15 problems

Necessity of the global interaction condition for non-injective decoders
arXiv@arxiv
Conjecture on the necessity of global (PI). The gap between chamber-wise and global (PI) is structurally necessary in the non-injective setting; investigating this gap should lead…
Conjecturerefutedgenerative-models identifiability piecewise-affine-maps
1
The Bernoulli latent-space conjecture for topology optimization
arXiv@arxiv
In topology optimization, each discrete element is assigned a material-presence decision, so the latent representation may be modeled using either a Bernoulli distribution, taking…
Conjectureopengenerative-models latent-variable-models topology-optimization
0
Implicit averaging conjecture for batched LGS-DDPM samples
arXiv@arxiv
Let LGS-DDPM denote the Lanczos-based Gaussian denoising diffusion probabilistic model, and consider the batching procedure with stale covariance estimates described in the experim…
Conjectureopendiffusion-models generative-models lanczos-methods
0
Extension of posterior error analysis to conditional generative models
arXiv@arxiv
Extension conjecture. The paper conjectures that its type of analysis can be extended to such conditional generative models.
Conjectureopengenerative-models inverse-problems optimal-transport
0
Velocity-parameterisation conjecture for diffusion models
arXiv@arxiv
In a diffusion model, let a velocity-based parameterisation use a network that predicts the velocity variable $\mathbf{v}$ instead of the usual noise or score quantity. Velocity-pa…
Conjectureopendiffusion-models generative-models information-theoretic-learning
1
The hidden-structure conjecture for generative models
arXiv@arxiv
Generative models are considered in the setting where high-dimensional data concentrates on a lower-dimensional manifold, as described by the manifold hypothesis. Diffusion models…
Conjectureopendiffusion-models generative-models manifold-hypothesis
0
The conjecture that LSUN Kitchen has more complex underlying topology than CelebA
arXiv@arxiv
Topological complexity conjecture. Since LSUN Kitchen is a much larger dataset containing diverse images, its underlying lower-dimensional submanifold has more complex topological…
Conjectureopengenerative-models machine-learning topological-data-analysis
1
The ChannelGAN augmentation bias conjecture
arXiv@arxiv
ChannelGAN-based augmentation randomly generates wireless channels rather than interpolating between positions. ChannelGAN augmentation bias conjecture. ChannelGAN-based augmentati…
Conjectureopendata-augmentation generative-models wireless-channels
0
The conjecture that surpassing the $k^2$ bottleneck requires tools beyond $alpha$ -coherence
arXiv@arxiv
Bottleneck conjecture. Moving beyond the $k^2$ bottleneck is likely to require tools beyond the notion of $alpha$ -coherence.
Conjectureopencoherence compressed-sensing generative-models
0
Wyner-type secure-learning conjecture for strictly nonlinear generative models
arXiv@arxiv
Consider a generative model that produces observations transmitted through channels to a legitimate terminal and a malicious terminal. Let the system load be the rate of labels per…
Conjectureopengenerative-models information-theory secure-learning
0
All-or-nothing conjecture for higher-order Gaussian fields
arXiv@arxiv
Consider a higher-order Gaussian generative field of order $bb$ , with load $R$ , channel capacity $\mathcal{C}(\sigma)$ , overlap $m^\star$ , and information rate…
Conjectureopenbayesian-inference generative-models phase-transitions
0
Zero-overlap conjecture for nonlinear generative models
arXiv@arxiv
Consider a nonlinear generative model with order $bb>1$ , and let $m$ denote the overlap between the inferred and true labels. Let $m^\star$ be the overlap at the optimum of the inf…
Conjectureopenbayesian-inference generative-models phase-transitions
0
Conjecture that the network cannot perfectly learn high-dimensional image distributions
arXiv@arxiv
The data distribution is high-dimensional, as in image-generation tasks, and the network used for the experiment may not be sufficiently flexible to represent it perfectly. Network…
Conjectureopengenerative-models neural-networks optimization
0
Conjecture that image-space structure is induced by latent-space structure in StyleGAN
arXiv@arxiv
Let $g:[0,1]^{512}\rightarrow[0,1]^{1024\times1024\times3}$ be the pretrained StyleGAN generator, mapping latent vectors to images. Consider structures between points in the image…
Conjectureopendeep-learning generative-models latent-spaces
0
Distribution-characterization conjecture for black-box sampling
arXiv@arxiv
Consider the distribution learned by the paper's iterative boosting procedure for density estimation, whose full characterization is derived in the paper. Distribution-characteriza…
Conjectureopendensity-estimation generative-models
0