Related papers: Predicting Module-Lattice Reduction
We present the notion of multilevel slashing, where proof-of-stake blockchain validators can obtain gradual levels of assurance that a certain block is bound to be finalized in a global consensus procedure, unless an increasing and…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
Modular reduction is a crucial operation in many post-quantum cryptographic schemes, including the Kyber key exchange method or Dilithium signature scheme. However, it can be computationally expensive and pose a performance bottleneck in…
The variation of z in BTW model in presence of holes (dissipative sites) has been studied. The value of z decreases as the fraction of number of holes increases. Interstingly, it is observed that the variation of the rate of change of z…
We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable…
Blockchain consensus faces a trilemma of security, latency, and decentralization. High-throughput systems often require a reduction in decentralization or robustness against strong adversaries, while highly decentralized and secure systems…
The inference of Large language models (LLMs) requires immense computation and memory resources. To curtail these costs, quantisation has merged as a promising solution, but existing LLM quantisation mainly focuses on 8-bit. In this work,…
Heavy-meson semileptonic decays calculations on the lattice are reviewed. The focus is upon obtaining reliable matrix elements. Errors that depend upon the lattice spacing, $a$, are an important source of systematic error. Full $O(a)$…
The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the…
Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
We investigate grokking in transformers through the lens of inductive bias: dispositions arising from architecture or optimization that let the network prefer one solution over another. We first show that architectural choices such as the…
We consider FrodoKEM, a lattice-based cryptosystem based on LWE, and propose a new error correction mechanism to improve its performance. Our encoder maps the secret key block-wise into the Gosset lattice $E_8$. We propose two sets of…
Recent work have shown that the quantization for matrix multiplication problem can be optimally solved by quantizing each column in each matrix using a nested lattice code, and then multiplying the de-quantized matrices. It was further…
In recent years, persistence modules have been viewed as graded modules with gradation over a preordered set serving as the indexing set. We provide sufficient criteria for a projective module over a PID to be free when the indexing set is…
Lattices have been conceived as a powerful tool for data hiding. While conventional studies and applications focus on achieving the optimal robustness versus distortion tradeoff, in some applications such as data hiding in…
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of…
A finitely generated module over the ring L=Z[t, t^{-1}] of integer Laurent polynomials that has no Z-torsion is determined by a pair of sub-lattices of L^d. Their indices are the absolute values of the leading and trailing coefficients of…
The 2d XY model exhibits an essential phase transition, which was predicted long ago --- by Berezinskii, Kosterlitz and Thouless (BKT) --- to be driven by the (un)binding of vortex--anti-vortex pairs. This transition has been confirmed for…
The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…
Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with…