TaylorAECNet: A Taylor Style Neural Network for Full-Band Echo Cancellation

This paper describes aecX team's entry to the ICASSP 2023 acoustic echo cancellation (AEC) challenge. Our system consists of an adaptive filter and a proposed full-band Taylor-style acoustic echo cancellation neural network (TaylorAECNet) as a post-filter. Specifically, we leverage the recent advances in Taylor expansion based decoupling-style interpretable speech enhancement and explore its feasibility in the AEC task. Our TaylorAECNet based approach achieves an overall mean opinion score (MOS) of 4.241, a word accuracy (WAcc) ratio of 0.767, and ranks 5th in the non-personalized track (track 1)

Improved Bounds for Randomly Colouring Simple Hypergraphs

We study the problem of sampling almost uniform proper q-colourings in k-uniform simple hypergraphs with maximum degree ?. For any ? > 0, if k ? 20(1+?)/? and q ? 100?^({2+?}/{k-4/?-4}), the running time of our algorithm is O?(poly(? k)? n^1.01), where n is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Vuong, 2021; He, Sun, and Wu, 2021), and does not require ?(log n) colours unlike the work of Frieze and Anastos (2017)

Perfect sampling from spatial mixing

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like [Formula: see text] , our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer‐dimer models in such graphs

Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields

We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$.Comment: Major revision and new result

Rapid mixing from spectral independence beyond the Boolean domain

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ALO20]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations, and implies that the corresponding Glauber dynamics is rapidly mixing. As a concrete application, we show that Glauber dynamics for sampling proper $q$-colourings mixes in polynomial-time for the family of triangle-free graphs with maximum degree $\Delta$ provided $q\ge (\alpha^*+\delta)\Delta$ where $\alpha^*\approx 1.763$ is the unique solution to $\alpha^*=\exp(1/\alpha^*)$ and $\delta>0$ is any constant. This is the first efficient algorithm for sampling proper $q$-colourings in this regime with possibly unbounded $\Delta$. Our main tool of establishing spectral independence is the recursive coupling by Goldberg, Martin, and Paterson [GMP05]

A simple polynomial-time approximation algorithm for the total variation distance between two product distributions

We give a simple polynomial-time approximation algorithm for the totalvariation distance between two product distributions