New language model shows context length impacts generation quality and reasoning ability.
problem Analyzing the impact of context length and reasoning on autoregressive generation.
method Introduced synthetic hierarchical languages, used an exact k-gram ansatz, derived asymptotic predictions, and validated empirically.
result Reasoning models with limited context can generate sequences from the true language, improving exponentially over standard models.
This study examines how sequential correlations affect in-context learning in sequence models.
problem Understanding how in-context learning works with sequentially correlated data.
method Extended linear regression model to sequentially correlated data, tested on transformer architectures.
result Sequential correlations alter the effective context length and attention architecture effectiveness.
Paper proposes linear transformers for efficient in-context learning without context length limitations.
problem Quadratic complexity of softmax transformers limits data processing speed.
method Investigates linear transformers under domain generalization, showing they learn mappings from context distributions to response functions.
result Linear transformers achieve in-context learning with a linear complexity in context length, offering a dimension-independent convergence rate.
Mamba struggles with long context lengths, but spectrum scaling improves performance.
problem Mamba's performance degrades with increasing context length.
method Spectrum scaling applied to pre-trained Mamba models to improve long-context generalization.
result Spectrum scaling significantly improves performance in long-context settings.
New insights into how depth and width affect in-context learning in deep models.
problem Understanding how various resources impact in-context learning in deep models.
method Analyzed linear regression in a deep linear self-attention model, varying resources like depth, width, context length, and training steps.
result Increasing depth improves in-context learning even at infinite context length, contrary to previous findings.
The paper tackles long-context linear system identification with improved sample complexity bounds.
problem Identifying dynamical systems with long dependencies over fixed context windows.
method Established sample complexity bounds for systems with linear dependencies over a context window of length p.
result The learning process is not hindered by slow mixing properties in extended context windows.
Transformer learns context and regularization for ICL in inverse problems.
problem Learning context and effective regularization for transformer-based in-context learning (ICL) in inverse problems.
method Introduced a linear transformer to learn inverse mapping from contextual examples to weight vectors, addressing rank-deficient problems.
result Transformer implicitly learns a prior distribution and effective regularization strategy, outperforming traditional methods.
New insights into attention mechanisms reveal dramatic trade-offs between rank and heads.
problem Dramatic trade-offs between rank and number of heads in attention mechanisms.
method Presented a simple target function and proved theoretical limits.
result Full-rank attention is necessary for long contexts, while low-rank is sufficient for short ones.
We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichmüller space and strictly convex for generic laminations. We give some consequences of this result in the context of Thurston's asymmetric metric on Teichmüller space.
Unified framework for critical scaling of inverse temperature in self-attention.
problem Conflicting inverse-temperature laws for long-context self-attention.
method Counting gaps and defining an upper-tail accumulation scale.
result Critical inverse-temperature scale determined by gap-counting function.
Transformers converge linearly to optimal models for Gaussian mixtures classification.
problem Theoretical understanding of transformers' in-context classification.
method Gradient descent training of a single-layer transformer for Gaussian mixtures classification.
result Transformers converge linearly to globally optimal models for Gaussian mixtures classification.
Establishes a version of Bartnik's conjecture for Lorentzian length spaces.
problem Proving Bartnik's conjecture for Lorentzian length spaces.
method Using timelike completeness and non-negative timelike curvature bounds, the causal boundary is shown to be a single point.
result A globally hyperbolic Lorentzian length space splits as a metric Lorentzian product.
We present a technique for clustering categorical data by generating many dissimilarity matrices and averaging over them. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other techniques that have been proposed. Then we give conditions under which our method shoul…
Shorter adversarial prompts help protect LLMs from jailbreak attacks.
problem Protecting large language models from jailbreak attacks with long adversarial suffixes.
method Adversarial training on shorter adversarial suffixes to defend against longer adversarial suffixes.
result Aligning LLMs on shorter adversarial suffixes can effectively defend against jailbreak attacks with longer suffixes.
Random Transformers behave like polynomial models in ICL with asymptotic growth.
problem Understanding in-context learning capabilities of pretrained Transformers.
method Asymptotic analysis of a random Transformer with a fixed first layer and a trained second layer, considering growth in context length, input dimension, hidden dimension, and training parameters.
result The random Transformer's ICL error is equivalent to a finite-degree Hermite polynomial model.
A two-step approach efficiently selects hyperparameters for FCMs.
problem Efficiently selecting hyperparameters for FCMs in a computationally expensive process.
method Two-step sequential approach: first estimate context length k, then estimate α.
result The proposed method achieves comparable compression performance to exhaustive search but with reduced computational cost.
Transformers have a potential of learning longer-term dependency, but are limited by a fixed-length context in the setting of language modeling. We propose a novel neural architecture Transformer-XL that enables learning dependency beyond a fixed length without disrupting temporal coherence. It consists of a segment-le…
Study finds phase transition in context-sensitive language model with short-range interactions.
problem Understanding phase transitions in language models with short-range interactions.
method Constructed a random language model with short-range interactions and investigated its statistical properties.
result Phase transition occurs in context-sensitive language models with constant context length.
The study provides precise asymptotic theory for in-context learning by Transformers.
problem Understanding the sample complexity, pretraining task diversity, and context length for successful in-context learning.
method An exactly solvable model of linear regression task by linear attention, deriving sharp asymptotics.
result Double-descent learning curve with increasing pretraining examples, phase transition between low and high task diversity regimes.
Randomized positional encodings boost transformer performance on longer sequences.
problem Transformers struggle with generalizing to sequences of arbitrary length.
method Introduced randomized positional encodings that simulate longer sequences and randomly select positions.
result Randomized positional encodings increase test accuracy by 12.0% on average for sequences of unseen length.
Following \cite{citeSavelyevVirtualMorsetheoryonOmegaHam(Momega).}, we develop here a connection between Morse theory for the (positive) Hofer length functional L:ΩHam(M,ω)→R, with Gromov-Witten/Floer theory, for monotone symplectic manifolds (M,ω). This gives some immediate restrictio…
This paper evaluates LLMs on large graph property estimation tasks.
problem Limited context length of LLMs limits their evaluation on large graphs.
method Developed EstGraph dataset and introduced four tasks for LLMs to estimate large graph properties.
result LLMs perform better on graph property estimation tasks when provided with context-rich prompts based on random walks.
Our goal is to show, in two different contexts, that "random" surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus g for which any pants decomposition requires curves of total length at least g7/6−ε. Moreover, we prove that this bound holds for most metrics in the…
The abstract discusses a new type of space and its properties.
problem The abstract tackles the concept of non-Hilbertian (Lorentzian) length spaces.
method The abstract introduces a new type of space and analyzes its properties.
result The abstract finds that normed spaces without inner products have no sectional curvature bounds.
New framework handles dynamic contexts in reinforcement learning.
problem Learning in environments where contexts change over time.
method Dynamic Contextual Markov Decision Processes (DCMDPs) with logistic aggregation.
result Upper-confidence-bound style algorithm with regret bounds.
The study examines how extra compute during testing affects the performance of large language models.
problem Understanding the conditions under which test-time scaling improves model performance.
method An in-context weight prediction task for linear regression was used to train transformers. The performance was analyzed under varying levels of test-time compute.
result Training transformers on diverse, relevant, and hard tasks leads to the best performance for test-time scaling.
Task hinting improves transformer performance on longer tasks.
problem Transformers struggle with length generalization for certain tasks.
method Simultaneously train on a related auxiliary task during main task training.
result Significant improvement in length generalization for sorting tasks.
Transformers can be hijacked by context, but deeper models are more robust.
problem Robustness of Transformers against context hijacking for linear classification.
method Developed a theoretical analysis on the robustness of linear transformers, considering model depth, training context lengths, and number of hijacking context tokens.
result Deeper transformers are more robust to context hijacking.
This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these restaurants. Each day the same number of agents sequentially arrives and decides w…
Paper explores how uncertainty quantification improves Transformer's in-context learning ability.
problem Understanding and quantifying in-context learning ability of Transformers.
method Revisit linear regression tasks with bi-objective prediction (conditional expectation and variance).
result Trained Transformers achieve near Bayes-optimum performance, suggesting use of training distribution.
Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.
problem Challenging problems require deeper reasoning, but how do models generalize this to longer tasks?
method Theoretical analysis of transformers on synthetic state-tracking tasks, proving length generalization through attention concentration.
result Transformers can learn chain-of-thought reasoning for longer problems, proving length generalization.
The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.
problem Understanding and quantifying the dynamics of different market regimes in equity markets.
method Data-driven Hilbert--Huang Transform for regime identification, Holo--Hilbert Spectral Analysis for profiling, and Variable-Length Markov Chains for return dynamics modeling.
result Developed markets normalize more effectively as stress subsides, while developing markets retain residual tail dependence and downside persistence.
Paper studies how few pretraining tasks are needed for a linear model to solve new tasks.
problem How many pretraining tasks are needed for a linear model to solve new tasks?
method Pretrained a linear attention model for linear regression with a Gaussian prior.
result Effective pretraining requires a small number of independent tasks, and the model closely matches Bayes optimal.
New statistical models for predicting ranked preferences from partial orders.
problem Statistical models overlook information in list length.
method Composite and augmented ranking models for joint modeling of partial orders and list lengths.
result Augmented ranking models best predict both length and preferences.
Bayesian analysis reveals epistemic uncertainty as a key diagnostic for delayed generalization in in-context learning.
problem Delayed generalization in in-context learning from few examples.
method Bayesian perspective, modular arithmetic tasks, approximate Bayesian techniques, spectral mechanism analysis.
result Epistemic uncertainty collapses sharply when the model groks, indicating a practical diagnostic of generalization.
I-BERT extends Transformer's self-attention to arbitrary input lengths.
problem Transformer models struggle with inductive generalization to unseen input lengths.
method Replaces positional encodings with a recurrent layer.
result I-BERT achieves state-of-the-art results on algorithmic tasks.
New framework shows cross-attention improves multi-modal in-context learning.
problem Understanding multi-modal in-context learning in neural networks.
method Mathematical framework and linearized cross-attention mechanism.
result Cross-attention mechanism is provably optimal for multi-modal in-context learning.
The paper proves how Transformers learn from context and generalize well.
problem Understanding how Transformers generalize from diverse tasks.
method Developed a statistical theory for in-context learning, separating risk into Bayes Gap and Posterior Variance.
result The Posterior Variance is task-independent, and the Bayes Gap decreases with more in-context examples.
The paper explores how magnetic systems' spectra can identify metrics and 1-forms.
problem Can the marked magnetic action spectrum of magnetic systems with Anosov flow determine the metric and 1-form?
method The paper addresses this question in two settings: locally for systems with close metrics and 1-forms, and for metrics in the same conformal class.
result The paper answers the question affirmatively in both settings.
We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar construction of Clerc and Ørsted, is functorial and well-behaved under products; these …
Persistent homology enhances graph classification by capturing long-range graph properties.
problem Lack of formal assessment of persistent homology in graph learning.
method Brief introduction and theoretical discussion of persistent homology in graph context, followed by empirical analysis.
result Persistent homology improves graph classification, especially for data with prominent topological structures.
In this paper, we present our method of using fixed-size ordinally forgetting encoding (FOFE) to solve the word sense disambiguation (WSD) problem. FOFE enables us to encode variable-length sequence of words into a theoretically unique fixed-size representation that can be fed into a feed forward neural network (FFNN),…
Defines metrics for Lorentzian spaces and explores maximal developments.
problem Defining metrics and maximal developments in Lorentzian spaces.
method Defining Lorentzian spaces and using functorial properties.
result Explicit non-spacetime example of maximal globally hyperbolic Lorentzian space.
New method finds closed timelike geodesics on Lorentzian manifolds.
problem Existence of closed timelike geodesics in Lorentzian geometry.
method Introducing timelike geodesic homotopy and combining with a local length argument.
result Provides new results on the existence of closed timelike geodesics.
Study reveals how depth of reasoning affects generalization in models.
problem Understanding scaling behavior of generalization with CoT depth.
method Theoretical model of CoT in linear regression using random matrix theory.
result Sharp phase transition between exponential and polynomial improvement, saturation, and overthinking.
Timer-XL predicts multidimensional time series using a unified Transformer approach.
problem Unified time series forecasting across various tasks and contexts.
method Decoder-only Transformers with a universal TimeAttention mechanism and deft position embedding.
result State-of-the-art performance across multiple forecasting benchmarks.
FibQuant improves KV-cache compression for long-context inference.
problem Memory traffic bottleneck in long-context inference due to KV cache growth.
method Introduces FibQuant, a universal vector quantizer that combines Beta-quantile radii, Fibonacci/Roberts-Kronecker directions, and Lloyd-Max refinement.
result FibQuant achieves high compression rates with minimal loss in attention cosine similarity.
Transformers prefer simpler explanations in hierarchical tasks.
problem Navigating tasks with varying complexity levels.
method Well-controlled testbeds based on Markov chains and linear regression.
result Transformers favor the least complex sufficient explanation when presented with simpler data.