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Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…
Accelerating DNN execution on various resource-limited computing platforms has been a long-standing problem. Prior works utilize l1-based group lasso or dynamic regularization such as ADMM to perform structured pruning on DNN models to…
In this paper, we introduce a unified framework, inspired by classical regularization theory, for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares…
Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under…
We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is $O(\log^2 n)$, where $n$ is the length of the branching…
Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…
Randomized compiling (RC) is an efficient method for tailoring arbitrary Markovian errors into stochastic Pauli channels. However, the standard procedure for implementing the protocol in software comes with a large experimental overhead --…
Reinforcement Learning with Verifiable Rewards (RLVR) has become the leading paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard RLVR algorithms suffer from a well-documented pathology: while they improve…
Data dependent regularization is known to benefit a wide variety of problems in machine learning. Often, these regularizers cannot be easily decomposed into a sum over a finite number of terms, e.g., a sum over individual example-wise…
Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed…
Guessing random additive noise decoding (GRAND) is a universal decoding paradigm that decodes by repeatedly testing error patterns until identifying a codeword, where the ordering of tests is generated by the received channel values. On one…
We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP)…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…
The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail…
We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…
Due to the ever growing amounts of data leveraged for machine learning and scientific computing, it is increasingly important to develop algorithms that sample only a small portion of the data at a time. In the case of linear least-squares,…