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In speech separation, time-domain approaches have successfully replaced the time-frequency domain with latent sequence feature from a learnable encoder. Conventionally, the feature is separated into speaker-specific ones at the final stage of the network. Instead, we propose a more intuitive strategy that separates features earlier by expanding the feature sequence to the number of speakers as an extra dimension. To achieve this, an asymmetric strategy is presented in which the encoder and decoder are partitioned to perform distinct processing in separation tasks. The encoder analyzes features, and the output of the encoder is split into the number of speakers to be separated. The separated sequences are then reconstructed by the weight-shared decoder, which also performs cross-speaker processing. Without relying on speaker information, the weight-shared network in the decoder directly learns to discriminate features using a separation objective. In addition, to improve performance, traditional methods have extended the sequence length, leading to the adoption of dual-path models, which handle the much longer sequence effectively by segmenting it into chunks. To address this, we in

We provide necessary and sufficient conditions for a correspondence taking values in a finite-dimensional Euclidean space to be open so as to revisit the pioneering work of Schmeidler (1969), Shafer (1974), Shafer-Sonnenschein (1975) and Bergstrom-Rader-Parks (1976) to answer several questions they and their followers left open. We introduce the notion of separate convexity for a correspondence and use it to relate to classical notions of continuity while giving salience to the notion of separateness as in the interplay of separate continuity and separate convexity of binary relations. As such, we provide a consolidation of the convexity-continuity postulates from a broad inter-disciplinary perspective and comment on how the qualified notions proposed here have implications of substantive interest for choice theory.

Self-supervised training methods for transformers have demonstrated remarkable performance across various domains. Previous transformer-based models, such as masked autoencoders (MAE), typically utilize a single normalization layer for both the [CLS] symbol and the tokens. We propose in this paper a simple modification that employs separate normalization layers for the tokens and the [CLS] symbol to better capture their distinct characteristics and enhance downstream task performance. Our method aims to alleviate the potential negative effects of using the same normalization statistics for both token types, which may not be optimally aligned with their individual roles. We empirically show that by utilizing a separate normalization layer, the [CLS] embeddings can better encode the global contextual information and are distributed more uniformly in its anisotropic space. When replacing the conventional normalization layer with the two separate layers, we observe an average 2.7% performance improvement over the image, natural language, and graph domains.

A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras of quivers of a special form known as quipu quivers. Furthermore, we show how this derived equivalence can be used to produce a complete classification of linear Nakayama algebras with almost separate relations. As an application, we include a list of the derived equivalence classes of all Nakayama algebras of length $\leq 8$ with almost separate relations.

Determining the minimum number of states required by a finite automaton to separate a given pair of different words is an important problem. In this paper, we consider this problem for quantum automata (QFAs). We show that 2-state QFAs can separate any pair of words in nondeterministic acceptance mode and conjecture that they can separate any pair also with zero-error. Then, we focus on (a more general problem) separating a pair of two disjoint finite set of words. We show that QFAs can separate them efficiently in nondeterministic acceptance mode, i.e. the number of states is two to the power of the size of the small set. Additionally, we examine affine finite automata (AfAs) and show that two states are enough to separate any pair with zero-error. Moreover, AfAs can separate any pair of disjoint finite sets of words with one-sided bounded error efficiently like QFAs in nondeterministic mode.

We argue for the use of separate exchangeability as a modeling principle in Bayesian nonparametric (BNP) inference. Separate exchangeability is \emph{de facto} widely applied in the Bayesian parametric case, e.g., it naturally arises in simple mixed models. However, while in some areas, such as random graphs, separate and (closely related) joint exchangeable models are widely used, they are curiously underused for several other applications in BNP. We briefly review the definition of separate exchangeability, focusing on the implications of such a definition in Bayesian modeling. We then discuss two tractable classes of models that implement separate exchangeability, which are the natural counterparts of familiar partially exchangeable BNP models. The first is nested random partitions for a data matrix, defining a partition of columns and nested partitions of rows, nested within column clusters. Many recent models for nested partitions implement partially exchangeable models related to variations of the well-known nested Dirichlet process. We argue that inference under such models in some cases ignores important features of the experimental setup. We obtain the separately exchangea

Language-queried audio source separation (LASS) is a new paradigm for computational auditory scene analysis (CASA). LASS aims to separate a target sound from an audio mixture given a natural language query, which provides a natural and scalable interface for digital audio applications. Recent works on LASS, despite attaining promising separation performance on specific sources (e.g., musical instruments, limited classes of audio events), are unable to separate audio concepts in the open domain. In this work, we introduce AudioSep, a foundation model for open-domain audio source separation with natural language queries. We train AudioSep on large-scale multimodal datasets and extensively evaluate its capabilities on numerous tasks including audio event separation, musical instrument separation, and speech enhancement. AudioSep demonstrates strong separation performance and impressive zero-shot generalization ability using audio captions or text labels as queries, substantially outperforming previous audio-queried and language-queried sound separation models. For reproducibility of this work, we will release the source code, evaluation benchmark and pre-trained model at: https://gith

The rawly collected training data often comes with separate noisy labels collected from multiple imperfect annotators (e.g., via crowdsourcing). A typical way of using these separate labels is to first aggregate them into one and apply standard training methods. The literature has also studied extensively on effective aggregation approaches. This paper revisits this choice and aims to provide an answer to the question of whether one should aggregate separate noisy labels into single ones or use them separately as given. We theoretically analyze the performance of both approaches under the empirical risk minimization framework for a number of popular loss functions, including the ones designed specifically for the problem of learning with noisy labels. Our theorems conclude that label separation is preferred over label aggregation when the noise rates are high, or the number of labelers/annotations is insufficient. Extensive empirical results validate our conclusions.

In distributed storage systems (DSSs), the optimal tradeoff between node storage and repair bandwidth is an important issue for designing distributed coding strategies to ensure large scale data reliability. The capacity of DSSs is obtained as a function of node storage and repair bandwidth parameters, characterizing the tradeoff. There are lots of works on DSSs with clusters (racks) where the repair bandwidths from intra-cluster and cross-cluster are differentiated. However, separate nodes are also prevalent in the realistic DSSs, but the works on DSSs with clusters and separate nodes (CSN-DSSs) are insufficient. In this paper, we formulate the capacity of CSN-DSSs with one separate node for the first time where the bandwidth to repair a separate node is of cross-cluster. Consequently, the optimal tradeoff between node storage and repair bandwidth are derived and compared with cluster DSSs. A regenerating code instance is constructed based on the tradeoff. Furthermore, the influence of adding a separate node is analyzed and formulated theoretically. We prove that when each cluster contains R nodes and any k nodes suffice to recover the original file (MDS property), adding an extra

In this paper, we introduce the task of language-queried audio source separation (LASS), which aims to separate a target source from an audio mixture based on a natural language query of the target source (e.g., "a man tells a joke followed by people laughing"). A unique challenge in LASS is associated with the complexity of natural language description and its relation with the audio sources. To address this issue, we proposed LASS-Net, an end-to-end neural network that is learned to jointly process acoustic and linguistic information, and separate the target source that is consistent with the language query from an audio mixture. We evaluate the performance of our proposed system with a dataset created from the AudioCaps dataset. Experimental results show that LASS-Net achieves considerable improvements over baseline methods. Furthermore, we observe that LASS-Net achieves promising generalization results when using diverse human-annotated descriptions as queries, indicating its potential use in real-world scenarios. The separated audio samples and source code are available at https://liuxubo717.github.io/LASS-demopage.

(abridged version) The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in $Λ$CDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity $f_{\rm NL}^{\rm loc}$, and hence does not contribute to a scale-dependent galaxy bias $Δb \propto k^{-2

The problem of speech separation, also known as the cocktail party problem, refers to the task of isolating a single speech signal from a mixture of speech signals. Previous work on source separation derived an upper bound for the source separation task in the domain of human speech. This bound is derived for deterministic models. Recent advancements in generative models challenge this bound. We show how the upper bound can be generalized to the case of random generative models. Applying a diffusion model Vocoder that was pretrained to model single-speaker voices on the output of a deterministic separation model leads to state-of-the-art separation results. It is shown that this requires one to combine the output of the separation model with that of the diffusion model. In our method, a linear combination is performed, in the frequency domain, using weights that are inferred by a learned model. We show state-of-the-art results on 2, 3, 5, 10, and 20 speakers on multiple benchmarks. In particular, for two speakers, our method is able to surpass what was previously considered the upper performance bound.

Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have been derived for the case of continuous-variable systems obeying the Heisenberg-Weyl (position- momentum) commutator. To address the question of experimental verification more generally, we develop a sufficiency criterion for arbitrary states of two arbitrary systems. When applied to the recent study by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 - 403 (2001)] of spin-state entanglement of two separate, macroscopic samples of atoms, our new criterion confirms the presence of spin entanglement.

We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreting the Einstein tensor as an effective stress energy tensor, the condition is that the effective stress energy comoves with freely falling synchronous observers who establish the local expansion, so that the local curvature is conserved. By matching the expansion history of these synchronous observers in cosmological simulations, one can establish and test consistency relations even in the nonlinear regime of modified gravity theories.

In light of the growing number of user privacy violations in centralized social networks, the need to define effective platforms for decentralized online social networks (DOSNs) is deeply felt. Interesting solutions have been proposed in the past, which own the necessary mechanisms to allow users keeping control over their personal information and setting the rules to regulate the access of other users. Unfortunately, the effectiveness of this type of solutions is severely reduced by the fact that different user communities with a shared interest could be disconnected/separated from each other. This translates into a reduced ability in effectively spreading data of common interest towards all interested users, as it currently happens in centralized social networks. In order to overcome the cited limitation, this paper proposes a disruptive approach, which exploits the availability of a new class of Internet of Things (IoT) devices with autonomous social behaviors and cognitive abilities. Such devices can be leveraged as friendship intermediaries between devices' owners who are connected to a DOSN platform and share the same interest. We will demonstrate that clear advantages can be