NPO enables stable unlearning of 50%+ training data in LLMs on TOFU by making collapse exponentially slower than gradient ascent, preserving sensible outputs where prior methods fail.
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KTO: Model Alignment as Prospect Theoretic Optimization
Canonical reference. 73% of citing Pith papers cite this work as background.
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Pith papers citing it
Background
73% of classified citations
abstract
Kahneman & Tversky's $\textit{prospect theory}$ tells us that humans perceive random variables in a biased but well-defined manner (1992); for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them belonging to a family of loss functions that we call $\textit{human-aware losses}$ (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach KTO, and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B, despite only learning from a binary signal of whether an output is desirable. More broadly, our work suggests that there is no one HALO that is universally superior; the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.
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- abstract Kahneman & Tversky's $\textit{prospect theory}$ tells us that humans perceive random variables in a biased but well-defined manner (1992); for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them belonging to a family of loss functions that we call $\textit{human-aware losses}$ (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect th
- method ate a base set of N responses, denoted as Dbase = {(x, ri, ai)}N i=1, where ri is the textual response anda i ∈ Ais the corresponding attribute. To embed the target distributionP∗ into the train- ing data, we explicitly control the generation fre- quency such that the count Nk of responses exhibit- ing attributea k satisfies: Nk =round(N·P ∗(ak|x))(6) For instance, given a target distribution of {Male: 0.99, Female: 0.01} and N= 100 , Dbase will contain 99 responses with the Male attribute and 1
- method policy log-probability ratios against pairwise preference data relative to a fixed reference model. This reformulation reduces alignment to a stable classification-style objective while retaining strong em- pirical performance. As a result, DPO has inspired a growing family of reference-based, reward-free alignment methods, including IPO [11], KTO [12], SimPO [13], ORPO [14], and iterative or online variants such as SPIN [15]. Preprint. arXiv:2605.08037v1 [cs.LG] 8 May 2026 The pairwise and list
- background non-linear optimization problems involving phys- ical dynamics. We follow a scalable backtrans- lation based synthetic data generation strategy described in Section 3.2. 2.3. RL for Reasoning and Code Generation Group Relative Policy Optimization (GRPO) [31] eliminates the critic model from PPO [32] by sampling groups of outputs and normalizing ad- vantages within each group; DeepSeek-R1 [33] showed that complex reasoning strategies emerge from GRPO with verifiable rewards alone, and Dr. GRPO [3
- background Orpo: Monolithic preference optimization without reference model. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 11170-11189, 2024. [63] Yu Meng, Mengzhou Xia, and Danqi Chen. Simpo: Simple preference optimization with a reference-free reward.Advances in Neural Information Processing Systems, 37:124198- 124235, 2024. [64] Kawin Ethayarajh, Winnie Xu, Niklas Muennighoff, Dan Jurafsky, and Douwe Kiela. Kto: Model alignment as prospect theoretic opti
- background [172] Chongyu Fan, Yihua Zhang, Jinghan Jia, Alfred Hero, and Sijia Liu. Cyclicreflex: Im- proving large reasoning models via cyclical reflection token scheduling. arXiv preprint arXiv:2506.11077, 2025. [173] Siqi Fan, Peng Han, Shuo Shang, Yequan Wang, and Aixin Sun. Cothink: Token-efficient reasoning via instruct models guiding reasoning models. arXiv preprint arXiv:2505.22017, 2025. [174] Tiantian Fan, Lingjun Liu, Yu Yue, Jiaze Chen, Chengyi Wang, Qiying Yu, Chi Zhang, Zhiqi Lin, Ruofei Zhu,
- background [59] proposed a two-stage strat- egy combining SFT and Feasibility-and-Optimality-Aware Reinforcement Learning (FOARL) to guide LLMs and improve solution quality. 3.2.2 Reinforcement Learning RL strategies are introduced to enhance model robustness. To address hallucina- tion issues in LLMs, Jiang et al. [60] incorporated Kahneman-Tversky Optimization (KTO) [61] along with self-correction mechanisms, and proposed LLMOPT, which has been validated across six real-world datasets spanning 20 domains
co-cited works
representative citing papers
ORPO performs preference alignment during supervised fine-tuning via a monolithic odds ratio penalty, allowing 7B models to outperform larger state-of-the-art models on alignment benchmarks.
CrossVLA introduces a surrogate log-probability estimator to enable DPO on flow-matching VLAs, reports DoRA yielding +10.4 pp mean gains over SFT on LIBERO with 600 trials, and shows inference caching limited to 21% speedup with some strategies harming success rates.
DPO-RLHF equivalence holds only conditionally on the optimal policy preferring human-preferred responses; otherwise DPO optimizes relative advantage and can prefer worse outputs, addressed by introducing CPO.
Pion modifies Muon's Newton-Schulz iterations into a controllable high-pass filter that anchors dominant singular values at 1 while suppressing noisy tails, outperforming Muon and AdamW in VLA and RLVR regimes.
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
TBPO posits a token-level Bradley-Terry model and derives a Bregman-divergence density-ratio matching loss that generalizes DPO while preserving token-level optimality.
dGRPO merges outcome-based policy optimization with dense teacher guidance from on-policy distillation, yielding more stable long-context reasoning on the new LongBlocks synthetic dataset.
Introduces Block-R1 benchmark, Block-R1-41K dataset, and a conflict score to handle domain-specific optimal block sizes in RL post-training of diffusion LLMs.
PNAPO augments preference data with prior noise pairs and uses straight-line interpolation to create a tighter surrogate objective for offline alignment of rectified flow models.
The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
PairAlign learns compact audio token sequences via self-alignment of paired content views using an autoregressive decoder, achieving strong cross-view consistency and edit-distance preservation while reducing token count by 55% on TIMIT.
Standard DPO surrogates are inconsistent for equicontinuous neural nets; SA-DPO provides structure-aware H-consistency bounds by adapting margins to semantic distance and shows heavy-tailed losses yield superior guarantees for capacity-bounded models via the Margin-Capacity Profile.
RLHF should decompose annotations into dimensions each matched to one of three models—extension, evidence, or authority—instead of applying a single unified pipeline.
HiPO improves LLM reasoning performance by optimizing preferences separately on response segments rather than entire outputs.
DDO-RM turns reward scores into a target distribution and applies KL-regularized mirror-descent projection on finite candidates to improve policies, outperforming DPO on Pythia-410M.
CapTrack shows post-training causes drift beyond facts, with instruction fine-tuning producing stronger behavioral changes than preference optimization across model families.
EyeMulator augments CodeLLM fine-tuning loss with token weights derived from human eye-tracking scan paths, producing large gains on code translation and summarization across StarCoder, Llama-3.2 and DeepSeek-Coder.
Magpie synthesizes 300K high-quality alignment instructions from Llama-3-Instruct via auto-regressive prompting on partial templates, enabling fine-tuned models to match official instruct performance on AlpacaEval, ArenaHard, and WildBench.
COALA applies convex optimization reformulations of neural networks to direct preference optimization, claiming single-GPU training with ~18% of DPO's TFLOPs and competitive performance on multiple datasets and models up to 8B parameters.
Introduces AIR, an asymmetric regularization that anchors open-ended safety prompts to verifiable ones via stop-gradient, improving invariance and accuracy when combined with group preference optimization.
DEFLECT is an offline post-training method that improves async VLA policy success rates under high inference delays by using flow-matching likelihood ratios on counterfactual fresh/stale action pairs from a frozen reference policy.
GPRL carries a k-dimensional skew-symmetric preference structure into policy updates with per-dimension advantages and a drift monitor, yielding 56.51% length-controlled win rate on AlpacaEval 2.0 from Llama-3-8B-Instruct while outperforming SimPO and SPPO on other benchmarks.
Super-Linear Advantage Shaping (SLAS) introduces a non-linear geometric policy update for RL post-training of text-to-image models that reshapes the local policy space via advantage-dependent Fisher-Rao weighting to reduce reward hacking and improve performance over GRPO baselines.
citing papers explorer
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Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning
NPO enables stable unlearning of 50%+ training data in LLMs on TOFU by making collapse exponentially slower than gradient ascent, preserving sensible outputs where prior methods fail.
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ORPO: Monolithic Preference Optimization without Reference Model
ORPO performs preference alignment during supervised fine-tuning via a monolithic odds ratio penalty, allowing 7B models to outperform larger state-of-the-art models on alignment benchmarks.
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CrossVLA: Cross-Paradigm Post-Training and Inference Optimization for Vision-Language-Action Models
CrossVLA introduces a surrogate log-probability estimator to enable DPO on flow-matching VLAs, reports DoRA yielding +10.4 pp mean gains over SFT on LIBERO with 600 trials, and shows inference caching limited to 21% speedup with some strategies harming success rates.
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Conditional Equivalence of DPO and RLHF: Implicit Assumption, Failure Modes, and Provable Alignment
DPO-RLHF equivalence holds only conditionally on the optimal policy preferring human-preferred responses; otherwise DPO optimizes relative advantage and can prefer worse outputs, addressed by introducing CPO.
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Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR
Pion modifies Muon's Newton-Schulz iterations into a controllable high-pass filter that anchors dominant singular values at 1 while suppressing noisy tails, outperforming Muon and AdamW in VLA and RLVR regimes.
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Learning from Language Feedback via Variational Policy Distillation
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
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TokenRatio: Principled Token-Level Preference Optimization via Ratio Matching
TBPO posits a token-level Bradley-Terry model and derives a Bregman-divergence density-ratio matching loss that generalizes DPO while preserving token-level optimality.
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Combining On-Policy Optimization and Distillation for Long-Context Reasoning in Large Language Models
dGRPO merges outcome-based policy optimization with dense teacher guidance from on-policy distillation, yielding more stable long-context reasoning on the new LongBlocks synthetic dataset.
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Block-R1: Rethinking the Role of Block Size in Multi-domain Reinforcement Learning for Diffusion Large Language Models
Introduces Block-R1 benchmark, Block-R1-41K dataset, and a conflict score to handle domain-specific optimal block sizes in RL post-training of diffusion LLMs.
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Offline Preference Optimization for Rectified Flow with Noise-Tracked Pairs
PNAPO augments preference data with prior noise pairs and uses straight-line interpolation to create a tighter surrogate objective for offline alignment of rectified flow models.
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Rethinking Importance Sampling in LLM Policy Optimization: A Cumulative Token Perspective
The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
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PairAlign: A Framework for Sequence Tokenization via Self-Alignment with Applications to Audio Tokenization
PairAlign learns compact audio token sequences via self-alignment of paired content views using an autoregressive decoder, achieving strong cross-view consistency and edit-distance preservation while reducing token count by 55% on TIMIT.
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Mind the Gap: Structure-Aware Consistency in Preference Learning
Standard DPO surrogates are inconsistent for equicontinuous neural nets; SA-DPO provides structure-aware H-consistency bounds by adapting margins to semantic distance and shows heavy-tailed losses yield superior guarantees for capacity-bounded models via the Margin-Capacity Profile.
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Three Models of RLHF Annotation: Extension, Evidence, and Authority
RLHF should decompose annotations into dimensions each matched to one of three models—extension, evidence, or authority—instead of applying a single unified pipeline.
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HiPO: Hierarchical Preference Optimization for Adaptive Reasoning in LLMs
HiPO improves LLM reasoning performance by optimizing preferences separately on response segments rather than entire outputs.
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DDO-RM: Distribution-Level Policy Improvement after Reward Learning
DDO-RM turns reward scores into a target distribution and applies KL-regularized mirror-descent projection on finite candidates to improve policies, outperforming DPO on Pythia-410M.
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CapTrack: Multifaceted Evaluation of Forgetting in LLM Post-Training
CapTrack shows post-training causes drift beyond facts, with instruction fine-tuning producing stronger behavioral changes than preference optimization across model families.
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EyeMulator: Improving Code Language Models by Mimicking Human Visual Attention
EyeMulator augments CodeLLM fine-tuning loss with token weights derived from human eye-tracking scan paths, producing large gains on code translation and summarization across StarCoder, Llama-3.2 and DeepSeek-Coder.
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Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing
Magpie synthesizes 300K high-quality alignment instructions from Llama-3-Instruct via auto-regressive prompting on partial templates, enabling fine-tuned models to match official instruct performance on AlpacaEval, ArenaHard, and WildBench.
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Convex Optimization for Alignment and Preference Learning on a Single GPU
COALA applies convex optimization reformulations of neural networks to direct preference optimization, claiming single-GPU training with ~18% of DPO's TFLOPs and competitive performance on multiple datasets and models up to 8B parameters.
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Towards Context-Invariant Safety Alignment for Large Language Models
Introduces AIR, an asymmetric regularization that anchors open-ended safety prompts to verifiable ones via stop-gradient, improving invariance and accuracy when combined with group preference optimization.
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DEFLECT: Delay-Robust Execution via Flow-matching Likelihood-Estimated Counterfactual Tuning for VLA Policies
DEFLECT is an offline post-training method that improves async VLA policy success rates under high inference delays by using flow-matching likelihood ratios on counterfactual fresh/stale action pairs from a frozen reference policy.
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General Preference Reinforcement Learning
GPRL carries a k-dimensional skew-symmetric preference structure into policy updates with per-dimension advantages and a drift monitor, yielding 56.51% length-controlled win rate on AlpacaEval 2.0 from Llama-3-8B-Instruct while outperforming SimPO and SPPO on other benchmarks.
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Power Reinforcement Post-Training of Text-to-Image Models with Super-Linear Advantage Shaping
Super-Linear Advantage Shaping (SLAS) introduces a non-linear geometric policy update for RL post-training of text-to-image models that reshapes the local policy space via advantage-dependent Fisher-Rao weighting to reduce reward hacking and improve performance over GRPO baselines.
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Training-Free Cultural Alignment of Large Language Models via Persona Disagreement
DISCA converts within-country disagreement among World Values Survey personas into a bounded logit correction that reduces cultural misalignment by 10-24% on MultiTP for models 3.8B and larger across 20 countries, without any weight updates.
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Positive Alignment: Artificial Intelligence for Human Flourishing
Positive Alignment introduces AI systems that support human flourishing pluralistically and proactively while remaining safe, as a necessary complement to traditional safety-focused alignment research.
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Team-Based Self-Play With Dual Adaptive Weighting for Fine-Tuning LLMs
TPAW uses teams of current and historical model checkpoints that collaborate and compete, plus adaptive weightings for responses and players, to improve self-supervised LLM alignment and outperform baselines.
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Beyond Pairs: Your Language Model is Secretly Optimizing a Preference Graph
GraphDPO generalizes pairwise DPO to a graph-structured Plackett-Luce objective over DAGs induced by rollout rankings, enforcing transitivity with linear complexity and recovering DPO as a special case.
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Threshold-Guided Optimization for Visual Generative Models
A threshold-guided alignment method lets visual generative models be optimized directly from scalar human ratings instead of requiring paired preference data.
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Gradient-Gated DPO: Stabilizing Preference Optimization in Language Models
Gate-DPO attenuates gradients on low-probability rejected responses to reduce probability collapse and improve chosen-response likelihood during preference optimization.
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Multilingual Safety Alignment via Self-Distillation
MSD enables cross-lingual safety transfer in LLMs via self-distillation with Dual-Perspective Safety Weighting, improving safety in low-resource languages without target response data.
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PERSA: Reinforcement Learning for Professor-Style Personalized Feedback with LLMs
PERSA combines RLHF with selective parameter-efficient updates to top transformer layers, raising style alignment scores from 35% to 96% on code feedback benchmarks while holding correctness near 100%.
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Model Organisms Are Leaky: Perplexity Differencing Often Reveals Finetuning Objectives
Perplexity gaps between finetuned and reference models on random-prefill completions often reveal the original finetuning objectives across diverse model organisms.
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Aligning Language Models for Lyric-to-Melody Generation with Rule-Based Musical Constraints
Rule-generated preference data aligned via sequential DPO and KTO reduces musical constraint violations and improves coherence in lyric-to-melody generation over baselines.
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Representation-Guided Parameter-Efficient LLM Unlearning
REGLU guides LoRA-based unlearning via representation subspaces and orthogonal regularization to outperform prior methods on forget-retain trade-off in LLM benchmarks.
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AutoOR: Scalably Post-training LLMs to Autoformalize Operations Research Problems
AutoOR uses synthetic data generation and RL post-training with solver feedback to enable 8B LLMs to autoformalize linear, mixed-integer, and non-linear OR problems, matching larger models on benchmarks.
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Bridging What the Model Thinks and How It Speaks: Self-Aware Speech Language Models for Expressive Speech Generation
SA-SLM uses variational information bottleneck for intent-aware bridging and self-criticism for realization-aware alignment to close the semantic-acoustic gap, outperforming open-source models and nearing GPT-4o-Audio expressiveness on EchoMind after training on 800 hours of data.
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Pioneer Agent: Continual Improvement of Small Language Models in Production
Pioneer Agent automates the full lifecycle of adapting and continually improving small language models via diagnosis-driven data synthesis and regression-constrained retraining, delivering gains of 1.6-83.8 points on benchmarks and large lifts in production-style tasks.
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Target Policy Optimization
TPO constructs a target distribution q proportional to the old policy times exp(utility) and trains the policy to match it via cross-entropy, matching or beating PPO and GRPO especially under sparse rewards.
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Controlling Distributional Bias in Multi-Round LLM Generation via KL-Optimized Fine-Tuning
A hybrid fine-tuning objective using KL divergence for token calibration and Kahneman-Tversky optimization for semantic binding enables LLMs to produce outputs that match desired attribute distributions across repeated prompts.
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rePIRL: Learn PRM with Inverse RL for LLM Reasoning
rePIRL learns effective process reward models for LLM reasoning via a dual policy-PRM update process inspired by inverse RL, unifying online and offline methods with reported gains over prior approaches on math and coding datasets.
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f-GRPO and Beyond: Divergence-Based Reinforcement Learning Algorithms for General LLM Alignment
f-GRPO and f-HAL estimate f-divergences between reward-aligned and reward-unaligned response distributions and prove expected reward improvement for general LLM alignment.
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Multiplayer Nash Preference Optimization
MNPO extends NLHF to multiplayer Nash games, inheriting equilibrium guarantees while showing empirical gains on instruction-following benchmarks under diverse preferences.
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RLBFF: Binary Flexible Feedback to bridge between Human Feedback & Verifiable Rewards
RLBFF extracts binary principles from human feedback to train reward models that outperform Bradley-Terry models on RM-Bench and JudgeBench and enable customizable inference-time focus for LLM alignment.
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LLM Hypnosis: Exploiting User Feedback for Unauthorized Knowledge Injection to All Users
A single attacker can use strategic upvoting and downvoting on language model outputs to inject facts, security flaws, or fake news that persist in the model for all users after preference tuning.
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Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning
High-entropy minority tokens drive RLVR gains, so restricting gradients to the top 20% maintains or improves performance over full updates on Qwen3 models, especially larger ones.
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Supervising the search process produces reliable and generalizable information-seeking agents
Process supervision via RAG-Gym produces more reliable and generalizable search agents, with gains driven by higher-quality queries on out-of-domain multi-hop tasks.
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Preference Goal Tuning: Post-Training as Latent Control for Frozen Policies
PGT optimizes latent goal embeddings for frozen policies via trajectory-level preference objectives, reporting 72-81.6% relative gains on 17 Minecraft tasks and 13.4% better OOD performance than fine-tuning.
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DataComp-LM: In search of the next generation of training sets for language models
DCLM-Baseline dataset lets a 7B model reach 64% 5-shot MMLU accuracy after 2.6T tokens, beating prior open-data models by 6.6 points on MMLU with 40% less compute.
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StarCoder 2 and The Stack v2: The Next Generation
StarCoder2-15B matches or beats CodeLlama-34B on code tasks despite being smaller, and StarCoder2-3B outperforms prior 15B models, with open weights and exact training data identifiers released.