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Almost covering all the layers of hypercube with multiplicities

Announce Type: replace-cross Abstract: Given a hypercube $\mathcal{Q}^{n} := \{0,1\}^{n}$ in $\mathbb{R}^{n}$ and $k \in \{0, \dots, n\}$, the $k$-th layer $\mathcal{Q}^{n}_{k}$ of $\mathcal{Q}^{n}$ denotes the set of all points in $\mathcal{Q}^{n}$ whose coordinates contain exactly $k$ many ones. For a fixed $t \in \mathbb{N}$ and $k \in \{0, \dots, n\}$, let $P \in \mathbb{R}\left[x_{1}, \dots, x_{n}\right]$ be a polynomial that has zeroes of multiplicity at least $t$ at all points of...

arXiv CS 2d ago

A thalamus–brainstem attractor network drives history-biased decisions

Abstract Natural environments often change gradually, making it adaptive to bias decisions on the basis of the recent past — a phenomenon known as serial dependence1,2,3. Large-scale recordings during behaviour have identified that serial dependence is a common motif for decision-making, with neural representations of past experiences found throughout the brain4,5,6,7,8,9,10,11. However, it remains unclear whether this bias arises from dedicated neural circuits with history-specific...

Nature 21h ago

Discrete Incremental Voting: New Bounds for General Graphs and Expanders

arXiv:2606.06381v1 Announce Type: new Abstract: We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion.

arXiv CS 5d ago

Diverse binding poses of agonistic neurotoxins on human Na<sub>v</sub>1.6

Abstract Voltage-gated sodium (Nav) channels are key targets of various venomous toxins. Deciphering the binding poses and mechanisms of action of representative toxins will help to dissect the functional mechanism of the channels and facilitate therapeutic development targeting Nav channels1,2. Here we present cryo-electron microscopy (cryo-EM) structures of distinct binding poses of three agonistic peptide toxins on the human Nav1.6–β1 channel complex.

Nature 21h ago

Complementary Time-Space Tradeoff for Self-Stabilizing Leader Election: Polynomial States Meet Sublinear Time

arXiv:2505.23649v3 Announce Type: replace Abstract: We study the self-stabilizing leader election (SS-LE) problem in the population protocol model, assuming exact knowledge of the population size $n$. Burman, Chen, Chen, Doty, Nowak, Severson, and Xu [BCC+21a] (PODC) showed that this problem can be solved in $O(n)$ expected time with $O(n)$ states. Recently, G\k{a}sieniec, Grodzicki, and Stachowiak [GGS25] (PODC) proved that $n+O(\log n)$ states suffice to achieve $O(n \log n)$ time both in...

arXiv CS 8d ago

Gauss Circle Lattices with Geometric Convolutions for Synthesizing High Dimensional Image-Source Room Impulse Responses

arXiv:2606.04358v1 Announce Type: new Abstract: The image-source model (ISM) is a widely adopted method for efficiently simulating acoustic room impulse responses (RIRs) under specular reflection assumptions. Acoustic paths between source and receiver are traced to lattice points computed from successive reflections over bounding planes of the room.

arXiv CS 6d ago

Repeated Descent: A Framework for Online Budget-Feasible Auctions

arXiv:2606.01142v1 Announce Type: new Abstract: We study budget feasible procurement auctions, in which $n$ agents, each with a privately held service cost, offer their services to an employer. The employer seeks to maximize a public submodular valuation function over the set of hired agents, while facing a hard budget constraint. We consider an online posted-price setting, in which agents arrive in a uniformly random order (a.k.a. \emph{secretary arrivals}) and the employer must make...

arXiv CS 8d ago

Hard labels sampled from sparse targets mislead rotation invariant algorithms

Announce Type: replace-cross Abstract: One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic regression, the feedback can be either soft labels, corresponding to the true conditional probability of the data (as in distillation), or sampled hard labels (taking values $\pm 1$).

arXiv CS 2d ago

Local MixVR: Breaking the Communication-Sample Dependence in Distributed Learning

arXiv:2606.01128v1 Announce Type: new Abstract: Communication overhead is a crucial bottleneck in scalable distributed learning. While existing methods aim to efficiently utilize data points, such as Local SGD, Minibatch SGD, and their accelerated variants, they still exhibit communication-round complexity that scales with the total number of samples $N$. In this paper, we introduce Local MixVR, a distributed framework that integrates local updates with variance-reduction techniques to...

arXiv CS 8d ago

KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices

Announce Type: replace Abstract: The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to training instability and restricted scalability. The Manifold-Constrained Hyper-Connections (mHC) mitigate these challenges by projecting the residual connection space onto a Birkhoff polytope, however, it faces two issues: 1) its iterative Sinkhorn-Knopp (SK) algorithm does not always yield exactly doubly stochastic residual matrices; 2) mHC incurs a...

arXiv CS 8d ago