Decentralizing Coherent Joint Transmission Precoding via Fast ADMM with Deterministic Equivalents

Inter-cell interference (ICI) suppression is critical for multi-cell multi-user networks. In this paper, we investigate advanced precoding techniques for coordinated multi-point (CoMP) with downlink coherent joint transmission, an effective approach for ICI suppression. Different from the centralized precoding schemes that require frequent information exchange among the cooperating base stations, we propose a decentralized scheme to minimize the total power consumption. In particular, based on the covariance matrices of global channel state information, we estimate the ICI bounds via the deterministic equivalents and decouple the original design problem into sub-problems, each of which can be solved in a decentralized manner. To solve the sub-problems at each base station, we develop a low-complexity solver based on the alternating direction method of multipliers (ADMM) in conjunction with the convex-concave procedure (CCCP). Simulation results demonstrate the effectiveness of our proposed decentralized precoding scheme, which achieves performance similar to the optimal centralized precoding scheme. Besides, our proposed ADMM solver can substantially reduce the computational complexity, while maintaining outstanding performance.

Decentralizing Coherent Joint Transmission Precoding via Deterministic Equivalents

In order to control the inter-cell interference for a multi-cell multi-user multiple-input multiple-output network, we consider the precoder design for coordinated multi-point with downlink coherent joint transmission. To avoid costly information exchange among the cooperating base stations in a centralized precoding scheme, we propose a decentralized one by considering the power minimization problem. By approximating the inter-cell interference using the deterministic equivalents, this problem is decoupled to sub-problems which are solved in a decentralized manner at different base stations. Simulation results demonstrate the effectiveness of our proposed decentralized precoding scheme, where only 2 ~ 7% more transmit power is needed compared with the optimal centralized precoder.

Spectrum of non-Hermitian deep-Hebbian neural networks

Neural networks with recurrent asymmetric couplings are important to understand how episodic memories are encoded in the brain. Here, we integrate the experimental observation of wide synaptic integration window into our model of sequence retrieval in the continuous time dynamics. The model with non-normal neuron-interactions is theoretically studied by deriving a random matrix theory of the Jacobian matrix in neural dynamics. The spectra bears several distinct features, such as breaking rotational symmetry about the origin, and the emergence of nested voids within the spectrum boundary. The spectral density is thus highly non-uniformly distributed in the complex plane. The random matrix theory also predicts a transition to chaos. In particular, the edge of chaos provides computational benefits for the sequential retrieval of memories. Our work provides a systematic study of time-lagged correlations with arbitrary time delays, and thus can inspire future studies of a broad class of memory models, and even big data analysis of biological time series.

Statistical physics of unsupervised learning with prior knowledge in neural networks

Integrating sensory inputs with prior beliefs from past experiences in unsupervised learning is a common and fundamental characteristic of brain or artificial neural computation. However, a quantitative role of prior knowledge in unsupervised learning remains unclear, prohibiting a scientific understanding of unsupervised learning. Here, we propose a statistical physics model of unsupervised learning with prior knowledge, revealing that the sensory inputs drive a series of continuous phase transitions related to spontaneous intrinsic-symmetry breaking. The intrinsic symmetry includes both reverse symmetry and permutation symmetry, commonly observed in most artificial neural networks. Compared to the prior-free scenario, the prior reduces more strongly the minimal data size triggering the reverse symmetry breaking transition, and moreover, the prior merges, rather than separates, permutation symmetry breaking phases. We claim that the prior can be learned from data samples, which in physics corresponds to a two-parameter Nishimori plane constraint. This work thus reveals mechanisms about the influence of the prior on unsupervised learning.

Minimal model of permutation symmetry in unsupervised learning

Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks with two or more hidden units. However, a theoretical study of the permutation symmetry is still lacking. Here, we propose a minimal model with only two hidden units in a restricted Boltzmann machine, which aims to address how the permutation symmetry affects the critical learning data size at which the concept-formation (or spontaneous symmetry breaking in physics language) starts, and moreover semi-rigorously prove a conjecture that the critical data size is independent of the number of hidden units once this number is finite. Remarkably, we find that the embedded correlation between two receptive fields of hidden units reduces the critical data size. In particular, the weakly-correlated receptive fields have the benefit of significantly reducing the minimal data size that triggers the transition, given less noisy data. Inspired by the theory, we also propose an efficient fully-distributed algorithm to infer the receptive fields of hidden units. Overall, our results demonstrate that the permutation symmetry is an interesting property that affects the critical data size for computation performances of related learning algorithms. All these effects can be analytically probed based on the minimal model, providing theoretical insights towards understanding unsupervised learning in a more general context.