We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure as arising via the Born rule from a translation invariant matrix product state.
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48 results for “language invariance”
Triangulation filters spurious circuits in multilingual models.
problem Unreliable explanations of multilingual models across languages.
method Formalizes reference families and introduces triangulation as a causal acceptance rule.
result Triangulation provides a falsifiable standard for mechanistic claims.
We describe how to formulate Khovanov's functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts' Type D and Type A structures in Khovanov homology, and his algebra , in terms of Khovanov's theory of modules over …
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in fact organized in the language topological quantum field theory.
We explore Jaeger's state model for the HOMFLYPT polynomial. We reformulate this model in the language of Gauss diagrams and use it to obtain Gauss diagram formulas for a two-parameter family of Vassiliev invariants coming from the HOMFLYPT polynomial. These formulas are new already for invariants of degree 3.
We employ the language of Cartan's geometry to present a model for studying vector spaces of Killing two-tensors defined in pseudo-Riemannian spaces of constant curvature under the action of the corresponding isometry group. We also discuss geometric properties of joint invariants of Killing two-tensors defined in the …
A new sliced IGW distance for Gromov-Wasserstein alignment.
problem Scalability issues in Gromov-Wasserstein alignment for high-dimensional problems.
method Proposed a sliced IGW distance with rotational invariance.
result Natural rotational invariance of the sliced IGW distance.
SAM improves deep learning tasks by promoting balancedness, reducing outlier impact.
problem Improving generalization in deep learning tasks, especially with scale-invariant problems.
method Introduces balancedness as a new concept to depict global behaviors of SAM, focusing on the difference between squared norms of two variables.
result SAM promotes balancedness and is data-responsive, outperforming SGD in outlier scenarios.
Deep Sets improve reinforcement learning agent's object-centered navigation and generalization.
problem Improving reinforcement learning agents' ability to generalize to unseen objects and goals.
method Combining object-wise permutation invariant networks (Deep Sets) and gated-attention mechanisms.
result Agent demonstrates strong generalization to out-of-distribution goals in a procedurally-generated 2D world.
The paper proves impossibilities and positive results for universal machine translation.
problem Learning shared sentence representations across multiple language pairs.
method Formal proofs and analysis of natural generative processes.
result Lower bound on translation error and positive results under natural structure.
New proof and formula linking fusion trees to quantum knot invariants.
problem Quantum knot invariants encoding in non-semisimple TQC.
method Connection between fusion trees and Lawrence representations, using graphical calculus.
result Explicit encoding of quantum knot invariants via fusion trees.
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many finite recurrent communicating classes and define our language model as the invarian…
This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get solutions of the generalized string equation and dilation equation and their var…
Introduces optimization geometrodynamics for dynamic geometric optimization.
problem Gradient-based optimization methods struggle with changing geometric constraints.
method Optimization geometrodynamics separates invariant and improvable geometric mismatches.
result Dynamic geometric complexity measures the minimum geometric cost to reduce optimization difficulty.
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…
Graph-Linksmath.GT
The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. I…
We provide an alternative proof that Koschorke's -invariant is injective on the set of link homotopy classes of -component homotopy Brunnian links . The existing proof (by Koschorke \cite{Koschorke97}) is based on the Pontryagin--Thom theory of framed cobordisms, whereas ours is closer in spirit to techni…
The paper explores invariants of graph drawings in the plane.
problem Understanding the invariants of almost embeddings of graphs in the plane.
method Proves relations between invariants, connects to homology, constructs examples.
result Constructs almost embeddings realizing some values of invariants.
Deterministic Inference across Tensor Parallel Sizes That Eliminates Training-Inference Mismatchcs.LG
New method ensures consistent inference across different tensor parallel sizes for large language models.
problem Non-deterministic inference in large language models due to inconsistent reduction orders across GPUs.
method Tree-Based Invariant Kernels (TBIK) that align intra- and inter-GPU reduction orders through a unified hierarchical binary tree structure.
result Bit-wise identical results across different tensor parallel sizes for RL training.
Starting from considering deeper relationship between conjugacy classes and irreducible representations of a finite group , we find some quite simple matrice defined by using finite groups. This construction produces many sets (or topological spaces) admitting braid group actions. We introduce conceptions "exten…
New approach connects 3D Chern-Simons theory to spectral networks.
problem Understanding Chern-Simons invariants in 3D manifolds.
method Constructing equivalences between bundles and spectral networks.
result New formulas for Chern-Simons invariants of 3D manifolds.
Two environments are enough to infer causal graphs and counterfactuals.
problem Inferring causal relations from multiple environments, especially for nonlinear mechanisms.
method Using structural causal models and the invariance principle, the study shows that only two auxiliary environments are sufficient for causal graph inference and counterfactual inference.
result Two auxiliary environments are sufficient for identifying causal graphs and counterfactuals.
The paper explains how continuous language models can produce discrete, interpretable meanings.
problem Semantic collapse in continuous systems of large language models.
method Formalizing large language models as Continuous State Machines (CSMs) and analyzing the associated transfer operator.
result The leading eigenfunctions of the transfer operator induce a finite number of invariant meaning basins, explaining how continuous computation can produce discrete, interpretable semantics.
STRING improves 2D and 3D position encodings for better performance.
problem Efficient and accurate position encoding for 2D and 3D applications.
method STRING extends Rotary Position Encodings with a unifying theoretical framework, maintaining translation invariance and low computational cost.
result STRING shows substantial gains in open-vocabulary object detection and robotics.
New approach uses compressible dynamics to train deep models efficiently.
problem Efficient training of deep overparameterized models with low-rank structures.
method Leveraging low-dimensional structures and compressible dynamics within model parameters.
result Improved training efficiency and reduced overfitting in language models.
Data augmented bootstrap: Unifying confidence interval construction by approximate invariancestat.ME
Data augmented bootstrap unifies various confidence interval construction methods.
problem Constructing confidence intervals from data transformations.
method Data augmented bootstrap (DAB) framework.
result Establishes theoretical coverage results for DAB methods.
Holographic Invariant Storage: Design-Time Safety Contracts via Vector Symbolic Architecturesstat.ML
Holographic Invariant Storage uses vector architectures to ensure LLM safety at design time.
problem Mitigating context drift in large language models (LLMs) during deployment.
method Introduces Holographic Invariant Storage (HIS) protocol that combines known properties of bipolar Vector Symbolic Architectures into a design-time safety contract.
result Closed-form guarantees for single-signal recovery fidelity, continuous-noise robustness, and multi-signal capacity degradation are provided and validated.
New ASR system handles multiple languages without needing language-specific encoding.
problem Joint training of data-rich and data-scarce languages in a single model.
method Transforms all languages to a single writing system through transliteration, separating modeling and rendering.
result Language-agnostic multilingual ASR system reduces WER up to 10% over language-dependent models.
Floer Field Philosophymath.SG
Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey provides an introduction to the categorical language for the construction and extension…
Study quantifies gender bias in language models across 7 languages.
problem Measuring gender bias in language models across multiple languages.
method Curated dataset of politicians, multilingual language models, probing language models.
result Larger language models do not show significant gender bias compared to smaller ones.
Data-driven models and computational tools for neurolinguistics: a language technology perspectivecs.LG
Paper reviews neurolinguistics and language technologies, emphasizing mutual enrichment.
problem Understanding brain activity during language processing.
method Brain imaging studies and natural language representations.
result Development of brain-aware natural language representations.
The systematic study of CR manifolds originated in two pioneering 1932 papers of Élie Cartan. In the first, Cartan classifies all homogeneous CR 3-manifolds, the most well-known case of which is a one-parameter family of left-invariant CR structures on , deforming the standard `spherical' structure…
New method adapts neural networks without losing prior knowledge.
problem Understanding and enabling flexible adaptation of neural networks.
method Differential geometry framework, functionally invariant paths (FIP).
result Achieves comparable state-of-the-art performance on continual learning and sparsification tasks.
New technique reduces language biases in large language models.
problem Gap between language and thought in large language models.
method Proposes Language-of-Thoughts (LoT) technique to adjust order and tokens.
result Significantly reduces language biases and improves reasoning tasks.
When a bilingual student learns to solve word problems in math, we expect the student to be able to solve these problem in both languages the student is fluent in,even if the math lessons were only taught in one language. However, current representations in machine learning are language dependent. In this work, we pres…
Paper introduces TrufLL for language model training without labeled data.
problem Training language models from scratch with reinforcement learning.
method Dynamic vocabulary truncation in RL for language generation.
result TrufLL successfully learns language generation policies from scratch.
We formulate a more conceptual interpretation of the Cappell-Lee-Miller glueing/splitting theorem using the new language of asymptotic maps and asymptotic exactness. Additionally, we present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local soluti…
Intelligence emerges from stabilizing invariant cycles in memory.
problem Understanding the nature of intelligence and its emergence.
method Structural-dynamical account rooted in a topological closure law: \(\partial^2=0\).
result Memory-amortized inference (MAI) mechanism that implements SbS \(
ightarrow\) CCUP.
We study a variation of Bagchi and Datta's -vector of a simplicial complex , whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of . We show that these invariants satisfy an Alexander-Dehn-Sommerville type identity, and behave nicely under natural operations on triangulated…
System identifies language of transliterated text.
problem Users struggle to understand non-native language transliterated text.
method Feature extraction of phonetic syllables using LSTM network.
result System accurately identifies language of transliterated text.
LLMs translate natural language trading intents into correct option strategies using a domain-specific language.
problem Challenges in translating natural language trading intents into correct option strategies due to the complexity of option chain data.
method Introduce Option Query Language (OQL) as a domain-specific intermediate representation to abstract option markets into high-level primitives under grammatical rules. Use LLMs as semantic parsers and validate queries by an engine.
result Significantly improves execution accuracy and logical consistency over direct baselines.
New findings show language models can't simultaneously avoid hallucinations and capture all language richness.
problem Achieving both valid output and full language richness in language generation.
method Investigates language generation within a statistical setting, focusing on consistency and breadth.
result For most collections of candidate languages, a language model cannot simultaneously avoid hallucinations and capture all language richness.
This paper proposes a new method to connect language and physical actions in reinforcement learning.
problem Connecting linguistic representations to the physical world in embodied agents.
method Language-conditioned goal generators to decouple sensorimotor learning from language acquisition.
result Agents can demonstrate a diversity of behaviors for any given instruction.
Julia accelerates machine learning in various fields with balance of efficiency and simplicity.
problem Efficiency and simplicity in machine learning algorithms.
method Developed and applied Julia language in machine learning.
result Julia balances efficiency and simplicity for machine learning.
Neural language modeling (LM) has led to significant improvements in several applications, including Automatic Speech Recognition. However, they typically require large amounts of training data, which is not available for many domains and languages. In this study, we propose a multilingual neural language model archite…
The paper applies math and physics to language models, introducing entropy and geometric concepts.
problem Understanding and improving language models to approximate intelligent language.
method Formal definitions, functional analysis, topology, thermodynamics, and set theory.
result Entropy function reveals key obstacles for LLMs and offers insights into language models.
Multilingual end-to-end (E2E) models have shown great promise in expansion of automatic speech recognition (ASR) coverage of the world's languages. They have shown improvement over monolingual systems, and have simplified training and serving by eliminating language-specific acoustic, pronunciation, and language models…
Benchmark tests spoken language models for infant language learning.
problem Understanding how infants learn language from speech.
method Developed a language-acquisition-friendly benchmark.
result Benchmarking shows models' strengths and weaknesses.