MP-DQN improves deep Q-learning for complex action spaces.
problem Learning with discrete actions and continuous parameters in reinforcement learning.
method Multi-pass deep Q-networks (MP-DQN) to handle parameterised actions.
result Significantly outperforms P-DQN and other methods in data efficiency and policy performance.
We show how to specify preferred parameterisations on a homogeneous curve in an arbitrary homogeneous space. We apply these results to limit the natural parameters on distinguished curves in parabolic geometries.
Wide neural networks with asymmetrical node scaling converge globally and learn features.
problem Global convergence and feature learning in over-parameterised shallow networks.
method Gradient-based optimisation of wide, shallow neural networks with asymmetrical node scaling.
result Gradient flow and gradient descent converge to a global minimum and learn features, unlike in the NTK parameterisation.
In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We further exhibit an arbit…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
The Industrial Internet of Things drastically increases connectivity of devices in industrial applications. In addition to the benefits in efficiency, scalability and ease of use, this creates novel attack surfaces. Historically, industrial networks and protocols do not contain means of security, such as authentication…
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory…
Extends hyperparameter transfer across model sizes and modules, improving training speed.
problem Training stability and performance of large-scale models with optimal hyperparameters.
method Complete(d) Parameterisation, per-module hyperparameter optimisation and transfer. result Hyperparameter transfer holds even in the per-module hyperparameter regime, improving training speed.
Automates reparameterization in probabilistic programs for better inference.
problem Performance of inference algorithms is affected by parameterization, requiring manual and non-intuitive transformations.
method Automates non-centring and related reparameterizations using interleaved sampling and variational formulation.
result New inference algorithms yield more efficient samplers than fixed parameterizations across various models.
New approach improves linear-time attention for language models.
problem Challenges of quadratic attention in long-sequence modelling, especially for discrete data.
method Reinterpreting linear attention through latent probabilistic graphical models, introducing asymmetric structure and recurrent parameterisation.
result Our model achieves competitive performance and outperforms existing linear attention variants on language modelling benchmarks.
UWM-JEPA predicts future scenarios in belief space, improving accuracy in partially observed environments.
problem Predicting future scenarios in partially observed environments with uncertainty.
method Introduces UWM-JEPA, a JEPA world model with a density-matrix latent and learned unitary predictor.
result UWM-JEPA achieves 0.77 accuracy on a hidden-velocity indicator task, outperforming LSTM-JEPA.
New statistical model improves protein alignment accuracy.
problem Improving accuracy in protein sequence alignment.
method Inferred a time-dependent Markov process from protein sequences.
result Developed a new optimal matrix (MMLSUM) for protein alignment.
Robot learns multiple tasks hierarchically by transferring knowledge.
problem Learning multiple complex tasks in open-ended environments.
method Task-oriented procedures, goal-babbling, imitation learning, active learning, intrinsic motivation.
result Robots can learn complex tasks more efficiently by transferring knowledge from simpler ones.
Wide stochastic networks show Gaussian behavior and improve training with PAC-Bayesian methods.
problem Analyzing and training over-parameterised neural networks with large width.
method Establishing Gaussian behavior for a stochastic architecture, applying PAC-Bayesian training.
result PAC-Bayesian training on large but finite-width networks outperforms standard methods.
Study constant mean curvature tori in R^3 using spectral data and Whitham deformations.
problem Parameterize spectral data of constant mean curvature tori in R^3.
method Use Whitham deformations, blowups, and spectral data analysis.
result Prove the Wente family is parameterized by the bisector of the right angle.
Gaussian process model learns Hamiltonian systems from noisy data.
problem Learning Hamiltonian systems from long, noisy trajectories.
method Efficient decoupled parameterisation, energy-conserving shooting method.
result Robust inference from short and long trajectories.
PRZI traders adapt their quote-prices based on a strategy parameter s, affecting market dynamics.
problem Understanding the dynamics of continuous double auction markets with adaptive traders.
method Introduced a new zero-intelligence trader PRZI that uses a parameterised probability distribution to generate quote-prices. Used a stochastic hill-climber algorithm to adapt strategies based on market conditions.
result The co-evolutionary dynamics of PRZI traders can lead to rich and complex market behaviors, including periods of stability and change.
The paper introduces new topological obstructions for positive scalar curvature metrics on manifolds.
problem Obstructing the existence of Γ-invariant metrics of positive scalar curvature on manifolds.
method Formulating new topological obstructions using cohomology of classifying spaces for proper actions.
result Proving the conjecture for certain classes of groups and manifolds.
Linear generalisation error with network size in neural networks.
problem Understanding generalisation in over-parameterised neural networks.
method Teacher-student setup with SGD dynamics captured by differential equations.
result Generalisation error increases linearly with network size.
InfoNCE objective is equivalent to ELBO in RPM, linking to self-supervised learning.
problem Improving self-supervised learning methods by connecting them to variational inference.
method Recognizing RPM and showing InfoNCE as a simplified lower bound on MI, equal to ELBO in infinite sample limit.
result The actual InfoNCE objective is equal to the ELBO (up to a constant) in the infinite sample limit.
Study solves sub-Laplacian equivalence on a specific Heisenberg group.
problem Contact equivalence problem for sub-Laplacians on the second Heisenberg group.
method Solves the contact equivalence problem for generalised sub-Laplacians on $\He^2$.
result Parameterises sub-Laplacians on $\He^2$ by R+. We use an elliptic differential equation of Tzitzeica type to construct a minimal Lagrangian surface in CH2 from the data of a compact hyperbolic Riemann surface and a small holomorphic cubic differential. The minimal Lagrangian surface is invariant under an SU(2,1) action of the fundamental group. We further parameter…
New kernel interprets 3D anisotropic data with rotations and improved predictions.
problem Capturing rotated anisotropy in 3D spatial fields.
method Introduces a Lie-algebraic kernel with three principal length-scales and an explicit rotation.
result Posterior recovers rotated anisotropy and improves prediction over axis-aligned kernels.
A new method for discrete data normalizing flows using latent transformations.
problem Challenges in parameterizing bijective transformations for discrete data.
method Predict a distribution over latent transformations to make the marginal likelihood differentiable.
result Discrete-data normalizing flows can be trained using gradient-based learning with unbiased score function estimation.
Meta-gradient RL learns to learn from experience.
problem Learning efficiency and adaptability in reinforcement learning.
method Meta-gradient descent to discover its own objective function.
result Meta-gradient RL adapts to learn more efficiently over time.
Improves financial instrument pricing using neural networks.
problem Financial instrument pricing within Black-Karasinski model.
method Enhances path-integral approximation with neural networks.
result Demonstrates superior outcomes for multiple calibrations.
Automatically learns flexible symmetry constraints in neural networks using gradients.
problem Fixed hard constraints on neural network functions that cannot be adapted.
method Improves parameterisations of soft equivariance and optimizes marginal likelihood using differentiable Laplace approximations.
result Achieves equivalent or improved performance on image classification tasks compared to baselines with hard-coded symmetry.
Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on S×R by the cotangent bundle of the Teichmüller space of S, we study how some geometric quantities, such as the Lorentzian Hausdorff dimension of the limit set, the width of the convex core and the Hölder exponen…
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.
Study on projective structures on a hyperbolic 3-orbifold using tetrahedra.
problem Analyzing projective structures on hyperbolic 3-orbifolds.
method Parameterization using classical invariants, traces, and geometric cross ratios.
result Computed and analyzed the moduli space of projective structures.
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed PGL2(C) local systems on the associated marked bordered surface. We prove that the image of this map is contained in…
Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of…
Let Σ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce regular globally hyperbolic anti-de Sitter structures on Σ×R and provide two parameterisations of their deformation space: as an enhanced product of two copies of the Fricke space of Σ and as the b…
Let Σ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on Σ×R and provide two parameterisations of their deformation space: as a quotient of the product of two copies of the Teichmüller space of crowned …
We study a networked version of the minority game in which agents can choose to follow the choices made by a neighbouring agent in a social network. We show that for a wide variety of networks a leadership structure always emerges, with most agents following the choice made by a few agents. We find a suitable parameter…
Let S be a closed oriented surface of genus at least 2. Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on S×R by the cotangent bundle over the Teichmüller space of S, we study the behaviour of these geometric structures along pinching…
The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In t…
MDP Playground tests RL agents across various dimensions for better understanding and debugging.
problem Understanding and debugging reinforcement learning agents across diverse environments and dimensions.
method Controlled testbed with adjustable dimensions for different RL challenges.
result Insights into agent performance and interaction with various dimensions.
Study on SGD dynamics in neural networks, revealing generalisation patterns.
problem Understanding generalisation in over-parameterised neural networks.
method Analysis of SGD dynamics in a teacher-student setup using differential equations.
result Network size affects generalisation error differently depending on training layers and activation functions.
We study here the large-time behaviour of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviours of …
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of th…
The study connects specific circle embeddings to 4-manifold diffeomorphisms.
problem Understanding diffeomorphisms of 4-manifolds from specific circle embeddings.
method Using a parameterised surgery map to relate framed embeddings of S^1 to mapping class groups.
result Established connections between grasper families and known diffeomorphisms.
Classifies complex structures on SL(2,C), finding new non-regular ones.
problem Classifying complex structures on SL(2,C) up to automorphisms.
method Classification via Lie group automorphisms and topological analysis.
result Found one new, non-regular complex structure.
Study shows non-polyhedral structure in moduli spaces for n≥8.
problem Identifying non-polyhedral structure in moduli spaces of pointed stable curves.
method Constructing an extremal non-polyhedral ray via maps on meromorphic strata of differentials.
result Moduli spaces are not Mori Dream Spaces for n≥8.
Study of wild mapping class groups on complex reflection groups.
problem Understanding deformations of wild Riemann surfaces.
method Construction of configuration spaces and combinatorial fission forests.
result Sharp parameterisation of admissible deformation classes of wild Riemann surfaces.
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…
Directly estimates CQC, improving interpretability and accuracy.
problem Inability to model and interpret CQC due to inversion issue.
method Direct doubly robust estimation of CQC without inversion.
result Improved estimation accuracy and interpretability.
Let Γ be a finite group acting linearly on $\C^n$, freely outside the origin. In previous work a generalisation of Kronheimer's construction of moduli of Hermitian-Yang-Mills bundles with certain invariance properties was given. This produced varieties Xζ (parameterised by $ζ\in\Q^N$) which are partial resolutions…