In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling. Our main result is a field-code compiler: any communicated transport field approximating an optimal empirical Monge map to error $η$ can be completed by sparse target-cell residuals into an exact-marginal value-certified sampler with scalar certificate $W_1(μ,ν)\leq U\leq W_1(μ,ν)+2Δ$, where $Δ$ is the public target-partition diameter.
arXiv:2607. 27078v1 Announce Type: cross Abstract: In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling.
arXiv:2607. 14375v1 Announce Type: cross Abstract: We study exact verification of ReLU networks in an adversarial smoothed model.
arXiv:2606. 30705v1 Announce Type: cross Abstract: Deterministic few-step generation succeeds on continuous image latents but collapses to incoherent text on continuous text latents, and we show the cause is geometric rather than a training or scaling deficiency: a smooth, regularity-limited deterministic map cannot resolve a discrete branch choice before a sharp categorical readout, so few-step failure is governed by decoder sharpness, not transport accuracy.
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.
arXiv:2608. 25138v1 Announce Type: new Abstract: Stochastic masking, cropping, or modality removal makes deterministic reconstruction an incomplete target: one observation can admit many clean completions.
Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-...
arXiv:2609.37887v1 Announce Type: new Abstract: Activation and key-value cache precision change what a quantized language model computes without altering its stored weights. Direct weight-code bounds...
arXiv:2608. 01547v1 Announce Type: cross Abstract: Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations.
arXiv:2608. 12026v1 Announce Type: new Abstract: Post-training quantization pipelines routinely leave the softmax output layer in high precision.
arXiv:2608. 15810v1 Announce Type: new Abstract: Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-level risk by a union bound over a pre-declared event count.
arXiv:2606. 18463v1 Announce Type: cross Abstract: Distributed stochastic gradient descent (SGD) is limited by communication rather than computation, since each iteration requires an AllReduce across processes.