New method maps protein sequences to embeddings encoding structural information.
problem Inferring structural properties from amino acid sequences when structures are unknown.
method Representation learning using bidirectional LSTM models with structural similarity and residue contact maps.
result Trained embeddings improve structural similarity prediction and transfer to other tasks.
Proposes a validator model to ensure valid sequences in deep generative models.
problem Invalid sequences hinder the utility of deep generative models for discrete spaces.
method Introduces a deep recurrent validator model to estimate sequence validity and constrain model output.
result Demonstrates improved validity in Python code and molecular structures.
BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we sh…
iStructTab improves multimodal learning by optimizing feature sequencing.
problem Redundancy, dispersion, and generalization issues in multimodal learning of images and tabular data.
method Graph-Enhanced Descriptor Sequencing (GEDS) algorithm that refines statistical descriptors through similarity graph-based computations.
result iStructTab effectively minimizes feature dispersion, improving predictive performance and robustness.
Study pinching sequences to understand degeneration of anti-de Sitter structures.
problem Understanding the degeneration of anti-de Sitter structures along pinching sequences.
method Parameterization of deformation space and analysis of pinching sequences.
result Regular anti-de Sitter structures appear as limiting points.
CF-VAE models capture multi-modal distributions for better structured sequence prediction.
problem Challenges in capturing multi-modality of future states in latent variable models.
method Conditional Flow Variational Autoencoders (CF-VAE) with conditional normalizing flows.
result CF-VAE achieves state-of-the-art results on multi-modal structured sequence prediction datasets.
Seq-SetNet processes sequence sets directly, improving protein structure prediction.
problem Processing sequence sets (MSAs) for structural inference without considering sequence order.
method Developed a symmetric function module to integrate features from MSAs.
result Seq-SetNet outperforms state-of-the-art approaches by 3.6% in precision.
GCRN models graph-structured sequences with CNN and RNN.
problem Predicting structured sequences of data.
method Combines CNN and RNN on graphs.
result Improves precision and learning speed.
ProteinNet provides a standardized data set for protein structure prediction.
problem Lack of standardized data sets for protein structure prediction.
method Created high-quality sequence alignments, multiple data splits, and validation sets.
result Facilitates fair assessment of machine learning models for protein structure.
Derives Atiyah sequence for noncommutative bundles.
problem Deciding when ∗-automorphisms lift to compatible ones. method Derivation-based Atiyah sequence derivation.
result Validates existence of compatible lifts.
Develops a hybrid model for text summarization.
problem Summarizing long text sequences concisely.
method Extends sequence encoders with a graph component to handle long-distance relationships in text.
result Hybrid models outperform pure sequence or graph models on summarization tasks.
Investigates conditions for spectral sequence degeneracy in holomorphic Poisson structures.
problem Conditions for spectral sequence degeneracy in holomorphic Poisson structures.
method Uses Lie bi-algebroids, generalized complex structures, and hypercohomology of bi-complexes.
result Investigates conditions for spectral sequence degeneracy on the first page.
This research tackles uncertainty estimation in autoregressive structured prediction tasks.
problem Ensuring safety and robustness of AI systems through accurate uncertainty estimation.
method Develops a unified probabilistic ensemble-based framework for token-level and sequence-level uncertainty estimation.
result Provides baselines for error and out-of-domain detection on translation and speech recognition datasets.
Introduces hierarchical uncertainty using U-sequences.
problem Tackles Ellsberg's paradox in multi-layer uncertainty.
method Uses category theory to construct U-sequences and endofunctors.
result Constructs a universal uncertainty space for multi-layer uncertainty.
Convolutional network predicts DNA chromatin structure from sequence images.
problem Predicting chromatin structure from DNA sequences.
method Developed a convolutional neural network using image-representation of DNA sequences.
result The method outperforms existing methods in prediction accuracy and training time.
We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical Kähler structure.
Partial AHS-structures extend G-structures and Cartan geometries to manifolds with involutive distributions.
problem Extending G-structures and Cartan geometries to manifolds with involutive distributions.
method Developing a canonical Cartan geometry for partial AHS-structures and constructing BGG sequences.
result Partial AHS-structures have analogs of BGG sequences, providing fine resolutions of sheaves.
Bayesian context trees capture complex dependencies in categorical sequences.
problem Complex, long-range dependencies in categorical sequences are not well captured by simple models.
method Parsimonious Bayesian context trees with model-based agglomerative clustering for efficient inference.
result The proposed framework outperforms existing models on real-world data.
ECL improves sequence modeling by learning evolutionary structure.
problem Ignoring evolutionary structure in sequence modeling leads to suboptimal performance.
method ECL progressively exposes models to sequences of increasing evolutionary distance.
result ECL improves performance across multiple biological domains and tasks.
ProGen models protein sequences for synthetic biology.
problem Generating proteins without structural annotations.
method Trained a 1.2B-parameter language model on 280M protein sequences.
result ProGen generates proteins with fine-grained control and accuracy.
AbDiffuser generates full-atom antibodies with sequence and structure fidelity.
problem Generating high-fidelity antibodies with both structure and sequence information.
method Equivariant and physics-informed diffusion model with novel protein structure representation.
result AbDiffuser generates antibodies with sequence and structural properties matching a reference set.
Model structures on multicomplexes help study complex geometry.
problem Understanding homotopy types of complex manifolds.
method Model category structures on N-multicomplexes with weak equivalences induced by quasi-isomorphisms. result Establishes a basis for studying almost and generalized complex manifolds.
We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de-Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geome…
Unimodal sequences of moves connect 3-manifold triangulations.
problem Understanding the structure of sequences of bistellar flips.
method Examined unimodal sequences of moves that increase and decrease triangulation size.
result Proved that any two one-vertex triangulations are connected by a unimodal sequence of moves.
Introduces internal Lagrangians for differential equations and connects them to presymplectic structures.
problem Understanding the geometry of differential equations and their solutions.
method Develops a spectral sequence related to internal Lagrangians and investigates connections to presymplectic structures.
result Interprets a term in Vinogradov's spectral sequence for gauge theories.
Cloned HMMs efficiently learn variable order sequences without local minima issues.
problem Learning long-term temporal structure in sequences.
method Constrained HMMs with a sparsity structure that maps hidden states deterministically to emissions.
result Cloned HMMs can model temporal dependencies at arbitrarily long distances and recognize contexts with 'holes'.
CODE2SEQ generates natural language sequences from code snippets.
problem Generating natural language descriptions from code.
method CODE2SEQ represents code as AST paths and uses attention to select relevant paths.
result CODE2SEQ outperforms previous models for code-to-text tasks.
Improves neural machine translation using bandit learning and attention.
problem Learning from partial feedback in neural sequence-to-sequence learning.
method Lifts linear bandit learning to neural sequence-to-sequence problems with attention and control variates.
result Improves BLEU score by up to 5.89 points for domain adaptation.
Study on the structure of classifier boundaries in DNA sequencing.
problem Understanding the structure of boundaries in a Bayes classifier for DNA sequencing.
method Examined the structure of the boundary in a Bayes classifier applied to DNA sequencing data. Introduced a new measure of uncertainty, Neighbor Similarity.
result The boundary is large and complex, and Neighbor Similarity effectively measures classifier uncertainty.
New method learns both module structure and sequencing in neural networks.
problem Learning only the parameters and order of execution of neural modules.
method Expands the approach to learn the internal structure of modules, including the ordering and combination of arithmetic operators.
result Performance comparable to hand-designed modules achieved without extra supervisory signals.
One of the basic problems in studying topological structures of deformation spaces for Kleinian groups is to find a criterion to distinguish convergent sequences from divergent sequences. In this paper, we shall give a sufficient condition for sequences of Kleinian groups isomorphic to surface groups to diverge in the …
Unsupervised framework learns symmetry from time sequences.
problem Learning symmetry from time sequences without labeled data.
method Meta-sequential prediction (MSP) framework that leverages stationary properties.
result Hidden disentangled structure emerges as a by-product of training.
New BGG sequences on manifolds help solve elasticity and relativity problems.
problem Develop numerical methods for elasticity and relativity.
method Generalized BGG sequences on manifolds.
result Constructs BGG sequences on Riemannian manifolds and manifolds with connections.
S3Attention improves long sequence attention with smoothed skeleton sketching.
problem Quadratic complexity of vanilla Attention makes it unsuitable for long sequence tasks.
method S3Attention uses smoothing and matrix sketching to balance information preservation and computation. result S3Attention significantly outperforms vanilla Attention and other Attention variants. GPT learns a causal world model from token predictions, validated in game sequences.
problem Does GPT implicitly learn a causal world model from token predictions?
method Derived a causal interpretation of GPT's attention mechanism and proposed zero-shot causal structure learning.
result GPT can generate legal next moves with high confidence for sequences with encoded causal structures, but fails for illegal moves.
A holomorphic Poisson structure induces a deformation of the complex structure as Hitchin's generalized geometry. Its associated cohomology naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is the Dolbeault cohomology with coefficients in the exterior a…
Transformers learn causal structure through gradient descent on self-attention mechanisms.
problem Understanding how transformers learn causal structure during training.
method In-context learning task and simplified two-layer transformer model.
result Gradient descent on a simplified transformer learns to encode latent causal graphs.
Study approximates sub-Riemannian structures with Riemannian metrics and analyzes spectral convergence.
problem Approximating sub-Riemannian structures for analysis.
method Constructing Riemannian metrics tailored to sub-Riemannian structures and studying spectral convergence.
result Riemannian volumes converge to Popp's volume and spectral convergence of Laplace operators is studied.
Szabó recently introduced a combinatorially-defined spectral sequence in Khovanov homology. After reviewing its construction and explaining our methodology for computing it, we present results of computations of the spectral sequence. Based on these computations, we make a number of conjectures concerning the structure…
Study examines linear Poisson structures tied to W*-algebras.
problem Understanding fiber-wise linear Poisson structures related to W*-algebras.
method Investigates structures defined by W*-algebra structure and shows their arrangement in a short exact sequence of VB-groupoids.
result Fiber-wise linear Poisson structures are arranged in a short exact sequence of VB-groupoids.
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
problem Accurately predicting changes in protein binding affinity due to mutations.
method Sequence-based machine learning approach using protein sequence information.
result PANDA achieves higher Pearson correlation coefficients than existing methods.
Study the relationship between canonical polynomials and elliptic sequences for elliptic singularities.
problem Understanding the relationship between canonical polynomials and elliptic sequences for elliptic singularities.
method An inductive setup of elliptic germs and comparison of their canonical polynomials.
result The exponents of the canonical polynomial determine the elliptic sequence and vice versa under certain conditions.
ASRNN adapts scales dynamically for better sequence modeling.
problem Fixed scales in multiscale RNNs don't match temporal patterns.
method Adaptively learns and adjusts scales based on temporal contexts.
result ASRNNs yield better performances with dynamical scaling.
Study sequences of static spacetimes using null distance convergence.
problem How to define convergence for sequences of spacetimes.
method Define null distance metric space structure compatible with Lorentzian structure.
result Prove VADB theorem for sequences of static spacetimes with null distance.
The study extends hypoellipticity to filtered manifolds and applies it to BGG sequences.
problem Analyzing hypoellipticity on general filtered manifolds.
method Extending Rockland criterion to pseudodifferential calculus, constructing parametrix, generalizing BGG machinery.
result Generalized BGG sequences are Rockland in a graded sense.
New diffiety theory leads to a well-posed KP hierarchy.
problem Formalizing diffieties for better hierarchy analysis.
method Definition of diffiety based on Frolicher structures.
result Formation of a well-posed Kadomtsev-Petviashvili hierarchy.
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…
Proves a conjecture for a specific group using spectral sequences and homology.
problem Proves the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4.
method Used the Adams spectral sequence and detection theorems to compute connective real k-homology.
result Determines differentials of the Adams spectral sequence and studies the cap structure of relevant sub-hopf algebras.