A Critical Analysis of the Theoretical Framework of the Extreme Learning Machine

• URL: http://arxiv.org/abs/2406.17427v1
• Date: Tue, 25 Jun 2024 10:06:07 GMT
• Title: A Critical Analysis of the Theoretical Framework of the Extreme Learning Machine
• Authors: Irina Perfilievaa, Nicolas Madrid, Manuel Ojeda-Aciego, Piotr Artiemjew, Agnieszka Niemczynowicz,
• Abstract summary: We refute the proofs of two main statements and a dataset that provides a counterexample to the ELM learning algorithm. We provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.
• Score: 1.9503475832401784
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main statements, and we also create a dataset that provides a counterexample to the ELM learning algorithm and explain its design, which leads to many such counterexamples. Finally, we provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.

Related papers

• From Axioms to Algorithms: Mechanized Proofs of the vNM Utility Theorem [0.0]
  We implement the classical axioms of preference-completeness, transitivity, continuity, and independence.<n>Our formalization captures the mathematical structure of preference relations over lotteries.<n>This formalization provides a rigorous foundation for applications in economic modeling, AI alignment, and management decision systems.
  arXiv  Detail & Related papers  (2025-06-08T10:09:54Z)
• DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning [67.93945726549289]
  DeepTheorem is a comprehensive informal theorem-proving framework exploiting natural language to enhance mathematical reasoning.<n>DeepTheorem includes a large-scale benchmark dataset consisting of 121K high-quality IMO-level informal theorems and proofs.<n>We devise a novel reinforcement learning strategy (RL-Zero) explicitly tailored to informal theorem proving, leveraging the verified theorem variants to incentivize robust mathematical inference.
  arXiv  Detail & Related papers  (2025-05-29T17:59:39Z)
• FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models [17.919212265668783]
  We present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems.<n>We introduce a novel human-in-the-loop autoformalization pipeline that integrates statement autoformalization, semantic verification, and negation-based disproof filtering strategies.<n>Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations.
  arXiv  Detail & Related papers  (2025-05-05T15:37:00Z)
• Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models [86.45058529521258]
  OlymMATH is a novel Olympiad-level mathematical benchmark designed to rigorously test the complex reasoning capabilities of LLMs. OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions.
  arXiv  Detail & Related papers  (2025-03-27T11:20:17Z)
• Hypothesis-Driven Theory-of-Mind Reasoning for Large Language Models [76.6028674686018]
  We introduce thought-tracing, an inference-time reasoning algorithm to trace the mental states of agents. Our algorithm is modeled after the Bayesian theory-of-mind framework. We evaluate thought-tracing on diverse theory-of-mind benchmarks, demonstrating significant performance improvements.
  arXiv  Detail & Related papers  (2025-02-17T15:08:50Z)
• One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs [57.48325300739872]
  Leveraging mathematical Large Language Models for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples.
  arXiv  Detail & Related papers  (2025-02-12T02:01:10Z)
• Alchemy: Amplifying Theorem-Proving Capability through Symbolic Mutation [71.32761934724867]
  This work proposes Alchemy, a framework for data synthesis that constructs formal theorems through symbolic mutation. For each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M.
  arXiv  Detail & Related papers  (2024-10-21T08:04:21Z)
• On the Diagram of Thought [12.304069891580658]
  Current large language models (LLMs) demonstrate impressive capabilities but struggle with complex, multi-step reasoning tasks. We introduce the Diagram of Thought (DoT) as a framework wherein a single auto-regressive LLM internally constructs and navigates a Directed Acyclic Graph (DAG) We formalize the reasoning DAG as a diagram within a suitable topos and prove that the final step, aggregating validated information, corresponds semantically to computing the colimit of the relevant sub-diagram.
  arXiv  Detail & Related papers  (2024-09-16T07:01:41Z)
• The Foundations of Tokenization: Statistical and Computational Concerns [51.370165245628975]
  Tokenization is a critical step in the NLP pipeline. Despite its recognized importance as a standard representation method in NLP, the theoretical underpinnings of tokenization are not yet fully understood. The present paper contributes to addressing this theoretical gap by proposing a unified formal framework for representing and analyzing tokenizer models.
  arXiv  Detail & Related papers  (2024-07-16T11:12:28Z)
• ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models [67.32868432113587]
  This paper introduces ConceptMath, a fine-grained benchmark that evaluates concept-wise mathematical reasoning of Large Language Models (LLMs) Unlike traditional benchmarks that evaluate general mathematical reasoning with an average accuracy, ConceptMath systematically organizes math problems under a hierarchy of math concepts.
  arXiv  Detail & Related papers  (2024-02-22T16:06:49Z)
• Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms [13.857921574409362]
  We introduce a federated gradient EM algorithm (FedGrEM) designed for the unsupervised learning of mixture models. We present a comprehensive finite-sample theory that holds for general mixture models. We then apply this general theory on specific statistical models to characterize the explicit estimation error of model parameters and mixture proportions.
  arXiv  Detail & Related papers  (2023-10-23T19:53:36Z)
• Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning [79.83792914684985]
  We prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem.
  arXiv  Detail & Related papers  (2022-11-26T21:02:09Z)
• Representation Theory for Geometric Quantum Machine Learning [0.0]
  Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Geometric Quantum Machine Learning (GQML) will play a crucial role in developing problem-specific and quantum-aware models. We present an introduction to representation theory tools from the optics of quantum learning, driven by key examples involving discrete and continuous groups.
  arXiv  Detail & Related papers  (2022-10-14T17:25:36Z)
• Making Linear MDPs Practical via Contrastive Representation Learning [101.75885788118131]
  It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. We consider an alternative definition of linear MDPs that automatically ensures normalization while allowing efficient representation learning. We demonstrate superior performance over existing state-of-the-art model-based and model-free algorithms on several benchmarks.
  arXiv  Detail & Related papers  (2022-07-14T18:18:02Z)
• Efficient Performance Bounds for Primal-Dual Reinforcement Learning from Demonstrations [1.0609815608017066]
  We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. Existing inverse reinforcement learning methods come with strong theoretical guarantees, but are computationally expensive. We introduce a novel bilinear saddle-point framework using Lagrangian duality to bridge the gap between theory and practice.
  arXiv  Detail & Related papers  (2021-12-28T05:47:24Z)
• Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory [26.555110725656963]
  We show examples of Lieant's theorem, Lie groups, Lie algebras, and the Harish-Chandra--Itzyintegrals formulas. We then present an introduction to optimization theory -- an indispensable mathematical toolkit for capturing continuous symmetries.
  arXiv  Detail & Related papers  (2021-09-02T16:44:44Z)
• Training a First-Order Theorem Prover from Synthetic Data [50.23600875138756]
  A major challenge in applying machine learning to automated theorem proving is the scarcity of training data. We propose an approach that relies on training purely with synthetically generated theorems, without any human data aside from axioms. Our neural prover outperforms the state-of-the-art E-prover on this synthetic data in both time and search steps.
  arXiv  Detail & Related papers  (2021-03-05T17:01:34Z)
• Learning to Prove from Synthetic Theorems [41.74768503409581]
  A major challenge in applying machine learning to automated theorem proving is the scarcity of training data. We propose an approach that relies on training with synthetic theorems, generated from a set of axioms. We show that such theorems can be used to train an automated prover and that the learned prover transfers successfully to human-generated theorems.
  arXiv  Detail & Related papers  (2020-06-19T17:48:09Z)

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.