Noise adaptive training for subspace Gaussian mixture models

Noise adaptive training (NAT) is an effective approach to normalise the environmental distortions in the training data. This paper investigates the model-based NAT scheme using joint uncertainty decoding (JUD) for subspace Gaussian mixture models (SGMMs). A typical SGMM acoustic model has much larger number of surface Gaussian components, which makes it computationally infeasible to compensate each Gaussian explicitly. JUD tackles the problem by sharing the compensation parameters among the Gaussians and hence reduces the computational and memory demands. For noise adaptive training, JUD is reformulated into a generative model, which leads to an efficient expectation-maximisation (EM) based algorithm to update the SGMM acoustic model parameters. We evaluated the SGMMs with NAT on the Aurora 4 database, and obtained higher recognition accuracy compared to systems without adaptive training. Index Terms: adaptive training, noise robustness, joint uncertainty decoding, subspace Gaussian mixture model

Joint Uncertainty Decoding with Unscented Transform for Noise Robust Subspace Gaussian Mixture Models

Common noise compensation techniques use vector Taylor series (VTS) to approximate the mismatch function. Recent work shows that the approximation accuracy may be improved by sampling. One such sampling technique is the unscented transform (UT), which draws samples deterministically from clean speech and noise model to derive the noise corrupted speech parameters. This paper applies UT to noise compensation of the subspace Gaussian mixture model (SGMM). Since UT requires relatively smaller number of samples for accurate estimation, it has significantly lower computational cost compared to other random sampling techniques. However, the number of surface Gaussians in an SGMM is typically very large, making the direct application of UT, for compensating individual Gaussian components, computationally impractical. In this paper, we avoid the computational burden by employing UT in the framework of joint uncertainty decoding (JUD), which groups all the Gaussian components into small number of classes, sharing the compensation parameters by class. We evaluate the JUD-UT technique for an SGMM system using the Aurora 4 corpus. Experimental results indicate that UT can lead to increased accuracy compared to VTS approximation if the JUD phase factor is untuned, and to similar accuracy if the phase factor is tuned empirically. 1

Combinatorial Lower Bounds for 3-Query LDCs

A code is called a $q$-query locally decodable code (LDC) if there is a randomized decoding algorithm that, given an index $i$ and a received word $w$ close to an encoding of a message $x$, outputs $x_i$ by querying only at most $q$ coordinates of $w$. Understanding the tradeoffs between the dimension, length and query complexity of LDCs is a fascinating and unresolved research challenge. In particular, for $3$-query binary LDCs of dimension $k$ and length $n$, the best known bounds are: $2^{k^{o(1)}} \geq n \geq \tilde{\Omega}(k^2)$. In this work, we take a second look at binary $3$-query LDCs. We investigate a class of 3-uniform hypergraphs that are equivalent to strong binary 3-query LDCs. We prove an upper bound on the number of edges in these hypergraphs, reproducing the known lower bound of $\tilde{\Omega}(k^2)$ for the length of strong $3$-query LDCs. In contrast to previous work, our techniques are purely combinatorial and do not rely on a direct reduction to $2$-query LDCs, opening up a potentially different approach to analyzing 3-query LDCs.Comment: 10 page

On the hardness of learning sparse parities

This work investigates the hardness of computing sparse solutions to systems of linear equations over F_2. Consider the k-EvenSet problem: given a homogeneous system of linear equations over F_2 on n variables, decide if there exists a nonzero solution of Hamming weight at most k (i.e. a k-sparse solution). While there is a simple O(n^{k/2})-time algorithm for it, establishing fixed parameter intractability for k-EvenSet has been a notorious open problem. Towards this goal, we show that unless k-Clique can be solved in n^{o(k)} time, k-EvenSet has no poly(n)2^{o(sqrt{k})} time algorithm and no polynomial time algorithm when k = (log n)^{2+eta} for any eta > 0. Our work also shows that the non-homogeneous generalization of the problem -- which we call k-VectorSum -- is W[1]-hard on instances where the number of equations is O(k log n), improving on previous reductions which produced Omega(n) equations. We also show that for any constant eps > 0, given a system of O(exp(O(k))log n) linear equations, it is W[1]-hard to decide if there is a k-sparse linear form satisfying all the equations or if every function on at most k-variables (k-junta) satisfies at most (1/2 + eps)-fraction of the equations. In the setting of computational learning, this shows hardness of approximate non-proper learning of k-parities. In a similar vein, we use the hardness of k-EvenSet to show that that for any constant d, unless k-Clique can be solved in n^{o(k)} time there is no poly(m, n)2^{o(sqrt{k}) time algorithm to decide whether a given set of m points in F_2^n satisfies: (i) there exists a non-trivial k-sparse homogeneous linear form evaluating to 0 on all the points, or (ii) any non-trivial degree d polynomial P supported on at most k variables evaluates to zero on approx. Pr_{F_2^n}[P(z) = 0] fraction of the points i.e., P is fooled by the set of points

Signatures of non-thermal dark matter with kination and early matter domination. Gravitational waves versus laboratory searches

The non-thermal production of dark matter (DM) usually requires very tiny couplings of the dark sector with the visible sector and therefore is notoriously challenging to hunt in laboratory experiments. Here we propose a novel pathway to test such a production in the context of a non-standard cosmological history, using both gravitational wave (GW) and laboratory searches. We investigate the formation of DM from the decay of a scalar field that we dub as the reheaton, as it also reheats the Universe when it decays. We consider the possibility that the Universe undergoes a phase with kination-like stiff equation-of-state (wkin > 1/3) before the reheaton dominates the energy density of the Universe and eventually decays into Standard Model and DM particles. We then study how first-order tensor perturbations generated during inflation, the amplitude of which may get amplified during the kination era and lead to detectable GW signals. Demanding that the reheaton produces the observed DM relic density, we show that the reheaton’s lifetime and branching fractions are dictated by the cosmological scenario. In particular, we show that it is long-lived and can be searched by various experiments such as DUNE, FASER, FASER-II, MATHUSLA, SHiP, etc. We also identify the parameter space which leads to complementary observables for GW detectors such as LISA and u-DECIGO. In particular we find that a kination-like period with an equation-of-state parameter wkin ≈ 0.5 and a reheaton mass O(0.5–5) GeV and a DM mass of O(10–100) keV may lead to sizeable imprints in both kinds of searches

Probing High Scale Dirac Leptogenesis via Gravitational Waves from Domain Walls

We propose a novel way of probing high scale Dirac leptogenesis, a viable alternative to canonical leptogenesis scenario where the total lepton number is conserved, keeping light standard model (SM) neutrinos purely Dirac. The simplest possible seesaw mechanism for generating light Dirac neutrinos involve heavy singlet Dirac fermions and a singlet scalar. In addition to unbroken global lepton number, a discrete $Z_2$ symmetry is imposed to forbid direct coupling between right and left chiral parts of light Dirac neutrino. Generating light Dirac neutrino mass requires the singlet scalar to acquire a vacuum expectation value (VEV) that also breaks the $Z_2$ symmetry, leading to formation of domain walls in the early universe. These walls, if made unstable by introducing a soft $Z_2$ breaking term, generate gravitational waves (GW) with a spectrum characterized by the wall tension or the singlet VEV, and the soft symmetry breaking scale. The scale of leptogenesis depends upon the $Z_2$-breaking singlet VEV which is also responsible for the tension of the domain wall, affecting the amplitude of GW produced from the collapsing walls. We find that most of the near future GW observatories will be able to probe Dirac leptogenesis scale all the way upto $10^{11}$ GeV.Comment: 7 pages, 4 captioned figures, matches version accepted for publication in Phys. Rev.

Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH

The k-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over F_2, which can be stated as follows: given a generator matrix A and an integer k, determine whether the code generated by A has distance at most k. Here, k is the parameter of the problem. The question of whether k-Even Set is fixed parameter tractable (FPT) has been repeatedly raised in literature and has earned its place in Downey and Fellows\u27 book (2013) as one of the "most infamous" open problems in the field of Parameterized Complexity. In this work, we show that k-Even Set does not admit FPT algorithms under the (randomized) Gap Exponential Time Hypothesis (Gap-ETH) [Dinur\u2716, Manurangsi-Raghavendra\u2716]. In fact, our result rules out not only exact FPT algorithms, but also any constant factor FPT approximation algorithms for the problem. Furthermore, our result holds even under the following weaker assumption, which is also known as the Parameterized Inapproximability Hypothesis (PIH) [Lokshtanov et al.\u2717]: no (randomized) FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only 0.99-satisfiable (where the parameter is the number of variables). We also consider the parameterized k-Shortest Vector Problem (SVP), in which we are given a lattice whose basis vectors are integral and an integer k, and the goal is to determine whether the norm of the shortest vector (in the l_p norm for some fixed p) is at most k. Similar to k-Even Set, this problem is also a long-standing open problem in the field of Parameterized Complexity. We show that, for any p > 1, k-SVP is hard to approximate (in FPT time) to some constant factor, assuming PIH. Furthermore, for the case of p = 2, the inapproximability factor can be amplified to any constant