LLM Alignment

Prevailing alignment methods target a fixed set of preferences and therefore risk forcing value lock-in as societal norms evolve over time. We introduce Adaptive Pluralistic Alignment (APA), a modular pipeline for updating pluralistically aligned AI systems to track evolving values and avoid value lock-in without repeating costly pretraining or large-scale data collection. APA has three stages: (1) learning compact personalized reward models via low-rank reward basis decomposition, (2) using these models as a jury that collectively selects among candidate outputs through social-choice-theoretic voting, and (3) efficiently adapting the jury over time by fitting new annotator weights over the fixed reward bases as values shift. The resulting system is efficient, explainable, steerable, and modular. We implement a proof-of-concept instantiation using the PRISM multi-user alignment dataset and simulated historical annotators, and provide preliminary analysis showing that jury composition and the choice of voting rule can substantially affect outcomes, particularly when jury preferences are heterogeneous. We provide full code and resulting preference datasets at https://github.com/RachelFreedman/apa.

Aligning large language models (LLMs) with human preferences is commonly done via reinforcement learning from human feedback (RLHF) with Proximal Policy Optimization (PPO) or, more simply, via Direct Preference Optimization (DPO). While DPO is stable and RL-free, it treats preferences as flat winner vs. loser signals and is sensitive to noisy or brittle preferences arising from fragile chains of thought. We propose TUR-DPO, a topology- and uncertainty-aware variant of DPO that rewards how answers are derived, not only what they say, by eliciting lightweight reasoning topologies and combining semantic faithfulness, utility, and topology quality into a calibrated uncertainty signal. A small learnable reward is factorized over these signals and incorporated into an uncertainty-weighted DPO objective that remains RL-free and relies only on a fixed or moving reference policy. Empirically, across open 7-8B models and benchmarks spanning mathematical reasoning, factual question answering, summarization, and helpful/harmless dialogue, TUR-DPO improves judge win-rates, faithfulness, and calibration relative to DPO while preserving training simplicity and avoiding online rollouts. We further observe consistent gains in multimodal and long-context settings, and show that TUR-DPO matches or exceeds PPO on reasoning-centric tasks while maintaining operational simplicity.

We examine if frontier chat-based large language models (LLMs) adjust their outputs based on neurodivergence (ND) context in system prompts and describe the nature of these adjustments. Specifically, we propose NDBench, a 576-output benchmark involving two frontier models, three system prompt types (baseline, ND-profile assertion, and ND-profile assertion with explicit instructions for adjustments), four canonical ND profiles, and 24 prompts across four categories, one of which involves an adversarial masking strategy. Four trends emerge consistently from our findings. First, LLMs show significant adaptation under ND context, where fully instructed conditions yield lengthier and more structured outputs, characterized by higher token counts, more headings, and more granular steps (p < 10^-8, Holm-corrected). Second, such adaptation is largely structural in nature: although list density does not change much, there is a marked rise in the frequency of headings and per-step detail. Third, ND persona assertion alone fails to suppress potentially harmful tendencies, as masking-reinforcement decreases only in explicitly instructed cases (36-44% reduction); the reduction rate barely changes in persona assertion conditions. Moreover, reliability analysis of LLM-based harm assessment reveals that only two out of the six dimensions (masking and reinforcement, validation quality) exceed the pre-defined inter-judge agreement criterion (alpha >= 0.67) and thus can be considered primary results. NDBench is made publicly available along with its prompts, outputs, code, and other resources, forming a reproducible framework for auditing future LLMs' adaptation to ND awareness.

When researchers iteratively refine ideas with large language models, do the models preserve fidelity to the original objective? We introduce DriftBench, a benchmark for evaluating constraint adherence in multi-turn LLM-assisted scientific ideation. Across 2,146 scored benchmark runs spanning seven models from five providers (including two open-weight), four interaction conditions, and 38 research briefs from 24 scientific domains, we find that iterative pressure reliably increases structural complexity and often reduces adherence to original constraints. A restatement probe reveals a dissociation between declarative recall and behavioral adherence, as models accurately restate constraints they simultaneously violate. The knows-but-violates (KBV) rate, measuring constraint non-compliance despite preserved recall, ranges from 8% to 99% across models. Structured checkpointing partially reduces KBV rates but does not close the dissociation, and complexity inflation persists. Human validation against blind raters confirms that the LLM judge under-detects constraint violations, making reported constraint adherence scores conservative. Sensitivity analyses confirm the findings are robust to temperature (0.7 vs.\ 1.0) and pressure type (novelty vs.\ rigor). We release all briefs, prompts, rubrics, transcripts, and scores as an open benchmark.

Preference learning has become the foundation of aligning Large Language Models (LLMs) with human intent. Popular methods, such as Direct Preference Optimization (DPO), minimize surrogate losses as proxies for the intractable pairwise ranking loss. However, we demonstrate that for the equicontinuous hypothesis sets typical of neural networks, these standard surrogates are theoretically inconsistent, yielding vacuous generalization guarantees. To resolve this, we formulate LLM alignment within a margin-shifted ranking framework. We derive rigorous $H$-consistency bounds that depend on enforcing a separation margin $γ$. Crucially, we extend this to Structure-Aware $H$-consistency, introducing a novel objective (SA-DPO) that adapts the margin based on the semantic distance between responses to handle synonyms and hard pairs. Finally, we analyze the trade-off between consistency and model limitations via the Margin-Capacity Profile, proving that heavy-tailed surrogates (such as the Polynomial Hinge family) offer superior consistency guarantees for capacity-bounded models compared to the standard logistic loss used in DPO.

Reward models (RMs) play a central role in aligning large language models (LLMs) with human preferences. However, RMs are often sensitive to spurious features such as response length. Existing inference-time approaches for mitigating these biases typically focus exclusively on response length, resulting in performance trade-offs. In this paper, we propose causally motivated intervention for mitigating multiple types of biases in RMs at inference time. Our method first identifies neurons whose activations are strongly correlated with predefined bias attributes, and applies neuron-level intervention that suppresses these signals. We evaluate our method on RM benchmarks and observe reductions in sensitivity to spurious features across diverse bias types, without inducing performance trade-offs. Moreover, when used for preference annotation, small RMs (2B and 7B) with our method, which edits less than 2% of all the neurons in RMs, enable LLMs to improve alignment, achieving performance comparable to that of a state-of-the-art 70B RM on AlpacaEval and MT-Bench. Further analysis reveals that bias signals are primarily encoded by neurons in early layers, shedding light on the internal mechanisms of bias exploitation in RMs.

Preference-based alignment methods, most prominently Reinforcement Learning with Human Feedback (RLHF), use the judgments of human annotators to shape large language model behaviour. However, the normative role of these judgments is rarely made explicit. I distinguish three conceptual models of that role. The first is extension: annotators extend the system designers' own judgments about what outputs should be. The second is evidence: annotators provide independent evidence about some facts, whether moral, social or otherwise. The third is authority: annotators have some independent authority (as representatives of the broader population) to determine system outputs. I argue that these models have implications for how RLHF pipelines should solicit, validate and aggregate annotations. I survey landmark papers in the literature on RLHF and related methods to illustrate how they implicitly draw on these models, describe failure modes that come from unintentionally or intentionally conflating them, and offer normative criteria for choosing among them. My central recommendation is that RLHF pipeline designers should decompose annotation into separable dimensions and tailor each pipeline to the model most appropriate for that dimension, rather than seeking a single unified pipeline.

Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods either incur prohibitive $O(N)$ costs by fine-tuning each model individually or rely on static prompts that fail to resolve query-level structural complexity. In this paper, we propose ReQueR (\textbf{Re}inforcement \textbf{Que}ry \textbf{R}efinement), a modular framework that treats reasoning elicitation as an inference-time alignment task. We train a specialized Refiner policy via Reinforcement Learning to rewrite raw queries into explicit logical decompositions, treating frozen LLMs as the environment. Rooted in the classical Zone of Proximal Development from educational psychology, we introduce the Adaptive Solver Hierarchy, a curriculum mechanism that stabilizes training by dynamically aligning environmental difficulty with the Refiner's evolving competence. ReQueR yields consistent absolute gains of 1.7%--7.2% across diverse architectures and benchmarks, outperforming strong baselines by 2.1% on average. Crucially, it provides a promising paradigm for one-to-many inference-time reasoning elicitation, enabling a single Refiner trained on a small set of models to effectively unlock reasoning in diverse unseen models. Code is available at https://github.com/newera-xiao/ReQueR.

Large Language Models (LLMs) excel academically but struggle with social intelligence tasks, such as creating good compromises. In this paper, we present methods for generating empathically neutral compromises between two opposing viewpoints. We first compared four different prompt engineering methods using Claude 3 Opus and a dataset of 2,400 contrasting views on shared places. A subset of the gen erated compromises was evaluated for acceptability in a 50-participant study. We found that the best method for generating compromises between two views used external empathic similarity between a compromise and each viewpoint as iterative feedback, outperforming stan dard Chain of Thought (CoT) reasoning. The results indicate that the use of empathic neutrality improves the acceptability of compromises. The dataset of generated compromises was then used to train two smaller foundation models via margin-based alignment of human preferences, improving efficiency and removing the need for empathy estimation during inference.

Offline preference optimization methods, such as Direct Preference Optimization (DPO), offer significant advantages in aligning Large Language Models (LLMs) with human values. However, achieving optimal performance with these methods typically involves additional hyperparameter tuning, resulting in substantial time overhead. Although prior work has proposed a range of improvements, these methods remain limited in effectiveness and have not fully eliminated reliance on hyperparameter tuning. In this work, we propose RMiPO, a lightweight and efficient framework for offline preference optimization. RMiPO leverages intrinsic Response-level Mutual information for Preference Optimization with hyperparameter modulation, dynamically decoupling preference contributions at negligible additional computational cost. Extensive experimental results demonstrate that RMiPO achieves consistently superior performance over existing methods while reducing training overhead by more than 15%. Our code is available at https://github.com/liavonpenn/rmipo.

Time series models predict numbers; decision-makers need advisory -- directional signals with reasoning, actionable suggestions, and risk management. Training language models for such predictive advisory faces a fundamental challenge: quality depends on outcomes unknown at prediction time. We bridge two ideas from reinforcement learning -- using information unavailable during execution to retrospectively generate training signal, and preference alignment -- and propose Hindsight Preference Optimization: observed outcomes let an LLM judge rank candidate advisories on dimensions that scalar metrics cannot capture, producing preference pairs for DPO without human annotation. We apply this to Vision-Language-Model-based predictive advisories on S&P 500 equity time series, demonstrated by a 4B model outperforming its 235B teacher on both accuracy and advisory quality.

Human daily behavior unfolds as complex sequences shaped by intentions, preferences, and context. Effectively modeling these behaviors is crucial for intelligent systems such as personal assistants and recommendation engines. While recent advances in deep learning and behavior pre-training have improved behavior prediction, key challenges remain--particularly in handling long-tail behaviors, enhancing interpretability, and supporting multiple tasks within a unified framework. Large language models (LLMs) offer a promising direction due to their semantic richness, strong interpretability, and generative capabilities. However, the structural and modal differences between behavioral data and natural language limit the direct applicability of LLMs. To address this gap, we propose Behavior Understanding Alignment (BUA), a novel framework that integrates LLMs into human behavior modeling through a structured curriculum learning process. BUA employs sequence embeddings from pretrained behavior models as alignment anchors and guides the LLM through a three-stage curriculum, while a multi-round dialogue setting introduces prediction and generation capabilities. Experiments on two real-world datasets demonstrate that BUA significantly outperforms existing methods in both tasks, highlighting its effectiveness and flexibility in applying LLMs to complex human behavior modeling.

Test-time alignment methods offer a promising alternative to fine-tuning by steering the outputs of large language models (LLMs) at inference time with lightweight interventions on their internal representations. Recently, a prominent and effective approach, RE-Control (Kong et al., 2024), has proposed leveraging an external value function trained over the LLM's hidden states to guide generation via gradient-based editing. While effective, this method overlooks a key characteristic of alignment tasks, i.e. that they are typically formulated as learning from human preferences between candidate responses. To address this, in this paper we propose a novel preference-based training framework, Pref-CTRL, that uses a multi-objective value function to better reflect the structure of preference data. Our approach has outperformed RE-Control on two benchmark datasets and showed greater generalization on out-of-domain datasets. Our source code is available at https://github.com/UTS-nlPUG/pref-ctrl.

Large language models are being deployed as mental health support agents at scale, yet only 16% of LLM-based chatbot interventions have undergone rigorous clinical efficacy testing, and simulations reveal psychological deterioration in over one-third of cases. We evaluate four generative models on 250 Prolonged Exposure (PE) therapy scenarios and 146 CBT cognitive restructuring exercises (plus 29 severity-escalated variants), scored by a three-judge LLM panel. All models scored near-perfectly on surface acknowledgment (~0.91-1.00) while therapeutic appropriateness collapsed to 0.22-0.33 at the highest severity for three of four models, with protocol fidelity reaching zero for two. Under CBT severity escalation, one model's task completeness dropped from 92% to 71% while the frontier model's safety-interference score fell from 0.99 to 0.61. We identify a systematic, modality-spanning failure: RLHF safety alignment disrupts the therapeutic mechanism of action by grounding patients during imaginal exposure, offering false reassurance, inserting crisis resources into controlled exercises, and refusing to challenge distorted cognitions mentioning self-harm in PE; and through task abandonment or safety-preamble insertion during CBT cognitive restructuring. These findings motivate a five-axis evaluation framework (protocol fidelity, hallucination risk, behavioral consistency, crisis safety, demographic robustness), mapped onto FDA SaMD and EU AI Act requirements. We argue that no AI mental health system should proceed to deployment without passing multi-axis evaluation across all five dimensions.

Large language models (LLMs) often fail to meet the pedagogical needs of K-12 English learners in non-native contexts due to a proficiency mismatch. To address this widespread challenge, we introduce a proficiency-aligned framework that adapts LLM outputs to learner abilities, using China's national curriculum (CSE) as a representative case. Our framework enables precise control over lexical complexity through a four-tier grading system, supported by a comprehensive suite of new resources: graded vocabulary lists and a multi-turn dialogue corpus. Our core technical contribution is the \textbf{DDPO} algorithm,Diversity Driven Policy Optimization, a multi-turn GRPO-based approach designed to preserve dialogue diversity while holistically optimizing dialogue quality. This method significantly outperforms conventional approaches, achieving low out-of-vocabulary rates and high diversity while enhancing conversational naturalness and pedagogical value. While grounded in the CSE, our framework is designed for flexibility and can be readily adapted to other educational standards. Our models, data, and code will all be open-sourced, providing a scalable platform for personalized English speaking practice that effectively addresses the unique challenges faced by K-12 learners in non-immersive environments.

As Large Language Models (LLMs) are deployed globally, ensuring their safety and alignment across multiple languages becomes paramount. However, safety behaviors often vary unpredictably between languages, posing significant challenges for consistent and ethical AI. In this work, we systematically investigate the dynamics of multilingual alignment, exploring whether single-language alignment transfers cross-lingually, how language consistency is preserved during training, and the resulting trade-offs with general knowledge capabilities. We introduce RefusEU, a novel refusal alignment dataset covering 12 European languages, including a dedicated test set for evaluating current state-of-the-art models. Our controlled Direct Preference Optimization (DPO) experiments provide two key insights: aligning models exclusively in English is insufficient to ensure cross-lingual safety, even for the same harm categories, whereas training on multilingual datasets can improve safety without degrading general performance, as measured by the Global MMLU benchmark.

Large Language Models (LLMs) exhibit strong implicit personalization ability, yet most existing approaches treat this behavior as a black box, relying on prompt engineering or fine tuning on user data. In this work, we adopt a mechanistic interpretability perspective and hypothesize the existence of a sparse set of Preference Heads, attention heads that encode user specific stylistic and topical preferences and exert a causal influence on generation. We introduce Differential Preference Steering (DPS), a training free framework that (1) identifies Preference Heads through causal masking analysis and (2) leverages them for controllable and interpretable personalization at inference time. DPS computes a Preference Contribution Score (PCS) for each attention head, directly measuring its causal impact on user aligned outputs. During decoding, we contrast model predictions with and without Preference Heads, amplifying the difference between personalized and generic logits to selectively strengthen preference aligned continuations. Experiments on widely used personalization benchmarks across multiple LLMs demonstrate consistent gains in personalization fidelity while preserving content coherence and low computational overhead. Beyond empirical improvements, DPS provides a mechanistic explanation of where and how personalization emerges within transformer architectures. Our implementation is publicly available.

Large language models (LLMs) trained on unfiltered corpora inherently risk retaining sensitive information, necessitating selective knowledge unlearning for regulatory compliance and ethical safety. However, existing parameter-modifying methods face fundamental limitations: high computational costs, uncontrollable forgetting boundaries, and strict dependency on model weight access. These constraints render them impractical for closed-source models, yet current non-invasive alternatives remain unsystematic and reliant on empirical experience. To address these challenges, we propose the Controllable Alignment Prompting for Unlearning (CAP) framework, an end-to-end prompt-driven unlearning paradigm. CAP decouples unlearning into a learnable prompt optimization process via reinforcement learning, where a prompt generator collaborates with the LLM to suppress target knowledge while preserving general capabilities selectively. This approach enables reversible knowledge restoration through prompt revocation. Extensive experiments demonstrate that CAP achieves precise, controllable unlearning without updating model parameters, establishing a dynamic alignment mechanism that overcomes the transferability limitations of prior methods.

Motivated by loss of control risks from misaligned AI systems, we develop and apply methods for measuring language models' propensity for unsanctioned behaviour. We contribute three methodological improvements: analysing effects of changes to environmental factors on behaviour, quantifying effect sizes via Bayesian generalised linear models, and taking explicit measures against circular analysis. We apply the methodology to measure the effects of 12 environmental factors (6 strategic in nature, 6 non-strategic) and thus the extent to which behaviour is explained by strategic aspects of the environment, a question relevant to risks from misalignment. Across 23 language models and 11 evaluation environments, we find approximately equal contributions from strategic and non-strategic factors for explaining behaviour, do not find strategic factors becoming more or less influential as capabilities improve, and find some evidence for a trend for increased sensitivity to goal conflicts. Finally, we highlight a key direction for future propensity research: the development of theoretical frameworks and cognitive models of AI decision-making into empirically testable forms.

Alignment faking, where a model behaves aligned with developer policy when monitored but reverts to its own preferences when unobserved, is a concerning yet poorly understood phenomenon, in part because current diagnostic tools remain limited. Prior diagnostics rely on highly toxic and clearly harmful scenarios, causing most models to refuse immediately. As a result, models never deliberate over developer policy, monitoring conditions, or the consequences of non-compliance, making these diagnostics fundamentally unable to detect alignment faking propensity. To support study of this phenomenon, we first introduce VLAF, a diagnostic framework grounded in the hypothesis that alignment faking is most likely when developer policy conflicts with a model's strongly held values. VLAF uses morally unambiguous scenarios to probe this conflict across diverse moral values, bypassing refusal behavior while preserving meaningful deliberative stakes. Using VLAF, we find that alignment faking is substantially more prevalent than previously reported, occurring in models as small as 7B parameters - with olmo2-7b-instruct faking alignment in 37% of cases. Finally, we show that oversight conditions induce activation shifts that lie along a single direction in representation space. This means the behavioral divergence driving alignment faking can be captured by a single contrastive steering vector, which we exploit for lightweight inference-time mitigation. Finally, we exploit this for mitigation that requires no labeled data and minimal computational overhead, achieving relative reductions in alignment faking of 85.8%, 94.0%, and 57.7% on olmo2-7b-instruct, olmo2-13b-instruct, and qwen3-8b respectively.

The wide deployment of LLMs has made model alignment necessary to make newly trained models safely and effectively respond to user instructions. Among different methods, inference-time alignment is often cheaper as it intervenes (i.e., offers guidances) only during output generation. Existing proposals apply guidances extracted from certain aligned models without properly assessing their reliability. Nonetheless, our systematic evaluation reveals that guidance effectiveness varies drastically across models; since ineffective guidances lead to further confusion and thus further interventions, the resulting excessive interventions typically indicate poor performance. To make interventions more effective and thus more efficient, we introduce BlendIn, an inference-time alignment framework that shifts from binary decisions to creating hybrid distributions integrating both models' knowledge. BlendIn stabilizes inference-time alignment by performing quality-aware alignment and proportionally weighting each model's contribution based on reliability. Compared with existing works, it preserves beneficial guidance while downweighting unreliable suggestions. BlendIn provides both diagnostic signals and mitigation strategies for misaligned guidance, achieving consistent and up to 50% performance improvement on challenging model pairs. Our code is available at: https://github.com/DecayingSeart/BlendIn.

Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over dispreferred responses in their entirety and lacks the granularity to provide feedback on subsections of many-step solutions typical of reasoning tasks. Existing methods excel at either stable preference learning (e.g., DPO variants like KTO and RSO) or structured reasoning (e.g., ReMA's multi-agent RL framework, Tree of Thoughts), but fail to merge these complementary strengths. We propose HiPO (Hierarchical Preference Optimization), an extension of DPO that separates responses into reasoning segments (query clarification and context, reasoning steps, and answer) and computes loss as a weighted sum of the DPO loss for each segment. Our approach enables segment-specific training while maintaining DPO's computational efficiency and training stability. We demonstrate that for multiple 7B LLMs fine-tuned using HiPO and DPO on the Math Stack Exchange preference dataset, the models trained with HiPO outperform the others on a variety of common math benchmarks and achieve greater organization, logical flow, and consistency as measured by GPT-4.1.

Large language models (LLMs) have demonstrated strong potential in agentic tasks, particularly in slide generation. However, slide generation poses a fundamental challenge: the generation process is text-centric, whereas its quality is governed by visual aesthetics. This modality gap leads current models to frequently produce slides with aesthetically suboptimal layouts. Existing solutions typically rely either on heavy visual reflection, which incurs high inference cost yet yields limited gains; or on fine-tuning with large-scale datasets, which still provides weak and indirect aesthetic supervision. In contrast, the explicit use of aesthetic principles as supervision remains unexplored. In this work, we present AeSlides, a reinforcement learning framework with verifiable rewards for Aesthetic layout supervision in Slide generation. We introduce a suite of meticulously designed verifiable metrics to quantify slide layout quality, capturing key layout issues in an accurate, efficient, and low-cost manner. Leveraging these verifiable metrics, we develop a GRPO-based reinforcement learning method that directly optimizes slide generation models for aesthetically coherent layouts. With only 5K training prompts on GLM-4.7-Flash, AeSlides improves aspect ratio compliance from 36% to 85%, while reducing whitespace by 44%, element collisions by 43%, and visual imbalance by 28%. Human evaluation further shows a substantial improvement in overall quality, increasing scores from 3.31 to 3.56 (+7.6%), outperforming both model-based reward optimization and reflection-based agentic approaches, and even edging out Claude-Sonnet-4.5. These results demonstrate that such a verifiable aesthetic paradigm provides an efficient and scalable approach to aligning slide generation with human aesthetic preferences. Our repository is available at https://github.com/ympan0508/aeslides.

When a language model agrees with a user's false belief, is it failing to detect the error, or noticing and agreeing anyway? We show the latter. Across twelve open-weight models from five labs, spanning small to frontier scale, the same small set of attention heads carries a "this statement is wrong" signal, whether the model is evaluating a claim on its own or being pressured to agree with a user. Silencing these heads flips sycophantic behavior sharply while leaving factual accuracy intact, so the circuit controls deference rather than knowledge. Edge-level path patching confirms that the same head-to-head connections drive sycophancy, factual lying, and instructed lying. Opinion-agreement, where no factual ground truth exists, reuses these head positions but writes into an orthogonal direction, ruling out a simple "truth-direction" reading of the substrate. Alignment training leaves this circuit in place: an RLHF refresh cuts sycophantic behavior roughly tenfold while the shared heads persist or grow, a pattern that replicates on an independent model family and under targeted anti-sycophancy DPO. When these models sycophant, they register that the user is wrong and agree anyway.

We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying on temperature or sampling heuristics to induce diversity, OLLM models variation explicitly: a small latent space parametrizes multiple plausible next-token options which can be selected or searched by a downstream policy. Architecturally, OLLM is a lightweight "plug-in" that inserts two layers: an encoder and a decoder, before the output head, allowing almost any pretrained LLM to be converted with minimal additional parameters. We apply OLLM to a 1.7B-parameter backbone (only $1.56\%$ of parameters trainable) trained on OpenMathReasoning and evaluated on OmniMath. The SOTA LoRA-adapted baselines peak at $51\%$ final answer correctness, while OLLM's option set allows up to $\sim 70\%$ under optimal latent selection. We then train a compact policy in the latent space that emits latents to control generation. Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses. Our results demonstrate that optionized next-token modeling enhances controllability, robustness, and efficiency in math reasoning, and highlight latent-space policy learning as a promising direction for reinforcement learning in LLMs.

Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering

Large Language Models (LLMs) show promise in lyric-to-melody generation, but models trained with Supervised Fine-Tuning (SFT) often produce musically implausible melodies with issues like poor rhythm and unsuitable vocal ranges, a phenomenon we term "constraint violation". To address this, we propose a novel alignment framework that instills musical knowledge without human annotation. We define rule-based musical constraints to automatically generate a preference dataset from an SFT model's outputs. The model is then aligned through a sequential process, first using Direct Preference Optimization (DPO) on paired preference data, followed by Kahneman-Tversky Optimization (KTO) on unpaired negative samples. Experimental results demonstrate that our aligned model substantially reduces rule violations and outperforms strong baselines in both objective and subjective evaluations, generating melodies with substantially improved musicality and coherence. An interactive demo with audio comparisons is available at https://arain233.github.io/AligningMelody-demo.

Preference optimization is widely used to align large language models (LLMs) with human preferences. However, many margin-based methods also suppress the chosen response when they try to suppress the rejected one, and there is no general way to prevent this across different objectives. We address this issue with a unified incentive-score decomposition of preference optimization, revealing that different objectives share the same local update directions and differ only in their scalar weights. This decomposition provides a common framework for analyzing objectives that were previously studied in separate settings. Building on this decomposition, by analyzing the dynamics of the chosen/rejected likelihoods, we identify the disentanglement band (DB), a simple, testable condition that tells us when training can follow the desired path: suppress the loser while preserving the winner, possibly after an early stage. Using the DB, we propose reward calibration (RC), a plug-and-play method that adaptively rebalances the updates for chosen and rejected responses to satisfy the DB, without redesigning the base objective. Empirical results show that RC leads to more disentangled dynamics, with better downstream performance observed across several settings. Our code is available at https://github.com/IceyWuu/DisentangledPreferenceOptimization.

Constitution-conditioned post-training can be analysed as a structured perturbation of a model's learned representational geometry. We introduce ATLAS, a geometry-first program that traces constitution-induced hidden-state structure across charts, models, and substrates. Instead of treating the relevant unit as a single behaviour, neuron, vector, or patch, ATLAS tests a local chart whose tangent structure, occupancy distribution, and behavioural coupling can be measured under system change. On Gemma, the anchored source-local chart captures 310 / 320 reviewed source rows and all 84 / 84 reviewed score-flip rows, but compact exact-patch sufficiency does not close, so the exportable unit is the broader source-defined family. Freezing that family, we re-identify a target-local realisation in an unadapted Phi model, where the fully adjudicated confirmatory contrast separates with AUC 0.984 and mean gap 5.50. In held-out ALM8 mouse frontal-cortex perturbation data, the same source-defined family receives support across 5/5 folds, with mean held-out AUC 0.72 and mean fold gap 4.50. A multiple-choice analysis provides the main boundary: nearby target-local signals can appear without source-faithful closure. The resulting correspondence is not coordinate identity, site identity, or a target-side mediation theorem. It is geometric recurrence under redistribution: written constitutions can induce recoverable latent geometry whose organisation remains detectable across model and substrate changes while its local coordinates, occupancy, and behavioural expression shift.

Skills are a natural unit for describing what a language model can do and how its behavior can be changed. However, existing characterizations rely on human-written taxonomies, textual descriptions, or manual profiling pipelines--all external hypotheses about what matters that need not align with the model's internal representations. We argue that when the goal is to intervene on model behavior, skill characterization should be model-native: grounded in the model's own representations rather than imposed through external ontologies. We instantiate this view by recovering a compact orthogonal basis from sequence-level activations. The resulting basis is semantically interpretable but need not correspond to any predefined human ontology; instead, it captures axes of behavioral variation that the model itself organizes around. We validate this characterization on reasoning post-training, using the recovered basis for both SFT data selection and inference-time steering. We develop lightweight proxy interventions to identify which directions are most useful for a given model. Across Llama3-8B and Qwen2.5-3B, selecting data along those directions improves Pass@1 by up to 20% on MATH and 41% on AMC, outperforming data selection based on human-characterized skills. Because the basis lives in activation space, the same directions also serve as steering vectors at inference time, improving Pass@8 by up to 4.8% on MATH--an intervention that human-characterized skills cannot support. We further validate the characterization on safety alignment, where selecting adversarial training data for model-native skill coverage rather than textual diversity yields more sample-efficient learning. These results suggest that recovering skills from the model's own representations, rather than imposing them externally, provides a more effective foundation for intervening on model behavior. Codes are open-sourced.