Related papers: Finite-State Mutual Dimension
Vision Mambas (ViMs) achieve remarkable success with sub-quadratic complexity, but their efficiency remains constrained by quadratic token scaling with image resolution. While existing methods address token redundancy, they overlook ViMs'…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
The Ziegler-Rauk-Baerends multiplet sum method (MSM) assumes that density-functional theory (DFT) provides a good description of states dominated by a single determinant. It then uses symmetry to add static correlation to DFT. In our…
Differential Unitary Space-Time Modulation (DUSTM) and its earlier nondifferential counterpart, USTM, permit high-throughput MIMO communication entirely without the possession of channel state information (CSI) by either the transmitter or…
In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a…
Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…
Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…
A new technique permits high fidelity measurement of the tunneling density of states (TDOS) of the two-dimensional electron gas. The obtained TDOS contains no distortions arising from low 2D in-plane conductivity and includes the…
Let $R$ be a finite dimensional $k$-algebra over an algebraically closed field $k$ and $\mathrm{mod} R$ be the category of all finitely generated left $R$-modules. For a given full subcategory $\mathcal{X}$ of $\mathrm{mod} R,$ we denote by…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of…
We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs). Specifically, we show that the reduced density…
This paper develops the theory of pushdown dimension and explores its relationship with finite-state dimension. Pushdown dimension is trivially bounded above by finite-state dimension for all sequences, since a pushdown gambler can simulate…
For a partially ordered set $(S, \mathord\preceq)$, the order (monotone) dimension is the minimum cardinality of total orders (respectively, real-valued order monotone functions) on $S$ that characterize the order $\preceq$. In this paper…
We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate…
It is well-known that $\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential…
Deep state-space models (SSMs) have gained increasing popularity in sequence modelling. While there are numerous theoretical investigations of shallow SSMs, how the depth of the SSM affects its expressiveness remains a crucial problem. In…
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions: a family of dimensions depending on a parameter $\theta…
For frequency $\alpha$ of bounded type and coupling $\lambda>20$, we show that the density of states measure $\NN_{\alpha,\lambda}$ of the related Sturm Hamiltonian is exact upper and lower dimensional, however, in general it is not…
The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we…