O(2^{b})$
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Faster algorithms for k-Orthogonal Vectors in low dimension
Announce Type: replace Abstract: In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$. Straightforward algorithms for this problem run in $\mathcal{O}(n^2 \cdot d)$ or $\mathcal{O}(2^d \cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\cdot n^{2-\varepsilon}$ time algorithm that solves this problem for any...
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks
Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks This post is a high-level explainer for my Master’s thesis, which involves designing hardware architectures for ultrafast inference and online learning using the Kolmogorov-Arnold Network (KAN) architecture. I’ll assume familiarity with standard machine learning concepts, as well as some understanding of hardware and digital circuits; read my previous post here for the latter. Please read the two papers below for more...
Generating Rectifiable Measures through Neural Networks
Announce Type: replace Abstract: We derive universal approximation results for the class of (countably) $m$-rectifiable measures. Specifically, we prove that $m$-rectifiable measures can be approximated as push-forwards of the one-dimensional Lebesgue measure on $[0,1]$ using ReLU neural networks with arbitrarily small approximation error in terms of Wasserstein distance. What is more, the weights in the networks under consideration are quantized and bounded and the number of ReLU neural...
AudioRWKV: Efficient and Stable Bidirectional RWKV for Audio Pattern Recognition
Announce Type: replace Abstract: Recently, Transformers (e.g., Audio Spectrogram Transformers, AST) and state-space models (e.g., Audio Mamba, AuM) have achieved remarkable progress in audio modeling. However, the O(L^2) computational complexity of the Transformer architecture hinders efficient long-sequence processing, while the Mamba architecture tends to become unstable when scaling parameters and data.
Benchmarking Language Modeling for Lossless Compression of Full-Fidelity Audio
arXiv:2603.08683v2 Announce Type: replace Abstract: Autoregressive "language" models (LMs) trained on raw waveforms can be repurposed for lossless audio compression, but prior work is limited to 8-bit audio, leaving open whether such approaches work for practical settings (16/24-bit) and can compete with existing codecs. We benchmark LM-based compression on full-fidelity audio across diverse domains (music, speech, bioacoustics), sampling rates (16kHz-48kHz), and bit depths (8, 16, 24-bit)....
One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space
arXiv:2605.17540v4 Announce Type: replace Abstract: Motivated by the COLT 2023 open problem of Criscitiello, Mart\'inez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard manifolds, we study hyperbolic space \[ \HH^d_{-\kappaC^2} =\{X\in\R^{d+1}:\ipL{X}{X}=-1,\ X_0>0\}, \qquad \ip{U}{V}_X=\kappaC^{-2}\ipL{U}{V}. For every geodesically convex $M$-Lipschitz function \[ f:\bar B_{\HH}(x_0,r)\to\R,\qquad s=\kappaC r, \] we give a...
Whole-genome duplication shaped cell-type evolution in the vertebrate brain
Abstract The complex brains of vertebrates have more cell types than those of their closest relatives. Whole-genome duplications (WGDs) occurred during early vertebrate evolution1, but it is unclear whether the duplicated genes (ohnologues) facilitated cell-type evolution. Here using brain single-cell transcriptomes from five chordates—human2, mouse3, lizard4, lamprey5 and amphioxus—we report that many cell-type families with conserved core transcription factors in vertebrates do not show...
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.
Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions
arXiv:2606.06085v1 Announce Type: new Abstract: We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-approximate correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on...
Lignin to adipic acid in a high-yield chemical and biological redox process
Abstract Viable manufacturing pathways to produce bio-based chemicals from renewable feedstocks, such as lignin derived from plant biomass, are needed to decarbonize the chemicals manufacturing sector. Converting the recalcitrant lignin polymer to valuable bioproducts remains a longstanding challenge in biorefining, with the highest reported single-product yield from lignin currently around 20 wt% (refs. Most existing lignin depolymerization strategies target aryl–ether bond cleavage, which...