Related papers: Low Correlation Sequences from Linear Combinations…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
We investigate linear combinations of characters for minimal Virasoro models which are representable as a products of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the…
A large body of research into semantic textual similarity has focused on constructing state-of-the-art embeddings using sophisticated modelling, careful choice of learning signals and many clever tricks. By contrast, little attention has…
We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representations. There are connections with the Pastur-Marcenko…
We explain a discontinuous drop in the exponential growth rate for certain multivariate generating functions at a critical parameter value, in even dimensions d at least 4. This result depends on computations in the homology of the…
Identifying computational mechanisms for memorization and retrieval of data is a long-standing problem at the intersection of machine learning and neuroscience. Our main finding is that standard overparameterized deep neural networks…
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is…
Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence…
We introduce Flashback, a reversible string decomposition that repeatedly peels the maximal leading and trailing character runs from a sentinel-wrapped input, recording each pair as one bilateral token. Decomposition and reconstruction both…
Modern language models (LMs) are trained in an autoregressive manner, conditioned only on the prefix. In contrast, sequence labeling (SL) tasks assign labels to each individual input token, naturally benefiting from bidirectional context.…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with…
We combine character-level and contextual language model representations to improve performance on Discourse Representation Structure parsing. Character representations can easily be added in a sequence-to-sequence model in either one…
Unimodular sequences with good auto/cross-correlation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences. The main content is as follows: first, we…
Accurate modeling of the correlation between the sources plays a crucial role in the efficiency of distributed source coding (DSC) systems. This correlation is commonly modeled in the binary domain by using a single binary symmetric channel…
Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled…
{\bf Abstract.} Considered is the distribution of the cross correlation between $m$-sequences of length $2^m-1$, where $m$ is even, and $m$-sequences of shorter length $2^{m/2}-1$. The infinite family of pairs of $m$-sequences with…
We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to…