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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…
Categorization is an important topic both for biological and artificial neural networks. Here, we take an information theoretic approach to assess the efficiency of the representations induced by category learning. We show that one can…
Predictive coding networks are neural models that perform inference through an iterative energy minimization process, whose operations are local in space and time. While effective in shallow architectures, they suffer significant…
We consider the problem of sequential decision making on random fields corrupted by noise. In this scenario, the decision maker observes a noisy version of the data, yet judged with respect to the clean data. In particular, we first…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
Understanding a neural code requires knowledge both of the elementary symbols that transmit information and of the algorithm for translating these symbols into sensory signals or motor actions. We show that these questions can be separated:…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We consider approaches for controlling the buildup of noise by design of gates for chemical and biomolecular computing, in order to realize stable, scalable networks for multi-step information processing. Solvable rate-equation models are…
The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large…
Sparse codes in neuroscience have been suggested to offer certain computational advantages over other neural representations of sensory data. To explore this viewpoint, a sparse code is used to represent natural images in an optimal control…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
Recent coding strategies for deterministic and noisy relay networks are related to the pipelining of block Markov encoding. For deterministic networks, it is shown that pipelined encoding improves encoding delay, as opposed to end-to-end…
Living cells presumably employ optimized information transfer methods, enabling efficient communication even in noisy environments. As expected, the efficiency of chemical communications between cells depends on the properties of the…
Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…
In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning…
Neural networks in modern communication systems can be susceptible to internal numerical errors that can drastically effect decision results. Such structures are composed of many sections each of which generally contain weighting operations…
Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arrangement of convex open sets in Euclidean space. Previous…
An analog communication channel typically achieves its full capacity when the distribution of inputs is discrete, composed of just K symbols, such as voltage levels or wavelengths. As the effective noise level goes to zero, for example by…