arXiv:2608. 12655v1 Announce Type: new Abstract: A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer.
arXiv:2606. 31653v1 Announce Type: cross Abstract: Certified training aims to produce models whose predictions can be formally verified against adversarial perturbations, typically by optimising upper bounds on the worst-case loss over an allowed perturbation set.
arXiv:2608.24743v1 Announce Type: new Abstract: Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-...
The paper introduces a certified continuation framework for computing and training deep equilibrium networks (DEQs). It uses compact input homotopy and a rounded Newton tracker for inference, and augments local-plus-low-rank recurrence with programmable dormant bilinear rank‑one channels for training. The approach guarantees polynomial‑time bit complexity, with certified bounds on inference and training error budgets.
The paper introduces MACCHIATO, a training algorithm that builds a ReLU‑MLP from partial truth‑table data while simultaneously constructing an explicit Boolean circuit over AND, OR, and XOR gates that certifies the network’s computation. The method iteratively projects residuals onto low‑dimensional Boolean classes, compiles the resulting circuit into a ReLU‑MLP, and uses logic minimization and influence‑based variable selection to achieve a six‑layer network with provable truth‑table error bounds. Experiments on synthetic random‑junta tasks show that these certified networks outperform Adam‑trained MLPs in data‑sparse or projection‑aligned regimes and complete faster than flat ESPRESSO in certain settings.
arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.
arXiv:2607. 07665v1 Announce Type: new Abstract: Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules.
arXiv:2607. 08241v1 Announce Type: cross Abstract: Deploying classifier-free guidance (CFG) diffusion models under real-world compute budgets requires quantization, yet existing post-training quantization (PTQ) methods treat CFG models as single-branch networks, ignoring the paired conditional/unconditional structure that CFG inference fundamentally relies on.
Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant...
ExpTest is an autonomous learning‑rate controller that uses the training loss curve as an online signal to perform sequential statistical tests on theoretically motivated windows, detecting convergent behavior and triggering learning‑rate reductions. It combines a covariance‑based initial learning‑rate estimate, curvature‑motivated window sizing, and a two‑phase test‑driven decay, relying on the approximately exponential decay predicted under linearized network dynamics. Experiments on regression, classification, forecasting, and natural‑language tasks across various architectures show that ExpTest achieves competitive performance compared to hand‑tuned SGD baselines and recent learning‑rate‑free methods, without requiring manual initial learning‑rate selection or predefined scheduling.
The paper presents a Quadratic Constrained Binary Optimization (QCBO) framework that provides provable guarantees for training quantized neural networks. It characterizes the topology of zero‑loss level sets, compiles finite‑depth architectures into bounded QCBOs, and introduces a sample‑wise Decomposed Lower‑Bound Optimization (DLBO) to scale Ising‑based optimization. Experiments on a coherent Ising machine show high accuracy on binary Fashion‑MNIST at 1.1‑bit precision and validate the approach on multi‑class datasets.
arXiv:2604. 15613v4 Announce Type: replace-cross Abstract: We present Green-ELM, a non-iterative neural architecture that replaces gradient-based optimization of the output layer with a closed-form analytic solution over a fixed, high-dimensional random feature representation.
arXiv:2606. 06418v1 Announce Type: new Abstract: Many modern applications of deep learning involve training a neural network via a one-step prediction loss (e.