A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Formula for interleaving distance of rectangle persistence modules.
DAB enriches deep networks with uncertainty estimates using a codebook of training inputs.
Paper introduces DP TDA for near-optimal private persistence diagrams.
We prove that the space of persistence diagrams on points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dimension . Such an embedding enables utilisation of Hilbert space techniques on the space of persistence diagrams. We also prove that when …
Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessarily distort the metric on persistence diagrams. We show that persistence diagrams with the bottleneck distance do not even admit a coarse emb…
Study shows how non-uniform scaling affects persistence diagrams.
Maps persistence diagrams into Hilbert and Euclidean spaces with explicit distortions.
Graph rewiring method alleviates over-squashing in GNNs.
GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.
A new metric HSW derived from hierarchical Radon Transform addresses computational bottlenecks in sliced Wasserstein.
Topology-based information retrieval improves query accuracy.
New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.
A new algorithm reduces the size of datasets for TDA.
Study evaluates synthetic data augmentation for small datasets, highlighting inconsistencies in traditional metrics.
New framework improves experimental design using integral probability metrics.
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endo…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the p…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is…
New research shows non-bottlenecked autoencoders can outperform bottlenecked ones for anomaly detection.
Coupling the high-fidelity generation capabilities of label-conditional image synthesis methods with the flexibility of unconditional generative models, we propose a semantic bottleneck GAN model for unconditional synthesis of complex scenes. We assume pixel-wise segmentation labels are available during training and us…
GeoIB uses information geometry to control compression in deep learning models.
SCBMs model causal effects using low-dimensional bottlenecks.
A new invariant captures geometric features of circle embeddings.
Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an…
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the e…
The information bottleneck (IB) approach to clustering takes a joint distribution and maps the data to cluster labels which retain maximal information about (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their condit…
There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not apply to architectures that require one or more of the hidden layers to remain n…
Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly. Alignment-free methods, on the other hand, are based on abstract string comparisons …
Study shows bottlenecks improve image segmentation quality.
Deep ResNets favor low bottleneck rank with proper hyperparameters.
This paper analyzes speculative decoding, a method to speed up large language model inferences.
CB-APM uses analyst consensus as a bottleneck to interpret stock returns.
Auto-encoders are among the most popular neural network architecture for dimension reduction. They are composed of two parts: the encoder which maps the model distribution to a latent manifold and the decoder which maps the latent manifold to a reconstructed distribution. However, auto-encoders are known to provoke cha…
Paper compares dimension reduction methods using topological analysis on EEG data.
Paper improves Bayesian inference in federated learning with new algorithm VR-FALD*.
Wide neural networks become linear, but adding bottlenecks makes them bilinear or multilinear.
New method quantifies redundant information using information bottleneck.
Estimates path-valued data using signature metrics and local kernels.
The Mahler volume of a centrally symmetric convex body K is defined as M(K)= (Vol K)(Vol K^dual). Mahler conjectured that this volume is minimized when K is a cube. We introduce the bottleneck conjecture, which stipulates that a certain convex body K^diamond subset K X K^dual has least volume when K is an ellipsoid. If…
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. The information bottleneck has already been applied to doc…
MO2 learns useful behaviours from past experience for new tasks.
Graph neural networks struggle to propagate long-range information, causing over-squashing.
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expect…
MPNNs struggle with class-bottlenecks and heterophily, leading to performance limitations.
Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based reinforcement learning method which combines a learned, factorized …
Combining the Information Bottleneck model with deep learning by replacing mutual information terms with deep neural nets has proved successful in areas ranging from generative modelling to interpreting deep neural networks. In this paper, we revisit the Deep Variational Information Bottleneck and the assumptions neede…
Proposes Decodable Information Bottleneck for optimal representation learning.
We introduce the HSIC (Hilbert-Schmidt independence criterion) bottleneck for training deep neural networks. The HSIC bottleneck is an alternative to the conventional cross-entropy loss and backpropagation that has a number of distinct advantages. It mitigates exploding and vanishing gradients, resulting in the ability…