exact accuracy 0.99 at low noise · four synthetic models
Generic local caustics do not identify a group. Finite synthetic tests recover additional structure, while degenerate tangencies refute a universal cusp claim.
mean transport error 4.98 → 4.52 voxels · 3 held-out seeds
A measured transverse correction improves approximate cosmic transport. Matched detector comparisons establish where orientation lifting helps and where it fails.
$\dot x=u_1\cos\theta,\quad \dot y=u_1\sin\theta,\quad \dot\theta=u_2$
Your brain fills in contours that do not exist. Petitot's neurogeometry models oriented cortical states by a contact bundle; this article separates the free sub-Riemannian geodesics from their smooth Euler-elastica siblings.
A four-year-old child processes roughly one petabyte of visual information — fifty times more than GPT-4 has ever read — and learns effortlessly. Closing that gap is what's pushing AI past sequential token prediction toward predictive world models, retrieval-augmented memory, and Karpathy's Software 3.0 paradigm: the LLM as operating system.
Eighty lines of PyTorch — flips, rotation and ColorJitter for augmentation, DataParallel for multi-GPU, cross-entropy with Adam — fine-tune a pretrained ResNet-50 on the ImageNet Object Localization Challenge. Wrap it in a Dockerfile that pulls the dataset from Kaggle and you have a self-contained, reproducible 1000-class training pipeline.
A single LEFT JOIN against information_schema.table_constraints exposes every BASE TABLE missing a PRIMARY KEY — the silent latency tax that creeps in through schema migrations and ad-hoc DDL. Audit the whole cluster, then narrow to a single schema with one extra WHERE clause.
Matplotlib falls back to its non-interactive Agg backend whenever there's no X11 display — which is the default state inside almost every container. The fix is two parts: install the GUI toolkit dependencies in the image, then forward the host's X socket into the container at run time.
When a training run is GPU-bound, the bottleneck is rarely the model — it's the data pipeline starving the device. nvidia-smi dmon turns into a live, one-line-per-second dashboard for utilisation, memory, power draw, temperature and PCIe throughput, parseable from any shell loop.
Docker accumulates state silently — stopped containers, dangling image layers, unattached volumes, orphaned networks. Four short commands, run in the right order, reclaim gigabytes safely without touching anything that's currently running or in use.
A talk on what deep learning brings to software engineering: the tools, their pros and cons, how deep learning relates to symbolic representations, and the development and debugging cycle of deep-learning architectures.
