regression mean over a realistic prediction. We confront this with a compact latent world model that, given the present front-camera latent and a sequence of ego-actions, predicts future scene latents a frozen decoder renders to $256 \times 256$ frames up to 8 seconds ahead, evaluated on 150 held-out nuScenes scenes. We first benchmark where to predict: across six frozen encoders spanning four representation families, V-JEPA2 with temporal context reduces steering RMSE by 40% over the best single-frame encoder. We then train a latent Diffusion Transformer (DiT) and, through a controlled diagnosis, identify the four ingredients it needs: spatial tokens, the $x_0$ objective, residual anchoring, and sampling matched to target uncertainty. In a Stable-Diffusion-VAE encode-predict-decode pipeline we expose the central tension: distortion metrics (cosine similarity, SSIM) favor the blurry mean, masking that the diffusion model is far closer to the real frame distribution. Inception-based FID and KID reveal a clean perception-distortion frontier: diffusion attains KID 0.078 versus 0.375 for regression ($4.8\times$ better), and a deployable train-derived calibration makes this practical without test-time ground truth. The model is genuinely action-controllable (steering drives scene displacement, Spearman $\rho = 0.81$, vs $-0.18$ for regression). We trace limited single-pass motion to a shared-present anchor and engineer a compact 1.7M-parameter "jump" model that recovers full ground-truth motion magnitude ($1.02\times$ GT), where single-pass models capture less than half.

cs.CV

A Carleman Semi-Discrete Convexification Method Combined With Deep Learning for Electrical Impedance Tomography

In this paper, a new semi-discrete version of the Carleman estimate-based convexification globally convergent numerical method is developed. It is used for the delivery of the starting point for the training procedure of deep learning. An important feature of the continuous version of the convexification method is that its convergence to the true solution is independent on the availability of a good first guess about this solution. A new concept of the h-strong convexity is introduced, where h is the grid step size in the semi-discrete version of the convexification method. The h -strong convexity allows to obtain an a priori accuracy estimate of the starting point for the training step of the deep learning procedure. This approach is demonstrated for a highly nonlinear problem of Electrical Impedance Tomography. Results of numerical experiments for complicated media structures demonstrate the computational feasibility of this procedure.

math.AP

Solving the Stock Option Forecast problem by a numerical method for the Black-Scholes Equation with Machine Learning Classification Model

We proposed classification models that utilize the result from the Quasi-Reversibility Method, which solves the Black-Scholes equation to forecast the option prices one day in advance. Combining the minimizer from QRM with our machine learning classifications, we can classify the option as an increase or decrease in value. Based on the different classifications of the options, we can apply various trading strategies which we aim to figure out ways to improve the results from QRM's extrapolations. To further test the viability of our model, we collected 23548 options data from the real-world market for our model, and we will then feed in the data along with the minimizer from QRM to form decision trees and random forests, which we will later test for accuracy, precision, and recall.

math.OC