ResNets minimize circuit size for fitting data in HTMC regime.
problem Finding the simplest algorithm that fits data.
method Defining HTMC and ResNet norms to relate circuit size and function fitting.
result Minimizing ResNet norm is equivalent to finding a circuit with minimal nodes.
This study shows neural nets can approximate Turing machines with meaningful statistical properties.
problem Theoretical limitations in approximating Turing machines with neural networks.
method Formal definition of statistically meaningful approximation, analysis of boolean circuits and Turing machines using neural nets.
result Transformers can statistically meaningfully approximate Turing machines with polynomial sample complexity.
New algorithms save computation in agnostic learning with membership queries.
problem Efficiently learning touchstone classes with membership queries.
method Designing agnostic learning algorithms for circuits with sublinear gates.
result Agnostic learning algorithms for circuits with sublinear gates achieve significant computational savings.
SGLBO optimizes quantum circuits with fewer measurements, improving accuracy and noise resilience.
problem Efficiently optimizing parameterized quantum circuits with reduced measurement shots and noise.
method Developed SGLBO combining SGD and BO, with adaptive measurement-shot strategy and suffix averaging.
result Significantly reduces measurement-shot cost while improving accuracy and noise resilience.
New findings on boosting sample complexity and implications for hardcore theorem.
problem Understanding the sample complexity of smooth boosting and its implications.
method Analyzing the sample complexity of smooth boosting and relating it to the hardcore theorem.
result The sample complexity of smooth boosting matches existing overhead and provides a separation from distribution-independent boosting.
Complex architectures of biological neural circuits, such as parallel processing pathways, has been behaviorally implicated in many cognitive studies. However, the theoretical consequences of circuit complexity on neural computation have only been explored in limited cases. Here, we introduce a mechanism by which direc…
BOiLS optimizes circuit quality using Bayesian optimization.
problem Optimizing circuits with complex search spaces.
method Adapting Bayesian optimization to logic synthesis, using Gaussian process kernels and trust-region constrained acquisitions.
result Demonstrated superior performance in sample efficiency and QoR values.
We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry groups of the spheres that showed up. In Section 4 we introduce a new Goldberg-…
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrari…
Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomia…
COLEP improves robustness of conformal prediction via probabilistic circuits.
problem Adversarial perturbations can undermine the coverage guarantees of conformal prediction.
method COLEP uses probabilistic circuits to learn and reason about different semantic concepts, providing certifiable coverage guarantees.
result COLEP achieves higher prediction coverage and accuracy than a single model, especially with non-trivial knowledge models.
SymCircuit learns PC structure via entropy-regularized RL, improving inference efficiency and accuracy.
problem Greedy algorithms in PC structure learning lead to suboptimal solutions.
method Entropy-regularized reinforcement learning to train a learned generative policy for PC structure inference.
result SymCircuit learns the optimal policy as a tempered Bayesian posterior, improving inference efficiency and accuracy.
Quantum algorithm improves portfolio construction accuracy.
problem Efficiently constructing portfolios with real-world constraints.
method Sampling-based CVaR Variational Quantum Algorithm (VQA) combined with local-search post-processing.
result Achieved a relative solution error of 0.49% on IBM Heron processors.
The paper proves barriers to approximating functions with small weights and depth in neural networks.
problem Proving barriers to approximating functions with constant depth neural networks.
method Reduction to open problems and natural-proof barriers in circuit complexity, and a new approach to polynomially-bounded functions.
result There are fundamental barriers to proving results beyond depth 4 for constant-depth neural networks.
Study evaluates capacity and trainability of parametrized quantum circuits.
problem Finding the best type of circuits for hybrid quantum-classical algorithms.
method Geometric structure of parameter space, effective quantum dimension, and circuit expressiveness.
result Identifies a transition in quantum geometry leading to decay of quantum natural gradient for deep circuits.
The paper tests if LLMs' capabilities are executed by small subnetworks (circuits).
problem Understanding how LLMs execute their capabilities.
method Formalized criteria for circuits, developed hypothesis tests, applied to six circuits.
result Synthetic circuits align with idealized properties, while Transformer circuits vary in their alignment.
We prove overfitting in minimal and random NNs, tempering the effect.
problem Overfitting in minimal and random neural networks.
method Analyzing binary weight fitting to noisy data, proving overfitting is tempered.
result The overfitting of minimal and random neural networks is tempered.
Study detects if a circuit bounds a disc using curve intersections.
problem Determining if a circuit bounds an embedded disc.
method Analyzing the group generated by Dehn twists about curves in a circuit.
result Cycle relation between Dehn twists detects disc-boundability.
Evolutionary strategy optimizes quantum circuit design and parameters.
problem Optimizing quantum circuit design and parameters for NISQ devices.
method Simple evolutionary strategy to optimize both circuit architecture and parameters.
result Minor slowdown on actual quantum hardware compared to simulations, with insights into mutation operations.
Warm starts improve variational quantum algorithms by avoiding barren plateaus.
problem Barren plateaus in variational quantum algorithms limit scaling.
method Exploring warm starts in iterative variational methods for quantum circuits.
result Warm starts can lead to substantial gradients in small regions, suggesting trainability.
This work uses SVM to identify track component failures in AC Track Circuits.
problem Detecting and identifying specific track component failures in AC Track Circuits.
method Applied SVM classifier to STDS track circuit data.
result Successfully classified 15 different track component failures.
The statistical complexity of quantum circuits is studied using Rademacher complexity.
problem Measuring the richness of quantum hypothesis spaces.
method Applying Rademacher complexity to quantum circuits, investigating dependencies on resources, depth, width, and input/output registers.
result Bounds on the capacity of quantum neural networks constrained by circuit depth, width, and resource measures.
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. O…
Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural net…
The study examines how quantum resources enhance the complexity of quantum circuits.
problem Quantum resource enhancement on circuit complexity.
method Utilizing quantum resource theories, the study analyzes statistical complexities of quantum circuits with limited quantum resources.
result Bounds for statistical complexities of quantum circuits are derived and applied to specific cases.
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
PAC-MOO optimizes constrained multi-objective problems with preferences.
problem Optimizing with constraints and practitioner preferences over objectives.
method Preference-aware constrained multi-objective Bayesian optimization.
result Efficacy demonstrated on real-world analog circuit design problems.
Study bounds VAR model's circuit complexity, showing it's limited to TC^0 circuits.
problem Understanding the limitations of the Visual AutoRegressive model.
method Established circuit complexity bounds for the VAR model.
result VAR model is equivalent to a TC^0 threshold circuit with hidden dimension ≤ O(n).
CoT enhances transformer accuracy on serial tasks by enabling serial computation.
problem Improving accuracy of large language models on inherently serial problems.
method Integrating a chain of thought (CoT) into decoder-only transformers to enable serial computation.
result Constant-depth transformers with CoT can solve problems in AC^0, surpassing TC^0 without CoT.
In this work, a machine learning approach for identifying the multi-omics metabolic regulatory control circuits inside the pathways is described. Therefore, the identification of bacterial metabolic pathways that are more regulated than others in term of their multi-omics follows from the analysis of these circuits . T…
Study shows limitations and possibilities of learning quantum circuit output distributions.
problem Learnability of output distributions of local quantum circuits.
method Investigated within two oracle models: statistical query model and direct sample access model.
result Output distributions of super-logarithmic depth Clifford circuits are not efficiently learnable in the statistical query model.
Global routing has been a historically challenging problem in electronic circuit design, where the challenge is to connect a large and arbitrary number of circuit components with wires without violating the design rules for the printed circuit boards or integrated circuits. Similar routing problems also exist in the de…
Motivated by the resurgence of neural networks in being able to solve complex learning tasks we undertake a study of high depth networks using ReLU gates which implement the function x↦max{0,x}. We try to understand the role of depth in such neural networks by showing size lowerbounds against such network …
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …
We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the simil…
BiLiNGAM model reveals brain emotion circuit development in adolescents.
problem Understanding brain emotion circuit development during adolescence.
method Bayesian incorporated linear non-Gaussian acyclic model (BiLiNGAM) for multiple DAGs estimation.
result BiLiNGAM reveals unique developmental hub structures and group-specific patterns in emotion-related intra- and inter-modular connectivity.
Sum Product Networks (SPNs) are a recently developed class of deep generative models which compute their associated unnormalized density functions using a special type of arithmetic circuit. When certain sufficient conditions, called the decomposability and completeness conditions (or "D&C" conditions), are imposed on …
Spin networks boost quantum algorithms solving SU(2) symmetric problems.
problem Efficiently solving SU(2) symmetric problems on quantum hardware.
method Using SU(2) equivariant variational quantum circuits based on spin networks.
result Spin networks provide a direct implementation for SU(2) equivariant quantum circuits.
Enhances quantum circuit synthesis using deep learning and geometric methods.
problem Optimizing quantum circuits for time efficiency.
method Combining deep learning with geometric control techniques.
result Improved time-optimal control in quantum circuit synthesis.
Single T-gate makes distribution learning hard for deep circuits.
problem Learning probability distributions from quantum circuits.
method Characterization of learnability and simulatability of quantum circuit outputs.
result Injection of a single T-gate into depth n^Ω(1) circuits makes distribution learning hard.
We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as…
Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves …
Quantum circuits are hard to learn on average.
problem Learning the output distributions of quantum circuits is hard.
method Statistical query model analysis.
result Learning quantum circuits requires exponentially many queries.
Study improves probabilistic circuits using transformations for better predictions.
problem Predictive limitations of probabilistic circuits in robotic scenarios.
method Integrates transformations into joint probability trees, extending their capabilities.
result Achieves higher likelihoods with fewer parameters on various data sets.
Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not triv…
Quantum circuit optimization speeds up financial derivatives pricing.
problem Efficiently pricing financial derivatives on quantum computers.
method Pretraining conditional parameterized circuits for state-dependent functions.
result Quantum circuit implementation of derivatives' payoff function is more efficient.
Bayesian approach optimizes quantum circuits for noisy hardware.
problem Optimizing parameterized quantum circuits on noisy quantum hardware.
method Reformulate classical optimisation as Bayesian posterior, combining cost function and prior distribution. Apply dimension reduction and posterior sampling strategies.
result Bayesian approach generates faster, less noisy circuits than classical methods.
The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. How…