The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes

Large Language Models (LLMs) have achieved strong performance across natural language processing tasks, yet reliable reasoning remains an open challenge. Although modern LLMs show progress in structured inference, multi-step problem solving, and contextual understanding, their reasoning behavior is often inconsistent and sensitive to prompting strategies, task design, and model scale. This survey provides a systematic analysis of more than 300 recent papers from arXiv, Semantic Scholar, Google Scholar, Papers with Code, and the ACL Anthology to examine how reasoning capabilities emerge in LLMs and where they fail. We make three main contributions. First, we introduce a structured taxonomy of LLM reasoning research, covering Chain-of-Thought reasoning, multi-hop reasoning, mathematical reasoning, common sense reasoning, visual and temporal reasoning, code and algorithmic reasoning, retrieval-augmented reasoning, tool-augmented and agentic reasoning, and reinforcement learning-based reasoning. Second, we analyze methodological trends across these paradigms, including prompting methods, model architectures, training objectives, reward modeling, and evaluation benchmarks. Third, we synthesize recurring limitations and failure modes, such as reasoning hallucinations, brittle multi-step inference, weak causal abstraction, and poor cross-domain generalization. By organizing a rapidly expanding literature, this survey offers a unified view of the current capabilities and limitations of reasoning in LLMs. We also identify emerging research directions, including meta-reasoning, self-evolving reasoning frameworks, multimodal reasoning, and socially grounded reasoning. Overall, this work aims to serve as a reference for developing more robust, interpretable, and generalizable reasoning systems in future language models.

ZIPP:Zero-shot Image Personalization from Personas

Text-to-image diffusion models are increasingly deployed in open-ended creative contexts, yet their outputs remain impersonal, optimized for aggregate aesthetics rather than individual taste. Human preferences are pluralistic: one user favoring muted, nostalgic portraits may prefer vibrant street photography, while another gravitates toward dreamy film aesthetics. Existing methods require dense interaction histories or per-user fine-tuning, failing in cold-start settings and collapsing context-dependent preferences into a static representation. We introduce zero-shot image personalization from personas (ZIPP), which conditions image generation on natural-language personas (concise descriptors of a user's identity and aesthetic sensibilities) without any user-specific data or weight updates. ZIPP uses an LLM to rewrite prompts from the perspective of a given persona, steering diffusion models toward personalized outputs. To mine personas at scale, we train an inductive Graph Attention Network over a 22M-user Reddit interaction graph with dual contrastive objectives aligning graph structure with visual behavior, then verbalize learned representations into natural-language personas via an MLLM. We introduce ZIPBench, the first zero-shot personalization benchmark with 1.5K users, graph-mined personas, and 40K generated images. Across four benchmarks and 14 LLMs spanning five model families, persona conditioning yields consistent gains (13-20%), with frontier models benefiting most. In the few-shot setting, ZIPP matches or exceeds fine-tuned baselines trained on 100+ examples per user. ZIPP achieves the lowest preference distributional divergence (CMMD 0.16 vs. 0.55), and IPF-normalized demographic evaluation shows it substantially reduces subpopulation bias present in existing methods. Human evaluation confirms a 79% win rate over generic generation and 58-65% over all fine-tuned baselines.

Bridging Expert Knowledge and Automated Feature Engineering via Self-Evolution

In high-stakes settings such as brand compliance, clinical care, and content moderation, machine learning cannot be deployed as opaque oracles: practitioners inspect the features driving model decisions, and models must leverage the expert documentation governing these domains. In practice, the data arrives as unstructured content, and features extracted from it must be interpretable, discriminative, and aligned with what experts consider important. Existing methods fall short: they target tabular inputs, lack demonstrated expert alignment, and cannot operationalize qualitative criteria such as 'maintain professional tone' into precise features. We present FEST (Feature Engineering with Self-evolving Trees), combining dual-stream feature generation (semantic and deterministic), semantic deduplication, and tree-guided iterative evolution to discover auditable features from raw text and images. FEST leads in 17 of 20 classifier-task combinations across brand classification, content authenticity detection, and stress detection, with a mean gain of 4.2 pp over the strongest baseline across five classifiers. An LLM-as-judge evaluation shows FEST achieves 60-80% coverage of expert-designed brand features at strict semantic-alignment thresholds, corroborated by a human expert study rating features highly on relevance, clarity, and actionability. When seeded with expert guidelines, FEST refines qualitative criteria into operational features, improving accuracy by 6-12 pp on average across brands. To enable systematic evaluation of expert alignment in automated feature engineering, we release BrandGuide, the first dataset pairing expert-designed features with 1M+ assets across 2,683 brands. By grounding feature engineering in expert knowledge, FEST opens a practical pathway for interpretable ML in domains demanding human oversight.

IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning

Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited. We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi. Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages.

Better and Worse with Scale: How Contextual Entrainment Diverges with Model Size

Larger language models become simultaneously better and worse at handling contextual information -- better at ignoring false claims, worse at ignoring irrelevant tokens. We formalize this apparent paradox through the first scaling laws for contextual entrainment, the tendency of models to favor tokens that appeared in context regardless of relevance. Analyzing the Cerebras-GPT (111M-13B) and Pythia (410M-12B) model families, we find entrainment follows predictable power-law scaling, but with opposite trends depending on context type: semantic contexts show decreasing entrainment with scale, while non-semantic contexts show increasing entrainment. Concretely, the largest models are four times more resistant to counterfactual misinformation than the smallest, yet simultaneously twice as prone to copying arbitrary tokens. These diverging trends, which replicate across model families, suggest that semantic filtering and mechanical copying are functionally distinct behaviors that scale in opposition -- scaling alone does not resolve context sensitivity, it reshapes it.

Accelerating Social Science Research via Agentic Hypothesization and Experimentation

Data-driven social science research is inherently slow, relying on iterative cycles of observation, hypothesis generation, and experimental validation. While recent data-driven methods promise to accelerate parts of this process, they largely fail to support end-to-end scientific discovery. To address this gap, we introduce EXPERIGEN, an agentic framework that operationalizes end-to-end discovery through a Bayesian optimization inspired two-phase search, in which a Generator proposes candidate hypotheses and an Experimenter evaluates them empirically. Across multiple domains, EXPERIGEN consistently discovers 2-4x more statistically significant hypotheses that are 7-17 percent more predictive than prior approaches, and naturally extends to complex data regimes including multimodal and relational datasets. Beyond statistical performance, hypotheses must be novel, empirically grounded, and actionable to drive real scientific progress. To evaluate these qualities, we conduct an expert review of machine-generated hypotheses, collecting feedback from senior faculty. Among 25 reviewed hypotheses, 88 percent were rated moderately or strongly novel, 70 percent were deemed impactful and worth pursuing, and most demonstrated rigor comparable to senior graduate-level research. Finally, recognizing that ultimate validation requires real-world evidence, we conduct the first A/B test of LLM-generated hypotheses, observing statistically significant results with p less than 1e-6 and a large effect size of 344 percent.

LittiChoQA: Literary Texts in Indic Languages Chosen for Question Answering

Long-context question answering (QA) over literary texts poses significant challenges for modern large language models, particularly in low-resource languages. We address the scarcity of long-context QA resources for Indic languages by introducing LittiChoQA, the largest literary QA dataset to date covering many languages spoken in the Gangetic plains of India. The dataset comprises over 270K automatically generated question-answer pairs with a balanced distribution of factoid and non-factoid questions, generated from naturally authored literary texts collected from the open web. We evaluate multiple multilingual LLMs on non-factoid, abstractive QA, under both full-context and context-shortened settings. Results demonstrate a clear trade-off between performance and efficiency: full-context fine-tuning yields the highest token-level and semantic-level scores, while context shortening substantially improves throughput. Among the evaluated models, Krutrim-2 achieves the strongest performance, obtaining a semantic score of 76.1 with full context. While, in shortened context settings it scores 74.9 with answer paragraph selection and 71.4 with vector-based retrieval. Qualitative evaluations further corroborate these findings.

On Optimal Steering to Achieve Exact Fairness

To fix the 'bias in, bias out' problem in fair machine learning, it is important to steer feature distributions of data or internal representations of Large Language Models (LLMs) to ideal ones that guarantee group-fair outcomes. Previous work on fair generative models and representation steering could greatly benefit from provable fairness guarantees on the model output. We define a distribution as ideal if the minimizer of any cost-sensitive risk on it is guaranteed to have exact group-fair outcomes (e.g., demographic parity, equal opportunity)-in other words, it has no fairness-utility trade-off. We formulate an optimization program for optimal steering by finding the nearest ideal distribution in KL-divergence, and provide efficient algorithms for it when the underlying distributions come from well-known parametric families (e.g., normal, log-normal). Empirically, our optimal steering techniques on both synthetic and real-world datasets improve fairness without diminishing utility (and sometimes even improve utility). We demonstrate affine steering of LLM representations to reduce bias in multi-class classification, e.g., occupation prediction from a short biography in Bios dataset (De-Arteaga et al.). Furthermore, we steer internal representations of LLMs towards desired outputs so that it works equally well across different groups.

Spiritual-LLM : Gita Inspired Mental Health Therapy In the Era of LLMs

Traditional mental health support systems often generate responses based solely on the user's current emotion and situations, resulting in superficial interventions that fail to address deeper emotional needs. This study introduces a novel framework by integrating spiritual wisdom from the Bhagavad Gita with advanced large language model GPT-4o to enhance emotional well-being. We present the GITes (Gita Integrated Therapy for Emotional Support) dataset, which enhances the existing ExTES mental health dataset by including 10,729 spiritually guided responses generated by GPT-4o and evaluated by domain experts. We benchmark GITes against 12 state-of-the-art LLMs, including both mental health specific and general purpose models. To evaluate spiritual relevance in generated responses beyond what conventional n-gram based metrics capture, we propose a novel Spiritual Insight metric and automate assessment via an LLM as jury framework using chain-of-thought prompting. Integrating spiritual guidance into AI driven support enhances both NLP and spiritual metrics for the best performing LLM Phi3-Mini 3.2B Instruct, achieving improvements of 122.71% in ROUGE, 126.53% in METEOR, 8.15% in BERT score, 15.92% in Spiritual Insight, 18.61% in Sufficiency and 13.22% in Relevance compared to its zero-shot counterpart. While these results reflect substantial improvements across automated empathy and spirituality metrics, further validation in real world patient populations remains a necessary step. Our findings indicate a strong potential for AI systems enriched with spiritual guidance to enhance user satisfaction and perceived support outcomes. The code and dataset will be publicly available to advance further research in this emerging area.

Med-CoDE: Medical Critique based Disagreement Evaluation Framework

The emergence of large language models (LLMs) has significantly influenced numerous fields, including healthcare, by enhancing the capabilities of automated systems to process and generate human-like text. However, despite their advancements, the reliability and accuracy of LLMs in medical contexts remain critical concerns. Current evaluation methods often lack robustness and fail to provide a comprehensive assessment of LLM performance, leading to potential risks in clinical settings. In this work, we propose Med-CoDE, a specifically designed evaluation framework for medical LLMs to address these challenges. The framework leverages a critique-based approach to quantitatively measure the degree of disagreement between model-generated responses and established medical ground truths. This framework captures both accuracy and reliability in medical settings. The proposed evaluation framework aims to fill the existing gap in LLM assessment by offering a systematic method to evaluate the quality and trustworthiness of medical LLMs. Through extensive experiments and case studies, we illustrate the practicality of our framework in providing a comprehensive and reliable evaluation of medical LLMs.