arXiv research

Deep neural networks for natural language processing tasks are vulnerable to adversarial input perturbations. In this paper, we present a versatile language for programmatically specifying string transformations -- e.g., insertions, deletions, substitutions, swaps, etc. -- that are relevant to the task at hand. We then…

STRING improves 2D and 3D position encodings for better performance.

In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby determine global conditions for the existence of T-duals in heterotic string theory. In particular we find that T-duality exch…

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbol…

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponenti…

We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well. In particular, several new equations together with known transformations genera…

Proves loop coproduct invariance under simple homotopy equivalences.

Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding …

Defines non-Abelian gerbes with connections for physical applications.

Classifies colored links and spatial graphs up to colored link-homotopy.

The anholonomic frame method is generalized for non--Riemannian gravity models defined by string corrections to the general relativity and metric-affine gravity (MAG) theories. Such spacetime configurations are modeled as metric-affine spaces provided with generic off-diagonal metrics (which can not be diagonalized by …

Machine learning refactors knowledge to improve learning efficiency.

This paper compares Transformers and RNNs in various tasks, showing size differences.

Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been show…

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely define…

Finiteness predicts dualities in quantum gravity.

QP perspective on Poisson-Lie T-duality topology changes.

Derives path integrals for perturbative strings on various backgrounds.

Identifies all perturbative vacua in bosonic string theory.

Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.

Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.

String geometry theory connects strings to space-time and finds string vacua.

This paper applies knot theory to modern yo-yo play.

Derives path-integrals for superstrings on curved backgrounds using string geometry theory.

Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.

Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…

We prove all knots can be transformed into a trefoil using special diagrams.

We study Ricci flows of some classes of physically valuable solutions in Einstein and string gravity. The anholonomic frame method is applied for generic off-diagonal metric ansatz when the field/ evolution equations are transformed into exactly integrable systems of partial differential equations. The integral varieti…

A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connecti…

A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …

Randomized positional encodings boost transformer performance on longer sequences.

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

New formulas link string bordism to integers.

Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice virtual open string that is not ribbon. Definitions are extended to open n-strings.

BOSS optimizes string inputs using string kernels and genetic algorithms.

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…

String topology coproduct and Turaev cobracket computed for surfaces.

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connect…

Cobordism of virtual string links on $n$ strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$. This paper also shows that virtual string links up to unwelded equivalence are classified by those…

Paper shows string cobordism at 24 dims can be determined by elliptic genus.

We present a geometric approach to the field theory with higher order anisotropic interactions. The concepts of higher order space, or locally anisotropic, space (in brief, h-space, or la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimen…

Introduces string structures linking to loop spaces.

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…

A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We also discuss connections between virtual strings, Gauss words, and virtual knots.

Study topological G₂ and Spin(7) strings at 1-loop using double complexes.

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…

We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit …