The theory of full conformal prediction uses deterministic non-conformity measure, but modern usage of full conformal prediction often relies on machine learning training, making stochasticity inevitable. A simple sufficient condition of almost sure permutation invariance of the non-conformity measure can be too restrictive, so many have suggested the relaxation to permutation in distribution as a condition for full conformal prediction validity. We, however, show that this commonly known condition is actually insufficient. We then provide a correct sufficient condition: Conditional Independence & Permutation Invariance in Distribution, which encompasses several stochastic settings that may be used in machine learning.

Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order.

In many machine learning problems the output should not depend on the order of the inputs. Such ``permutation invariant'' functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recursive architectures. Existing solutions (e.g., DeepSets) mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to learning functions which are semi permutation invariant, e.g.

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recurrent architectures. We implement this idea via a novel form of stochastic regularization. Existing solutions mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design [Zaheer et al., 2017, Lee et al., 2019, Murphy et al., 2018]. Our approach of enforcing permutation invariance via regularization gives rise to models which are semi permutation invariant (e.g.

Diffusion models are powerful generative models in continuous data domains such as image and video data. Discrete graph diffusion models (DGDMs) have recently extended them for graph generation, which are crucial in fields like molecule and protein modeling, and obtained the SOTA performance. However, it is risky to deploy DGDMs for safety-critical applications (e.g., drug discovery) without understanding their security vulnerabilities. In this work, we perform the first study on graph diffusion models against backdoor attacks, a severe attack that manipulates both the training and inference/generation phases in graph diffusion models. We first define the threat model, under which we design the attack such that the backdoored graph diffusion model can generate 1) high-quality graphs without backdoor activation, 2) effective, stealthy, and persistent backdoored graphs with backdoor activation, and 3) graphs that are permutation invariant and exchangeable--two core properties in graph generative models. 1) and 2) are validated via empirical evaluations without and with backdoor defenses, while 3) is validated via theoretical results.

Do autoregressive Transformer language models require explicit positional encodings (PEs)? The answer is "no" as long as they have more than one layer -- they can distinguish sequences with permuted tokens without requiring explicit PEs. This property has been known since early efforts (those contemporary with GPT-2) adopting the Transformer for language modeling. However, this result does not appear to have been well disseminated and was even rediscovered recently. This may be partially due to a sudden growth of the language modeling community after the advent of GPT-2, but perhaps also due to the lack of a clear explanation in prior publications, despite being commonly understood by practitioners in the past. Here we review this long-forgotten explanation why explicit PEs are nonessential for multi-layer autoregressive Transformers (in contrast, one-layer models require PEs to discern order information of their input tokens). We also review the origin of this result, and hope to re-establish it as a common knowledge.