相关论文: Dp-rank and forbidden configurations
We develop the theory of the intertwining distributional versions of the LS-category and the sequential topological complexities of a space $X$, denoted by $\mathsf{icat}(X)$ and $\mathsf{iTC}_m(X)$, respectively. We prove that they satisfy…
We propose the notion of process resource-breaking channels that break the resource for a quantum information processing task. We examine the same using quantum dense coding and teleportation protocols. We prove that the sets DBT (dense…
Consider a scenario in which we have a huge labeled dataset ${\cal D}$ and a limited time to train some given learner using ${\cal D}$. Since we may not be able to use the whole dataset, how should we proceed? Questions of this nature…
We study inference on the optimal welfare in a policy learning problem and propose reporting a lower confidence band (LCB). A natural approach to constructing an LCB is to invert a one-sided t-test based on an efficient estimator for the…
The tetrad constraint is a condition of which the satisfaction signals a rank reduction of a covariance submatrix and is used to design causal discovery algorithms that detects the existence of latent (unmeasured) variables, such as FOFC.…
In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong…
If $T$ has dependent dividing, then the burden agrees with the dp-rank witnessed by NIP formulas. We use this observation to prove that if $T$ has dependent dividing, then the burden is sub-additive. We also state a connection between the…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we…
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…
It is evident that deep text classification models trained on human data could be biased. In particular, they produce biased outcomes for texts that explicitly include identity terms of certain demographic groups. We refer to this type of…
The Cognitive Theory of True Conditions (CTTC) is a proposal to design the implementation of cognitive abilities and to describe the model-theoretic semantics of symbolic cognitive architectures. The CTTC is formulated mathematically using…
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present…
The capacity to integrate information is a prominent feature of biological and cognitive systems. Integrated Information Theory (IIT) provides a mathematical approach to quantify the level of integration in a system, yet its computational…
We propose an effect called information constraint which is characterized by the existence of different decay rates of signal strengths propagating along opposite directions. It is an intrinsic property of a type of open quantum system,…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
Differentially private (DP) transfer learning, i.e., fine-tuning a pretrained model on private data, is the current state-of-the-art approach for training large models under privacy constraints. We focus on two key hyperparameters in this…
The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some…
Gradient-based deep-learning algorithms exhibit remarkable performance in practice, but it is not well-understood why they are able to generalize despite having more parameters than training examples. It is believed that implicit bias is a…
In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. Namely, the quality of sample compression schemes and of teaching sets for classes of low VC-dimension.…