Related papers: A Scaling Law for Bandwidth Under Quantization
While neural networks have advanced the frontiers in many applications, they often come at a high computational cost. Reducing the power and latency of neural network inference is key if we want to integrate modern networks into edge…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that…
It has been recently brought into spotlight that through the exploitation of network coding concepts at physical-layer, the interference property of the wireless media can be proven to be a blessing in disguise. Nonetheless, most of the…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
In this work, we consider a wide two-layer neural network and study the behavior of its empirical weights under a dynamics set by a stochastic gradient descent along the quadratic loss with mini-batches and noise. Our goal is to prove a…
Searching for a weak signal at an unknown frequency is a canonical task in experiments probing fundamental physics such as gravitational-wave observatories and ultra-light dark matter haloscopes. These state-of-the-art sensors are limited…
Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far…
The scaling exponent $\alpha$ in neural scaling laws $L(N) \propto N^{-\alpha}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $\alpha$ depends systematically on the optimizer. In controlled…
We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as…
This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements. The main contributions include the…
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…
Standard resampling ratios (e.g., $\alpha \approx 0.632$) are widely used as default baselines in ensemble learning for three decades. However, how these ratios interact with a base learner's intrinsic functional complexity in finite…
With bandwidths on the order of a gigahertz in emerging wireless systems, high-resolution analog-to-digital convertors (ADCs) become a power consumption bottleneck. One solution is to employ low resolution one-bit ADCs. In this paper, we…
Dynamic Spectrum Access systems exploit temporarily available spectrum (`white spaces') and can spread transmissions over a number of non-contiguous sub-channels. Such methods are highly beneficial in terms of spectrum utilization. However,…
We consider inhomogeneous square random matrices of size $N$ with independent entries of mean 0 and finite variance. We assume that the variance profile of this matrix is doubly stochastic and has a band-like structure with an appropriately…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in…
We present simple coding strategies, which are variants of the Schalkwijk-Kailath scheme, for communicating reliably over additive white noise channels in the presence of corrupted feedback. More specifically, we consider a framework…