arXiv AI
Jul 8
Transformers converge to invariant algorithmic cores
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
Hierarchical Grading in Large Language Models
arXiv:2607. 22757v1 Announce Type: cross Abstract: We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted scalar action through embeddings, self-attention, and the training objective.
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arXiv AI
Jun 11
Unifying Learning Dynamics and Generalization in Transformers Scaling Law
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
arXiv AI
4d ago
Demystifying LLM-as-a-Judge: Analytically Tractable Model for Inference-Time Scaling
arXiv:2512. 19905v3 Announce Type: replace-cross Abstract: Recent developments in large language models have shown advantages in reallocating a notable share of computational resource from training time to inference time.
arXiv AI
Sep 21
Large Language Models As Shannon Lossy Compressors Not Solomonoff Induction Estimators: The Singularity Is Not Near Without Symbolic Model Synthesis
The paper argues that Large Language Models (LLMs) do not function as Solomonoff induction estimators because their training objectives—cross‑entropy, negative log‑likelihood, and next‑token prediction—optimize fit to a supplied conditional distribution rather than a program‑weighted universal mixture. It further contends that additional computation alone does not transform these models into optimal predictors without external hyper‑parameter or architectural changes. The authors suggest that neurosymbolic machine learning, exemplified by models such as Fable and Astra, represents a shift toward symbolic model synthesis, moving beyond purely statistical LLMs.
arXiv AI
Sep 15
Large Language Models As Shannon Lossy Compressors Not Solomonoff Induction Estimators: The Singularity Is Not Near Without Symbolic Model Synthesis in Program Space
arXiv:2601.05280v4 Announce Type: replace-cross Abstract: On the one hand, the question of whether Large Language Models (LLMs) are Solomonoff induction estimators has become an explicit question at...
arXiv Machine Learning
Jul 23
On the Computational Complexity of Structural Generalization
arXiv:2607. 19573v1 Announce Type: cross Abstract: Structural generalization has been measured repeatedly by several benchmarks, yet it has never been formally defined.
arXiv AI
Aug 12
On Solomonoff Induction in Large Language Models and the Limits of Self-Improving: The Singularity Is Not Near Without Symbolic Model Synthesis
arXiv:2601. 05280v3 Announce Type: replace-cross Abstract: On the one hand, the question of whether large language models (LLMs) are Solomonoff induction estimators has become an explicit question at the intersection of Algorithmic Information Theory (AIT) and Machine Learning (ML) of great interest.
arXiv Machine Learning
Aug 11
Training-Free Universal Approximation by Prompting Random Transformers
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
arXiv Machine Learning
Jul 7
Equivalence of Context and Parameter Updates in Modern Transformer Blocks
arXiv:2511. 17864v3 Announce Type: replace Abstract: Recent research has established that the impact of context in a vanilla transformer can be represented implicitly by forming a token-dependent, rank-1 patch to its MLP weights.
arXiv Machine Learning
Aug 19
FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers
FishBack introduces a pullback Fisher geometry approach for activation steering in transformers, challenging the common Euclidean assumption of intermediate activation spaces. By deriving a closed‑form steering direction based on the Fisher information metric of the softmax layer, the method achieves target concept changes with minimal off‑target distortion, especially in early and middle layers. Experiments on GPT‑2 Small, Llama‑3‑8B, and Qwen3‑8B demonstrate significant reductions in off‑target KL divergence compared to existing steering baselines.
arXiv Machine Learning
Jun 19
Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling
arXiv:2606. 19354v1 Announce Type: cross Abstract: Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time.
arXiv Machine Learning
Sep 29
Mentored Decoding: Faster Inference meets Boosting
The paper introduces mentored decoding, a formal framework for lossy speculative decoding that can accelerate inference of autoregressive language models while potentially improving output quality. It connects this inference technique to boosting theory and extends it to all f‑divergences, revealing geometric insights for total variation, simple approximations tied to boosting compliance, and a divergence‑independent data structure enabling efficient optimal parameter queries and mentored distribution construction.