Speech foundation models have recently achieved remarkable capabilities across a wide range of tasks. However, their evaluation remains disjointed across tasks and model types. Different models excel at distinct aspects of speech processing and thus require different evaluation protocols. This paper proposes a unified taxonomy that addresses the question: Which evaluation is appropriate for which model? The taxonomy defines three orthogonal axes: the evaluation aspect being measured, the model capabilities required to attempt the task, and the task or protocol requirements needed to perform it. We classify a broad set of existing evaluations and benchmarks along these axes, spanning areas such as representation learning, speech generation, and interactive dialogue. By mapping each evaluation to the capabilities a model exposes (e.g., speech generation, real-time processing) and to its methodological demands (e.g., fine-tuning data, human judgment), the taxonomy provides a principled framework for aligning models with suitable evaluation methods. It also reveals systematic gaps, such as limited coverage of prosody, interaction, or reasoning, that highlight priorities for future benc
We introduce a measure Q of the "quality" of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The "quality" Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a-priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the Symmetric Quanton-Detecton System (SQDS). The SQDS can be regarded as two qubits trying to acquire which way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.
Tree-based learning methods such as Random Forest and XGBoost are still the gold-standard prediction methods for tabular data. Feature importance measures are usually considered for feature selection as well as to assess the effect of features on the outcome variables in the model. This also applies to survey data, which are frequently encountered in the social sciences and official statistics. These types of datasets often present the challenge of missing values. The typical solution is to impute the missing data before applying the learning method. However, given the large number of possible imputation methods available, the question arises as to which should be chosen to achieve the 'best' reflection of feature importance and feature selection in subsequent analyses. In the present paper, we investigate this question in a survey-based simulation study for eight state-of-the art imputation methods and three learners. The imputation methods comprise listwise deletion, three MICE options, four \texttt{missRanger} options as well as the recently proposed mixGBoost imputation approach. As learners, we consider the two most common tree-based methods, Random Forest and XGBoost, and an
In reinforcement learning (RL) with experience replay, experiences stored in a replay buffer influence the RL agent's performance. Information about how these experiences influence the agent's performance is valuable for various purposes, such as identifying experiences that negatively influence underperforming agents. One method for estimating the influence of experiences is the leave-one-out (LOO) method. However, this method is usually computationally prohibitive. In this paper, we present Policy Iteration with Turn-over Dropout (PIToD), which efficiently estimates the influence of experiences. We evaluate how correctly PIToD estimates the influence of experiences and its efficiency compared to LOO. We then apply PIToD to amend underperforming RL agents, i.e., we use PIToD to estimate negatively influential experiences for the RL agents and to delete the influence of these experiences. We show that RL agents' performance is significantly improved via amendments with PIToD.
We characterize the actions of compact tori on smooth manifolds for which the orbit space is a topological manifold (either closed or with boundary). For closed manifolds the result was originally proved by Styrt in 2009. We give a new proof for closed manifolds which is also applicable to manifolds with boundary. In our arguments we use the result of Provan and Billera who characterized matroid complexes which are pseudomanifolds. We study the combinatorial structure of torus actions whose orbit spaces are manifolds. In two appendix sections we give an overview of two theories related to our work. The first one is the combinatorial theory of Leontief substitution systems from mathematical economics. The second one is the topological Kaluza--Klein model of Dirac's monopole studied by Atiyah. The aim of these sections is to draw some bridges between disciplines and motivate further studies in toric topology.
The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.
Compact objects observed in gravitational-wave astronomy so far always come in pairs and never individually. Identifying the two components of a binary system is a delicate operation that is often taken for granted. The labeling procedure (i.e., which is object "1" and which is object "2") effectively acts as systematics, or, equivalently an unspecified prior, in gravitational-wave data inference. The common approach is to label the objects solely by their masses, on a sample-by-sample basis. We show that object identification can instead be tackled using the posterior distribution as a whole. We frame the problem in terms of constrained clustering -- a flavor of semi-supervised machine learning -- and find that unfolding the labeling systematics can significantly impact, and arguably improve, our interpretation of the data. In particular, the precision of black-hole spin measurements improves by up to 50%, multimodalities and tails tend to disappear, posteriors become closer to Gaussian distributions, and the identification of the nature of the object (i.e. black hole vs. neutron star) is facilitated. We estimate that about 10% of the LIGO/Virgo posterior samples are affected by t
Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular elements in certain subsemigroups of P(G) (Theorem 4.1 [11]) for compact G remains true for locally compact G. In addition, a complete description of algebraically regular elements in P(G) has been established when G is countable or uncountable where every proper subgroup is countable. In this case the standing assumption that every element is of finite order is not required. For compact Lie groups, Fourier transform techniques are also used to get more information on P(G). Several concrete examples are provided to illustrate the observations.
We give a characterization of the Anosov condition for reducible representations in terms of the eigenvalue magnitudes of the irreducible block factors of its block diagonalization. As in previous work, these Anosov representations comprise a collection of bounded convex domains in a finite-dimensional vector space, and this perspective allows us to conclude for many non-elementary hyperbolic groups that connected components of the character variety which consist entirely of Anosov representations do not contain reducible representations.
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix representation of Hermitian linear map, we show that every positive map which is not completely positive is a {\em difference} of two completely positive maps. A necessary and sufficient condition for a positive map which is not completely positive is also presented, which is illustrated by some examples.
An important result of Bilu deals with the equidistribution of the Galois orbits of a sequence $(α_n)_n$ in $\overline{\mathbb{Q}}^*$. Here, we prove a quantitative equidistribution theorem for a sequence of finite subsets in $\overline{\mathbb{Q}}^*$ which are not necessarily stable by Galois action. We follow a method of Mignotte.
In this note, we show that there exist non-unital right artinian rings which are not generalized Rickart. In particular, we provide examples to show that, [16, Corollary 2.31] is not true for non-unital artinian rings.
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining non-proper smooth real algebraic functions on smooth real algebraic manifolds satisfying explicit conditions on (non-)compactness of preimages whereas previously the manifolds are only semi-algebraic. Explicitly, this mainly contributes to two different regions of mathematics. One is singularity theory of differentiable maps and applications to differential topology. More precisely, construction of nice smooth maps with desired preimages. The other is real algebraic geometry. More precisely, explicit construction of smooth real algebraic functions and maps whereas we can know the existence and consider approximations of smooth maps by maps of such classes in considerable cases.
We prove that any cyclic Nakayama algebra which is a higher Auslander algebra can be uniquely constructed from Nakayama algebras of smaller ranks by reversing the syzygy filtration process. This creates chains of higher Auslander algebras upto $\boldsymbol\varepsilon$-equivalences. Therefore, the classification of all cyclic Nakayama algebras which are higher Auslander algebras reduces to the classification of linear ones. We give two applications of this: for any integer $k$ where $2\leq k\leq 2n-2$, there is a Nakayama algebra of rank $n$ which is a higher Auslander algebra of global dimension $k$ and the possible values of the global dimensions of cyclic Nakayama algebras which are higher Auslander algebras form the sets $\left\{2,\ldots,2n-2\right\}\setminus\left\{n-1\right\}$ if $n$ is even and $\left\{2,\ldots,2n-2\right\}\setminus\left\{ 2,n-1\right\}$ if $n$ is odd.
We introduce a new observable for reading out a which-way detector in a Young-type interferometer whose eigenstates either contain full which-way information or none at all. We calculate the which-way knowledge K that can be retrieved from this observable and find that K depends on the phase difference δthat the interfering object accumulates on its way from either slit to the detector. In particular, it turns out that K(δ) has an upper bound of 1, almost independent of the visibility V of the interference pattern generated by the interfering object on a screen, which is in marked contrast to the well-known inequality K^2 + V^2 <= 1 (cf. B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996)).
We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss examples which are "ft-independent" and examples which are not. We introduce (n,q)-finite invariants, which are generalizations of finite-type invariants based on Fox's (n,q) congruence classes of knots.
We deal with the finite family $\mathcal{F}$ of continuous maps on the Hausdorff space. A nonempty compact subset $A$ of such space is called a strict attractor if it has an open neighborhood $U$ such that $A=\lim_{n\to\infty}\mathcal{F}^n(S)$ for every nonempty compact $S\subset U$. Every strict attractor is a pointwise attractor, which means that the set $\{x\in X ; \lim_{n\to\infty}\mathcal{F}^n(x)=A\}$ contains $A$ in its interior. We present a class of examples of pointwise attractors - from the finite set to the Sierpiński carpet - which are not strict when we add to the system one nonexpansive map.
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the following question: which reaction networks have the capacity for multiple steady states? Mathematically, this asks: among certain parametrized families of polynomial systems, which admit multiple positive roots? No complete answer is known. This work analyzes the smallest networks, those with only a few chemical species or reactions. For these "smallest" networks, we completely answer the question of multistationarity and, in some cases, multistability too, thereby extending related work of Boros. Our results highlight the role played by the Newton polytope of a network (the convex hull of the reactant vectors). Also, our work is motivated by recent results that explain how a given network's capacity for multistationarity arises from that of certain related networks which are typically smaller. Hence, we are interested in classifying small multistationary networks, and our work forms a first step in this direction.
We introduce classes of rings which are close to being Gorenstein. These rings arise naturally as specializations of rings of countable CM type. We study these rings in detail, and along the way generalize an old result of Teter which characterized Artinian rings which are Gorenstein rings modulo their socle.
Which is the best metric for the space of collider events? Motivated by the success of the Energy Mover's Distance in characterizing collider events, we explore the larger space of unbalanced optimal transport distances, of which the Energy Mover's Distance is a particular case. Geometric and computational considerations favor an unbalanced optimal transport distance known as the Hellinger-Kantorovich distance, which possesses a Riemannian structure that lends itself to efficient linearization. We develop the particle linearized unbalanced Optimal Transport (pluOT) framework for collider events based on the linearized Hellinger-Kantorovich distance and demonstrate its efficacy in boosted jet tagging. This provides a flexible and computationally efficient optimal transport framework ideally suited for collider physics applications.