Permutation Invariance
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Related Articles from SNS
Quantum Time Lower Bounds by Permutation Invariance
arXiv:2606.05099v1 Announce Type: cross Abstract: Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample...
Learning Permutation-invariant Macroscopic Dynamics
Announce Type: new Abstract: Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed ordering of microscopic degrees of freedom in the input.
Learning Permutation-invariant Macroscopic Dynamics
Announce Type: cross Abstract: Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed ordering of microscopic degrees of freedom in the input.
Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
arXiv:2606.01532v2 Announce Type: replace Abstract: Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.e., they are Turing complete. We revisit this belief in the regime most...
Separation Power of Equivariant Neural Networks
arXiv:2406.08966v3 Announce Type: replace Abstract: The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks.
Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Announce Type: new Abstract: Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.e., they are Turing complete. We revisit this belief in the regime most relevant to long-form...
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
arXiv:2606.06809v1 Announce Type: new Abstract: We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation mismatch: the forecast is a labeled particle system, while the observations specify only a smoothed, permutation-invariant density. To address this mismatch, we define the forecast-observation discrepancy as a quadratic functional on probability measures after applying...
A Lightweight Slot-Attention Framework for Multi-Instrument Multi-Pitch Estimation
Announce Type: new Abstract: Multi-pitch estimation (MPE) typically predicts which pitches are active in a mixture, but not which instrument or source produced them. This paper investigates a lightweight slot-attention framework for multi-instrument MPE (MI-MPE), where a mixture CQT is mapped to an unordered set of source-like pitch maps. The model uses permutation-invariant Hungarian matching to avoid fixed output semantics and treats the number of slots as an upper bound on the number of...
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
arXiv:2606.06809v1 Announce Type: cross Abstract: We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation mismatch: the forecast is a labeled particle system, while the observations specify only a smoothed, permutation-invariant density. To address this mismatch, we define the forecast-observation discrepancy as a quadratic functional on probability measures after...
Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models
arXiv:2606.04307v1 Announce Type: new Abstract: Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the...