System uses neural networks to prove program equivalence via rewrite rules.
problem Proving equivalence between two dataflow graphs.
method Developed a graph-to-sequence neural network trained on example generation to find semantics-preserving rewrite rules.
result System correctly outputs a rewrite sequence for 96% of program pairs, proving equivalence.
Zipper logic is a graph rewrite system, consisting in only local rewrites on a class of zipper graphs. Connections with the chemlambda artificial chemistry and with knot diagrammatics based computation are explored in the article.
TFLMS optimizes neural network training with larger models by rewriting graphs.
problem Training large neural networks with limited accelerator memory.
method Rewriting the computational graph to swap out and in intermediate results to CPU memory.
result Trained ResNet-50 and 3DUnet with significantly larger batch sizes.
Serenity optimizes neural network execution for edge devices by scheduling with optimal memory footprint.
problem Order of nodes in irregular neural networks affects memory footprint, complicating execution under resource constraints.
method Memory-aware compiler using dynamic programming and graph rewriting to find optimal schedules.
result Achieves optimal peak memory and further improves it with graph rewriting, reducing memory usage by 1.68x-1.86x compared to TensorFlow Lite.
Graph neural networks can perform approximate reasoning in latent space for mathematical statements.
problem Can neural networks perform steps of approximate reasoning in a fixed dimensional latent space?
method Design and conduct an experiment using graph neural networks to predict rewrite-success of mathematical statements in a latent space.
result Graph neural networks can make non-trivial predictions about rewrite-success of statements in latent space.
Paper proposes a visual tool for analyzing financial markets.
problem Rational negligence in financial markets during the 2008 crisis.
method Visual declarative language based on port-graph rewriting.
result Visual tool for analyzing asset-backed securities.
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive procedure for constructing van Kampen diagrams with respect to a canonical fini…
Rewriting theory applied to diagrammatic algebras for categorification.
problem Finding bases in graded gl2-foams. method Algorithmic approach combining linear and higher rewriting, modulo rules capturing categorical properties.
result First proof of a basis theorem for graded gl2-foams. Develops higher representation theory for odd Khovanov homology and rewriting theory.
problem Quantum topology and higher algebraic structures.
method Higher representation theory and rewriting theory applied to Khovanov homology.
result Established a basis theorem for graded gl2-foams. Updates and rewrites a 1974 AMS Memoir on Lie groups.
problem Real reductive Lie groups and their representations.
method Rewriting and updating a 1974 AMS Memoir.
result Ties with recent approaches to geometric realization of unitary representations.
NeuRewriter learns to choose and rewrite heuristics in combinatorial problems.
problem Time-consuming tuning of heuristics in combinatorial optimization.
method NeuRewriter uses reinforcement learning to learn a policy for picking heuristics and rewriting solutions.
result NeuRewriter outperforms existing methods in various combinatorial tasks.
Extensive rewrite. Tables and proofs have been reformatted and/or rewritten for clarity.
This is the author's Master's thesis written under the supervision of Dr. Gregor Weingart at the National Autonomous University of Mexico. The purpose of this study is to rewrite differential supergeometry in terms of classical differential geometry. This rewriting from "first principles" has two main motivations: 1 av…
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang find a sufficient condition for …
A fast metric learning framework using Gershgorin disc alignment.
problem Learning effective metrics for graph-based data.
method Fast projection-free metric learning via Gershgorin disc alignment.
result Efficiently computed graph metric matrices outperform competing methods.
Paper introduces a new algorithm to detect LLM-generated text.
problem Detecting LLM-generated text to prevent misinformation.
method Adaptively learns the distance between original and rewritten text.
result Empirically, the new algorithm outperforms existing methods in most scenarios.
New basis and Schur-Weyl duality for loop Hecke algebra defined.
problem Define a new basis for the loop Hecke algebra.
method Use higher linear rewriting theory and combinatorics of Dyck paths.
result Yields a conjecture of Damiani-Martin-Rowell and provides a representation theoretic interpretation.
NIFTy.re accelerates imaging models and expands Gaussian processes and variational inference.
problem Slow performance and limited inference strategies in NIFTy.
method Rewritten NIFTy with new modeling principles, inference strategies, and JAX integration.
result Dramatic acceleration of models and new inference capabilities.
Rewriting history improves RL algorithms for solving multiple tasks.
problem Improving sample efficiency in multi-task reinforcement learning.
method Introducing hindsight relabeling as inverse RL to generalize goal-relabeling techniques.
result Relabeling data using inverse RL accelerates learning in multi-task settings.
We create a 3-skeleton for a symmetric group's classifying space.
problem Classifying space construction for symmetric groups.
method Combining rewriting systems and combinatorial methods.
result Correctness of the constructed 3-skeleton.
In this paper, a type of integrable evolution equation--the generalized Landau-Lifshitz equation into Sn is considered. We deal with this equation from a geometric point of view by rewriting it in a geometric form. Through the geometric energy method, we show the global well-posedness of the corresponding Cauchy pro…
Reformulated Markov's conjecture in combinatorial terms.
problem Markov's uniqueness conjecture in integral necklaces.
method Geometric reformulation and combinatorial description.
result Explicitly described set of lengths on modular torus.
We determine the Lyapunov spectrum of ball quotients arising from cyclic coverings. The computations are performed by rewriting the sum of Lyapunov exponents as ratios of intersection numbers and by the analysis of the period map near boundary divisors. As a corollary, we complete the classification of commensurability…
Unified approach for multicalibration in weakly supervised learning.
problem Existing multicalibration methods require clean input-label pairs, which are unavailable in weakly supervised learning.
method Developed estimators and post-hoc correction methods for multicalibration under weak supervision.
result Unified framework for estimating and correcting multicalibration under weak supervision with finite-sample guarantees.
Proves that emergent algebras right-distributivity implies left-distributivity.
problem Proving the implication between emergent algebra distributivity conditions.
method Analyzing families of quasigroup operations indexed by commutative groups.
result Emergent algebras right-distributive imply left-distributive.
Study holonomy flags in subRiemannian geometry and (2,3)-distributions.
problem Characterize holonomy in subRiemannian geometry.
method Define and calculate holonomy flags, rewrite Codazzi equations.
result New interpretation and calculation of holonomy flags.
We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of the Riemann curvature tensor and find conditions relating the harmonicity of the a…
PaRoT simplifies robust training for deep neural networks.
problem Training deep neural networks to be robust to small input changes.
method Developed a practical framework on TensorFlow for robust training without code modifications.
result PaRoT's performance is comparable to existing methods and is easy to use on real-world models.
We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid…
In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal Ricci flow on compact manifolds as well as on asymptotically flat manifolds. We…
Existence proved for complex 3-folds equation on a specific phase range.
problem Existence of solutions for a specific equation on complex 3-folds.
method New continuity path and Monge-Ampère equation with mixed sign coefficients.
result Existence result for the deformed Hermitian Yang-Mills equation on compact complex three-folds.
Mikhail Khovanov in math.QA/9908171 defined, for a diagram of an oriented classical link, a collection of groups numerated by pairs of integers. These groups were constructed as homology groups of certain chain complexes. The Euler characteristics of these complexes are coefficients of the Jones polynomial of the link.…
Investigates surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
problem Finding surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
method Rewriting the equations for mean and skew curvatures as linear first order ODEs with coefficients in hypercomplex numbers or real numbers.
result Solutions for surfaces of revolution with prescribed mean and skew curvatures.
Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include nilpotent groups, many relatively hyperbolic groups including geometrically…
Extends Euler class formula to general connections with metric.
problem Formula for Euler class with metric connection.
method Rewriting formula for general connections with metric.
result Rewritten Gauss-Bonnet theorem in dimension two.
A new framework for personalized ad retrieval in e-commerce search.
problem Difficulty in measuring ads retrieved using multiple signals (e.g. user profiles, clicks).
method Employing historical click data to initialize a hierarchical network representing signals, keys, and ads. Training a model to learn weights of edges and selecting the best edges.
result Framework achieves good performance, improving RPM/CTR.
We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an O(9,1)×O(1,9)⊂O(10,10)×R+ structure on the generalised tangent space. Using the notion of generalised connection and torsion, we introduce the analogue of the Levi-C…
We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to "negative frequencies":…
Researchers extend Gamma index theorem to non-compact spacetimes.
problem Establishing an L2-Gamma index for non-compact spacetimes. method Rewriting L2-Gamma index in terms of spectral flow and connecting to geometric expressions. result Extends Bär and Strohmaier's work to non-compact Cauchy hypersurfaces.
Study harmonicity of normal almost contact structures on Riemannian manifolds.
problem Understanding harmonicity of normal almost contact structures.
method Analyzing harmonicity through associated sections of a twistor bundle and rewriting equations in terms of curvature tensor.
result Conditions relating harmonicity of almost contact metric and almost complex structures.
We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated non…
The paper solves optimal control problems for stochastic delay equations.
problem Optimal control of stochastic delay differential equations.
method Rewriting the problem in an infinite-dimensional Hilbert space, using dynamic programming and viscosity solutions.
result Characterizes the value function as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.
Two methods find exact solutions to optimal portfolio execution, linking to Riccati equations.
problem Optimal execution of portfolio transactions.
method Two methods: rewriting and reparametrization.
result Equivalence to Riccati equations and exact solutions found.
Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many existing stochastic optimization algorithms cannot be parallelized efficiently. In t…
Corrects errors and completes missing parts in a paper on tangent cones.
problem Incorrect inequalities and missing definitions in a paper on tangent cones.
method Completely rewrote sections 5.1-5.4, providing missing definitions and proofs.
result Corrected inequalities and completed missing parts in the paper.
AI agents manage portfolios, improving on human oversight.
problem Improving strategic asset allocation for institutional investors.
method 50 specialized agents produce capital market assumptions, construct portfolios, critique, and vote on each other's output.
result Meta-agent compares forecasts with realized returns and improves agent performance.
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism …
New insights into using momentum for non-convex optimization.
problem Improving training of non-convex models like deep neural networks.
method Developed a Lyapunov analysis of SGD with momentum using stochastic primal averaging.
result Precise conditions under which SGD+M outperforms SGD and optimal hyper-parameter schedules.