Khovanov homology helps create quantum error-correcting codes.
problem Creating robust quantum error-correcting codes.
method Using Khovanov homology and its extensions to define and analyze quantum codes.
result New families of quantum codes with desirable properties.
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
problem Improving quantum error correction performance with hyperbolic lattices.
method Unified framework using Hyperbolic Cycle Basis algorithm for CSS codes construction and benchmarking.
result Achieved higher encoding rates and lower qubit overhead in hyperbolic quantum error correction codes.
Neural networks improve error correction in topological codes.
problem Finding optimal correction of errors in generic stabilizer codes is computationally hard.
method Systematic study of versatile neural-network decoders for topological codes.
result Neural decoders significantly improve error-correction threshold over leading efficient decoders.
Fault-tolerant neural networks inspired by biological error correction codes.
problem Achieving reliable computation with unreliable neurons.
method Using biological error correction codes from grid cells in the mammalian cortex to develop a fault-tolerant neural network.
result Noisy biological neurons operate below a fault-tolerance threshold, suggesting a mechanism for reliable computation in the brain.
New invariant for prime alternating knots from error-correcting codes
problem Distinguishing prime alternating knots
method Alexander-Briggs code
result New invariant succeeds in separating knots that other invariants fail
A deep learning autoencoder improves error correction for one-bit quantization.
problem Improving error correction for one-bit quantization in AWGN channels.
method Proposes a novel autoencoder-based coding scheme using turbo codes as implicit regularization.
result Empirically and theoretically shows nearly optimal performance of the proposed coding scheme.
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance nε. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers …
A new neural sequence prediction method using error-correcting codes improves accuracy and convergence.
problem Improving neural sequence prediction accuracy and speed.
method Error-correcting output codes, separable code maximization, latent variable mixture sampling.
result Consistent improvements on language modeling datasets and text generation tasks.
Paper introduces SCP to measure classifier distortion and optimized coding strategies.
problem Noise impacts binary classifier performance; goal is to minimize distortion.
method Developed a low-complexity estimate of SCP using quantization and polynomial multiplication. Also studied replication error-correcting codes for maximizing SCP.
result Introduced optimized coding strategies that specifically aim to maximize classification probability (minimizing distortion) for the same redundancy overhead.
Generative AI decodes quantum codes without labeled data.
problem Efficient decoding of quantum error-correcting codes.
method Generative Transformers learn logical operators from unsupervised syndromes.
result Significantly better decoding accuracy than traditional methods.
CodNN uses error-correcting codes to make neural networks more resilient to noise.
problem Neural networks are sensitive to noise, especially in critical applications.
method Construct robust neural networks by coding data or internal layers with error-correcting codes.
result Parity codes can guarantee robustness for a wide range of neural networks, including binarized networks.
New quantum codes improve error correction with local tests.
problem Improving quantum error correction efficiency.
method Introducing hemicubic codes and exploiting their local testability.
result Quantum codes with improved local testability and error correction.
A model corrects Lithuanian grammatical errors.
problem Lack of language skills and typing errors in Lithuanian.
method Transformer architectures for subword and byte-level approaches.
result F0.5=0.92 for Lithuanian grammatical error correction. Paper introduces deep neural decoders for near-term fault-tolerant quantum experiments.
problem Efficient decoders for quantum error correction under realistic noise.
method Deep neural decoders complemented by traditional algorithms.
result Deep neural decoders perform well in low noise regimes.
Paper designs optimal ECOCs using IP for robust multiclass classification.
problem Designing robust ECOCs for multiclass classification.
method Integer Programming formulation to minimize codebooks with desirable error-correcting properties, leveraging graph-theoretic structure and edge clique covers.
result IP-generated codebooks achieve high nominal and robust adversarial accuracy.
Quantum codes linked to abelian varieties, providing mathematical rigor.
problem Quantum error correction through complex abelian varieties.
method Mathematical formulation of Gottesman-Kitaev-Preskill codes using abelian varieties.
result Asymptotic isometry of encoding, precise gate realizations, and failure probability optimization.
Paper proposes IABF to improve NECST robustness.
problem Limited robustness of NECST learned coding networks.
method Infomax Adversarial-Bit-Flip (IABF) to improve stability and robustness.
result IABF achieves state-of-the-art performances on compression and error correction benchmarks.
ECNN combines binary classifiers to protect neural networks from adversarial attacks.
problem Vulnerability of neural networks to adversarial inputs.
method Designs an error-correcting code matrix to maximize row and column distances, training end-to-end.
result ECNN effectively defends against adversarial attacks with good accuracy on normal examples.
We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.
New algorithm for multi-player bandits with collision-dependent rewards.
problem Stochastic multi-player multi-armed bandits with collision-dependent reward distributions.
method Error-Correction Collision Communication (EC3) algorithm.
result EC3 algorithm achieves optimal regret approaching centralized MP-MAB regret.
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles …
Deep learning improves decoding of constrained sequence codes, reducing errors and increasing throughput.
problem Errors during transmission of constrained sequence codes.
method Deep learning, specifically MLP and CNN networks.
result Achieved low bit error rates close to MAP decoding and improved system throughput.
Neural decoder improves topological code performance.
problem Improving error correction for topological codes.
method Two-step neural network using pseudo-inverse of parity check matrix.
result Outperforms state-of-the-art non-neural decoders for 2D hexagonal color codes.
Jointly learns encoding and decoding for noisy channels.
problem Asymptotic optimality of source and channel separation in finite bit-length regimes.
method Discrete variational autoencoder model with noise simulation.
result Jointly learned codes are competitive and learn robust representations.
SPoC uses search to translate pseudocode into correct programs with error localization.
problem Mapping pseudocode to functionally correct long programs.
method Search-based approach guided by compilation errors for credit assignment.
result Search improves synthesis success rate from 25.6% to 44.7%.
Researchers found the maximum number of holes in polyominoes grows proportionally to the dimension.
problem Finding the maximum number of holes in polyominoes of varying dimensions.
method Used concepts from error-correcting codes and dynamical systems.
result Proved that fd(n)/no(d−1)/d as n goes to infinity for all d≥2. This paper designs neural associative memories that can correct many adversarial errors.
problem Designing neural associative memories that can correct many adversarial errors.
method Mapping the learning phase and recall phase to dictionary learning with a square dictionary and iterative error correction in an expander code.
result The designed associative memories can store datasets with exp(n) vectors and tolerate Ω(mpolylognn) adversarial errors. SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
A new algorithm reduces regret in multi-player bandits without collision info.
problem Decentralized multi-player multi-armed bandits with no collision info.
method EC-SIC algorithm using optimal error correction coding for reward statistics.
result Regret approaches that of centralized with collision info.
Study improves Persian handwritten letter recognition using ECOC ensemble method.
problem Improving accuracy in identifying Persian handwritten letters.
method ECOC ensemble method with feature selection and Support Vector Machine (SVM).
result ECOC ensemble method outperforms other methods in identifying Persian handwritten letters.
In my masters thesis I prove a square root bound on the distance of homological codes that come from two dimensional surfaces, as a result of the systolic inequality. I also give a detailed version of M.H. Freedman's proof that due to systolic freedom, this bound does not hold in higher dimensions.
Improved error correction using neural networks and belief propagation.
problem Inference in factor graphs with loops or poor approximations.
method Hybrid model combining FG-GNN and belief propagation.
result Hybrid model outperforms belief propagation in error correction tasks.
Study of manifolds with prime cyclic group actions and curvature properties.
problem Curvature properties of manifolds with Zp-actions. method Analysis of Zpr-actions on positively curved manifolds, use of error-correcting codes. result Improved symmetry-rank bounds for n-manifolds with p-actions, especially for small primes. Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
problem Overfitting in maximum likelihood estimation.
method Introduces a regularization approach based on gauge symmetry in Kullback-Leibler divergence.
result The method provides a theoretically guaranteed optimal model without frequent hyperparameter tuning.
Game theory improves smart road sign security against small perturbations.
problem Ensuring smart road signs are secure from small-scale adversarial attacks.
method Integrates game theory into smart road sign classification to detect imperceptible perturbations.
result Proposes a randomized detection strategy to ensure robustness against worst-case attackers.
Corrected samplers reduce discretization error in discrete flow models without additional computational cost.
problem Discretization error in samplers for discrete flow models.
method Established non-asymptotic error bounds for samplers, proposed time-corrected and location-corrected samplers.
result Location-corrected sampler has lower complexity and better generation quality.
Detects adversarial examples using binary code vectors.
problem Vulnerability of deep neural networks to adversarial examples.
method Key-based network using error correcting output codes.
result Effective detection of adversarial examples without prior knowledge.
Study on topological order on fractal geometries, proving no-go theorem and fault-tolerant gates.
problem Investigating topological order on fractal geometries embedded in n dimensions.
method Using quantum error-correcting codes and systolic geometry to diagnose topological order.
result Proves no-go theorem for topological order on 2D fractals, survival on higher dimensions, and construction of fault-tolerant gates.
Training-free method improves text-to-image generation quality.
problem Error accumulation in simultaneous token updates of masked diffusion models.
method Training-free self-correction framework exploiting inductive biases.
result Significantly improved generation quality on text-to-image tasks.
The use of Reinforcement Learning in real-world scenarios is strongly limited by issues of scale. Most RL learning algorithms are unable to deal with problems composed of hundreds or sometimes even dozens of possible actions, and therefore cannot be applied to many real-world problems. We consider the RL problem in the…
Study neural communication systems with bandwidth-limited channels.
problem Reliable message transmission despite noisy channels.
method Jointly model compression and error correction with neural networks; introduce prior for missing information; use auxiliary latent variables.
result Joint neural communication systems outperform separate models under expected information loss.
Deep learning optimizes polar codes for better performance.
problem Designing efficient polar codes for error correction.
method Representing polar code indices as neural network weights, optimizing through gradient descent.
result Significant performance improvements over existing methods.
This work proves L2-regularized ERM controls smCE without post-hoc correction.
problem Calibration of predicted probabilities in machine learning models.
method Canonical L2-regularized empirical risk minimization. result Theoretical proof that smCE is controlled by ERM without post-hoc correction.
Orthogonal coding matrices improve multi-class classification accuracy across various datasets.
problem Improving multi-class classification accuracy using orthogonal coding matrices.
method Optimized orthogonal coding matrices for multi-class classification, compared with other methods.
result Orthogonal coding matrices generally outperform random ECCs and are faster than 1 vs. 1.
We propose rectified factor networks (RFNs) to efficiently construct very sparse, non-linear, high-dimensional representations of the input. RFN models identify rare and small events in the input, have a low interference between code units, have a small reconstruction error, and explain the data covariance structure. R…
Graph-based approach repairs programs from diagnostic feedback.
problem Learning to repair programs from limited labeled data and compiler error messages.
method Introduces program-feedback graph and graph neural network for reasoning, and self-supervised learning with unlabeled programs.
result DrRepair significantly outperforms prior work, achieving high repair rates.
Tree-Transformer improves grammar correction in code and natural language.
problem Grammar correction in tree-structured data.
method Tree-Transformer neural network architecture for tree-structured data.
result Significant improvement in grammar correction accuracy.
LatentNN corrects neural network attenuation bias in astronomical data.
problem Neural networks underestimate extreme values due to measurement errors.
method Jointly optimizes network parameters and latent input values.
result LatentNN reduces attenuation bias across various signal-to-noise ratios.