On the Fundamental Limits of LLMs at Scale

• URL: http://arxiv.org/abs/2511.12869v1
• Date: Mon, 17 Nov 2025 01:55:33 GMT
• Title: On the Fundamental Limits of LLMs at Scale
• Authors: Muhammad Ahmed Mohsin, Muhammad Umer, Ahsan Bilal, Zeeshan Memon, Muhammad Ibtsaam Qadir, Sagnik Bhattacharya, Hassan Rizwan, Abhiram R. Gorle, Maahe Zehra Kazmi, Ayesha Mohsin, Muhammad Usman Rafique, Zihao He, Pulkit Mehta, Muhammad Ali Jamshed, John M. Cioffi,
• Abstract summary: Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations.<n>This work presents a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling.<n>We show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment.
• Score: 15.459708840379975
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5) multimodal misalignment. While existing surveys describe these phenomena empirically, they lack a rigorous theoretical synthesis connecting them to the foundational limits of computation, information, and learning. This work closes that gap by presenting a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling. First, computability and uncomputability imply an irreducible residue of error: for any computably enumerable model family, diagonalization guarantees inputs on which some model must fail, and undecidable queries (e.g., halting-style tasks) induce infinite failure sets for all computable predictors. Second, information-theoretic and statistical constraints bound attainable accuracy even on decidable tasks, finite description length enforces compression error, and long-tail factual knowledge requires prohibitive sample complexity. Third, geometric and computational effects compress long contexts far below their nominal size due to positional under-training, encoding attenuation, and softmax crowding. We further show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment. Across sections, we pair theorems and empirical evidence to outline where scaling helps, where it saturates, and where it cannot progress, providing both theoretical foundations and practical mitigation paths like bounded-oracle retrieval, positional curricula, and sparse or hierarchical attention.

Related papers

• CHIMERA: Compact Synthetic Data for Generalizable LLM Reasoning [44.519834940763964]
  CHIMERA is a compact synthetic reasoning dataset comprising 9K samples for generalizable cross-domain reasoning.<n>It has broad and structured coverage, spanning 8 major scientific disciplines and over 1K fine-grained topics organized via a model-generated hierarchical taxonomy.<n>It achieves strong performance on a suite of challenging reasoning benchmarks, including GPQA-Diamond, AIME 24/25/26, HMMT 25, and Humanity's Last Exam.
  arXiv  Detail & Related papers  (2026-03-01T03:23:41Z)
• Accordion-Thinking: Self-Regulated Step Summaries for Efficient and Readable LLM Reasoning [62.680551162054975]
  We introduce an end-to-end framework where LLMs learn to self-regulate the granularity of the reasoning steps through dynamic summarization.<n>We apply reinforcement learning to incentivize this capability further, uncovering a critical insight: the accuracy gap between the highly efficient Fold mode and the exhaustive Unfold mode progressively narrows.<n>Our Accordion-Thinker demonstrates that with learned self-compression, LLMs can tackle complex reasoning tasks with minimal dependency token overhead.
  arXiv  Detail & Related papers  (2026-02-03T08:34:20Z)
• Reasoning about Reasoning: BAPO Bounds on Chain-of-Thought Token Complexity in LLMs [16.81068280262534]
  In-time scaling via chain-of-thought (CoT) reasoning is a major driver of state-of-the-art LLM performance, but it comes with substantial latency and compute costs.<n>We address a fundamental theoretical question: how many reasoning tokens are required to solve a problem as input size grows?<n>We prove lower bounds on the CoT tokens required for three canonical BAPO-hard tasks: binary majority, triplet matching, and graph reachability.
  arXiv  Detail & Related papers  (2026-02-02T23:33:34Z)
• Solving Inequality Proofs with Large Language Models [42.667163027148916]
  Inequality proving is crucial across diverse scientific and mathematical fields.<n>This makes it a demanding frontier for large language models (LLMs)<n>We release IneqMath, an expert-curated dataset of Olympiad-level inequalities.
  arXiv  Detail & Related papers  (2025-06-09T16:43:38Z)
• Has LLM Reached the Scaling Ceiling Yet? Unified Insights into LLM Regularities and Constraints [0.0]
  Large Language Models (LLMs) have demonstrated remarkable capabilities, yet their scalability raises a critical question: Have we reached the scaling ceiling?<n>This paper develops a unified theoretical framework that integrates mathematical and statistical insights to explain the scaling dynamics of LLMs.<n>Future progress will require a shift from brute-force scaling to innovations in architecture, data quality, and training paradigms.
  arXiv  Detail & Related papers  (2024-12-21T02:19:07Z)
• Near-Optimal Solutions of Constrained Learning Problems [85.48853063302764]
  In machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy dual robustness variables. Our results show that rich parametrizations effectively mitigate non-dimensional, finite learning problems.
  arXiv  Detail & Related papers  (2024-03-18T14:55:45Z)
• On the Nonconvexity of Push-Forward Constraints and Its Consequences in Machine Learning [1.4061979259370274]
  The push-forward operation enables one to redistribute a probability measure through a map.<n>It plays a key role in statistics and: many problems from optimal transport impact to generative modeling.<n>This paper aims at helping researchers better understand predictors or algorithmic learning problems.
  arXiv  Detail & Related papers  (2024-03-12T10:06:48Z)
• Predicting Emergent Abilities with Infinite Resolution Evaluation [85.89911520190711]
  We introduce PassUntil, an evaluation strategy with theoretically infinite resolution, through massive sampling in the decoding phase. We predict the performance of the 2.4B model on code generation with merely 0.05% deviation before training starts. We identify a kind of accelerated emergence whose scaling curve cannot be fitted by standard scaling law function.
  arXiv  Detail & Related papers  (2023-10-05T02:35:00Z)
• Causal Triplet: An Open Challenge for Intervention-centric Causal Representation Learning [98.78136504619539]
  Causal Triplet is a causal representation learning benchmark featuring visually more complex scenes. We show that models built with the knowledge of disentangled or object-centric representations significantly outperform their distributed counterparts.
  arXiv  Detail & Related papers  (2023-01-12T17:43:38Z)
• Scaling Laws for Deep Learning [1.90365714903665]
  In this thesis we take a systematic approach to address the algorithmic and methodological limitations at the root of these costs. We first demonstrate that deep learning training and pruning are predictable and governed by scaling laws. We then show through the exploration of a noiseless realizable case that DL is in fact dominated by error sources very far from the lower error limit.
  arXiv  Detail & Related papers  (2021-08-17T15:37:05Z)
• Constrained Learning with Non-Convex Losses [119.8736858597118]
  Though learning has become a core technology of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced solutions.
  arXiv  Detail & Related papers  (2021-03-08T23:10:33Z)
• Lagrangian Duality for Constrained Deep Learning [51.2216183850835]
  This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. In energy domains, the combination of Lagrangian duality and deep learning can be used to obtain state-of-the-art results. In transprecision computing, Lagrangian duality can complement deep learning to impose monotonicity constraints on the predictor.
  arXiv  Detail & Related papers  (2020-01-26T03:38:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.