Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1906.06637

A Closer Look at Double Backpropagation

Christian Etmann
View original source ↗Read source document ↗Export metadata ↓

Abstract

In recent years, an increasing number of neural network models have included derivatives with respect to inputs in their loss functions, resulting in so-called double backpropagation for first-order optimization. However, so far no general description of the involved derivatives exists. Here, we cover a wide array of special cases in a very general Hilbert space framework, which allows us to provide optimized backpropagation rules for many real-world scenarios. This includes the reduction of calculations for Frobenius-norm-penalties on Jacobians by roughly a third for locally linear activation functions. Furthermore, we provide a description of the discontinuous loss surface of ReLU networks both in the inputs and the parameters and demonstrate why the discontinuities do not pose a big problem in reality.

Explore related subjects

cs.LGmath.OCstat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Christian Etmann. 2019-06-16. A Closer Look at Double Backpropagation. https://arxiv.org/abs/1906.06637

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Label Propagation for Physics-Informed Neural Networks and Physics-Informed Gaussian Processes

We present a series of empirical results of the application of semi-supervised label propagation techniques in training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training, therefore establishing a hybrid between these two main classes of physics-informed machine learning. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information from boundaries into the physical domain, including information from initial conditions in the case of solving stiff time-dependent partial differential equations, which is known to be a common failure mode of physics-informed machine learning.

cs.LG↗
arXiv2026

Multi-Armed Bernoulli Bandits via Minimax Single-Arm Stopping

We develop an index policy for finite-horizon Bernoulli multi-armed bandits from minimax solutions to single-arm bandit (SAB) problems. Each SAB problem involves choosing between an unknown Bernoulli arm and a known reward. We show that minimizing worst-case regret of SAB problems over all non-anticipative policies admits an exact semi-infinite linear programming formulation. The resulting stopping policies offer a natural way to compare arms: the higher the known reward against which a policy continues sampling, the more promising the unknown arm. We turn this intuition into indices based on cumulative continuation probabilities, with a monotone adjustment and a reward-shortfall cap. By relating index errors to the regret of single-arm stopping policies, we establish a distribution-free regret bound of $4.45\sqrt{KT}+10.75K$ for $K$ arms and horizon $T$. This bound matches the minimax-optimal regret order established in the literature. The guarantee extends to rewards supported on $[0,1]$ through Bernoulli randomization. We also provide a finite-grid implementation with quantified approximation loss. In numerical experiments, the SAB-based index policy achieves lower worst-case regret than every tested benchmark policy across all evaluated numbers of arms and horizons, while closely matching the grid-based MAB minimax policy in the two-arm setting.

cs.LG↗
arXiv2026

Autonomous Model Lifecycle Management for Digital Twin-Based Manufacturing Control

Manufacturing AI systems must autonomously adapt to continuous distributional shift from raw-material variability, ambient changes, and equipment aging, under strict safeguard and operator-trust requirements where model failures risk physical damage. This paper presents a closed-loop Cyber-Physical System (CPS) for autonomous model lifecycle management in automotive manufacturing, deployed since 2023. The system manages product-specialized model pairs: a sequence-to-sequence physics model (LPP) serving as a digital twin, and a deep Reinforcement Learning (RL) control policy (LCP) trained against it. Per retraining cycle, multiple model variants spanning architecture families and RL algorithms compete; only the best-scoring candidate advances. A Conductor orchestrator autonomously manages plant-wide model inventories with dependency-aware retraining and Proportional-Integral-Derivative (PID) fallback. Reflecting the principle of Human-Centric Intelligence, the LCP composite score embeds an operator-trust gate penalizing policies deviating from established practice; without it, 23% of policies are rejected by operators despite passing accuracy thresholds. Across multiple facilities, LCP-controlled processes achieve process stability improvements of 28-45% over uncontrolled baselines with zero safety incidents.

cs.LG↗