Diffusion language models (dLLMs) predict masked positions in arbitrary order, but their exact constrained decoders still encode constraints as sequential languages, whose state must track every unresolved dependency between positions. For relational constraints this encoding grows exponentially: for same-order copy, every finite automaton needs $4^k$ states, deterministic or nondeterministic, and every context-free grammar has size $2^{Ω(k)}$, while the factor graph of the same relation has size $O(k)$ and a 16-entry peak table. We introduce FactorDLM, a training-free decoder that represents finite-domain relations as a factor graph and, at each denoising step, conditions the model's mean-field prediction on that graph exactly by variable elimination. Decoding cost then grows exponentially with the induced width of the constraint graph, which replaces automaton size as the governing parameter. Because a finite automaton is a chain-shaped factor graph, one compiler enforces syntax and nonlocal relations together: on JSON records with cross-field references, a schema automaton alone leaves references dangling, relational factors alone produce malformed JSON, and the combined plan is valid on both counts, including on records of variable length. Across nine relational benchmarks and three backbones, every output satisfies every declared constraint at 0.4-6.9% projection overhead, where unconstrained decoding is 0-79% valid, and compiled projection answers repeated queries 13.6x faster than CP-SAT with eight parallel workers. Because model-free rules solve three of five standard benchmarks, we construct benchmarks with exact chance and fixed-template floors, on which selecting among exact constrained samples beats greedy projection. Which encoding is cheaper, sequential state or direct factors, depends on the constraint and is computable before decoding begins.
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Diffusion language models (dLLMs) predict masked positions in arbitrary order, but their exact constrained decoders still encode constraints as sequential languages, whose state must track every unresolved dependency between positions. For relational constraints this encoding grows exponentially: for same-order copy, every finite automaton needs $4^k$ states, deterministic or nondeterministic, and every context-free grammar has size $2^{Ω(k)}$, while the factor graph of the same relation has size $O(k)$ and a 16-entry peak table. We introduce FactorDLM, a training-free decoder that represents finite-domain relations as a factor graph and, at each denoising step, conditions the model's mean-field prediction on that graph exactly by variable elimination. Decoding cost then grows exponentially with the induced width of the constraint graph, which replaces automaton size as the governing parameter. Because a finite automaton is a chain-shaped factor graph, one compiler enforces syntax and nonlocal relations together: on JSON records with cross-field references, a schema automaton alone leaves references dangling, relational factors alone produce malformed JSON, and the combined plan is valid on both counts, including on records of variable length. Across nine relational benchmarks and three backbones, every output satisfies every declared constraint at 0.4-6.9% projection overhead, where unconstrained decoding is 0-79% valid, and compiled projection answers repeated queries 13.6x faster than CP-SAT with eight parallel workers. Because model-free rules solve three of five standard benchmarks, we construct benchmarks with exact chance and fixed-template floors, on which selecting among exact constrained samples beats greedy projection. Which encoding is cheaper, sequential state or direct factors, depends on the constraint and is computable before decoding begins.
Recent work has identified a human brain network specialized for abstract formal reasoning (Kean et al., 2025). Does the same hold true in language models? To answer this question, we introduce the minimal viable subspace (MVS) method, which searches for the lowest-rank activation subspace at a layer that preserves task performance when everything outside that subspace is ablated. Using MVS, we demonstrate low-rank subspaces supporting logical inference on Gemma and Qwen models. Furthermore, these subspaces exhibit a clear dissociation from model capacities on other tasks, such that retaining these late logic subspaces preserves inference while impairing factual knowledge, working memory, cognitive control, and arithmetic. Conversely, ablating them reduces logical inference accuracy to chance while largely sparing these other capacities. Our results suggest a functionally localizable core machinery for logic akin to that in the human brain.
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Recent work has identified a human brain network specialized for abstract formal reasoning (Kean et al., 2025). Does the same hold true in language models? To answer this question, we introduce the minimal viable subspace (MVS) method, which searches for the lowest-rank activation subspace at a layer that preserves task performance when everything outside that subspace is ablated. Using MVS, we demonstrate low-rank subspaces supporting logical inference on Gemma and Qwen models. Furthermore, these subspaces exhibit a clear dissociation from model capacities on other tasks, such that retaining these late logic subspaces preserves inference while impairing factual knowledge, working memory, cognitive control, and arithmetic. Conversely, ablating them reduces logical inference accuracy to chance while largely sparing these other capacities. Our results suggest a functionally localizable core machinery for logic akin to that in the human brain.
作者Rungui Zhou, Chuanzhi Zhou, Ruihuan Wang, Peng-Shuai Wang
Raw 3D point clouds are a core geometric representation. Establishing their ownership is challenging because point sets are irregular, unstructured, and frequently altered by resampling and geometric preprocessing. We present a blind watermarking framework that operates directly on xyz coordinates and supports both object-level shapes and scene-scale scans. At verification time, the embedded message is recovered from the observed point cloud alone, without access to the original point cloud, color, normals, or mesh connectivity. The method jointly learns watermark embedding and extraction through a feed-forward octree-based architecture, enabling efficient multi-scale geometric reasoning on large point sets. During training, a stochastic transformation layer exposes the decoder to common geometric perturbations, while progressive pose alignment improves robustness to pose changes. Experiments on object-level and scene-level benchmarks demonstrate reliable message recovery under common geometric processing while maintaining low geometric distortion. Qualitative comparisons further show that the learned perturbations are less visually conspicuous and less spatially structured than those of handcrafted alternatives.
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Raw 3D point clouds are a core geometric representation. Establishing their ownership is challenging because point sets are irregular, unstructured, and frequently altered by resampling and geometric preprocessing. We present a blind watermarking framework that operates directly on xyz coordinates and supports both object-level shapes and scene-scale scans. At verification time, the embedded message is recovered from the observed point cloud alone, without access to the original point cloud, color, normals, or mesh connectivity. The method jointly learns watermark embedding and extraction through a feed-forward octree-based architecture, enabling efficient multi-scale geometric reasoning on large point sets. During training, a stochastic transformation layer exposes the decoder to common geometric perturbations, while progressive pose alignment improves robustness to pose changes. Experiments on object-level and scene-level benchmarks demonstrate reliable message recovery under common geometric processing while maintaining low geometric distortion. Qualitative comparisons further show that the learned perturbations are less visually conspicuous and less spatially structured than those of handcrafted alternatives.
On-policy reasoning models can learn from task rewards or teacher signals, but these sources differ in form and can favor conflicting updates, leaving unclear which should guide a given reasoning action. We introduce Expected Reasoning-Step Return (ERSR), which treats semantic reasoning steps as macro-actions and uses Monte Carlo student-policy rollouts to estimate the expected final task reward of student-generated and teacher-proposed actions in a common return space for step-level comparison. ERSR analysis reveals an outcome-dependent asymmetry: student actions are more beneficial than teacher replacements on successful trajectories, whereas teacher replacements become more beneficial on failed trajectories. We further show that student answer-probe gains track student-step ERSR utility and distinguish beneficial from harmful reasoning steps. Based on these findings, we propose Return-Referenced On-Policy Learning (R$^2$OPL), which reinforces student reasoning on successful trajectories and distills teacher signals on failed ones, while using group success rate for difficulty scaling and student-probe gains for step-level modulation. Experiments across reasoning benchmarks and teacher--student configurations show that R$^2$OPL consistently outperforms strong baselines. ERSR training dynamics further show that R$^2$OPL jointly exploits substantial utility from both reward- and teacher-side signals, whereas existing hybrids often leave substantial residual utility in one branch.
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On-policy reasoning models can learn from task rewards or teacher signals, but these sources differ in form and can favor conflicting updates, leaving unclear which should guide a given reasoning action. We introduce Expected Reasoning-Step Return (ERSR), which treats semantic reasoning steps as macro-actions and uses Monte Carlo student-policy rollouts to estimate the expected final task reward of student-generated and teacher-proposed actions in a common return space for step-level comparison. ERSR analysis reveals an outcome-dependent asymmetry: student actions are more beneficial than teacher replacements on successful trajectories, whereas teacher replacements become more beneficial on failed trajectories. We further show that student answer-probe gains track student-step ERSR utility and distinguish beneficial from harmful reasoning steps. Based on these findings, we propose Return-Referenced On-Policy Learning (R$^2$OPL), which reinforces student reasoning on successful trajectories and distills teacher signals on failed ones, while using group success rate for difficulty scaling and student-probe gains for step-level modulation. Experiments across reasoning benchmarks and teacher--student configurations show that R$^2$OPL consistently outperforms strong baselines. ERSR training dynamics further show that R$^2$OPL jointly exploits substantial utility from both reward- and teacher-side signals, whereas existing hybrids often leave substantial residual utility in one branch.
Extracting conditional text embeddings from large language models (LLMs) is a promising paradigm, as it requires neither additional data nor fine-tuning. Existing methods incorporate conditions into prompts to guide LLMs to focus on specific aspects and elicit conditional text embeddings. However, relying solely on prompts often fails to produce high-quality conditional text embeddings, as they remain entangled with general text embeddings, ultimately degrading their quality. To this end, we propose an inference-time, plug-and-play Self-Contrastive Steering (SCS) method that constructs unconditional general text embeddings and uses them to refine conditional text embeddings, making them more focused on the target condition. Specifically, we modify the attention mask and positional encodings to mask the condition, thereby obtaining unconditional text embeddings and intervening in the multi-head self-attention computation process. Notably, our method is highly efficient, requiring only a single additional multi-head self-attention computation at inference time. Extensive experiments on clustering, Semantic Textual Similarity, and triplet alignment datasets demonstrate that our method can seamlessly improve the performance of existing prompt-based methods across different LLMs in a training-free and plug-and-play manner. Our code will be released at https://github.com/zifengcheng/SCS
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Extracting conditional text embeddings from large language models (LLMs) is a promising paradigm, as it requires neither additional data nor fine-tuning. Existing methods incorporate conditions into prompts to guide LLMs to focus on specific aspects and elicit conditional text embeddings. However, relying solely on prompts often fails to produce high-quality conditional text embeddings, as they remain entangled with general text embeddings, ultimately degrading their quality. To this end, we propose an inference-time, plug-and-play Self-Contrastive Steering (SCS) method that constructs unconditional general text embeddings and uses them to refine conditional text embeddings, making them more focused on the target condition. Specifically, we modify the attention mask and positional encodings to mask the condition, thereby obtaining unconditional text embeddings and intervening in the multi-head self-attention computation process. Notably, our method is highly efficient, requiring only a single additional multi-head self-attention computation at inference time. Extensive experiments on clustering, Semantic Textual Similarity, and triplet alignment datasets demonstrate that our method can seamlessly improve the performance of existing prompt-based methods across different LLMs in a training-free and plug-and-play manner. Our code will be released at https://github.com/zifengcheng/SCS
作者Jeongho Yoon, Chanhee Park, Yongchan Chun, Duong Tuan Thanh, Sungbin Han, Chanjun Park, Hyeonseok Moon, Heuiseok Lim
Cloud-based large language models (LLMs) require users to disclose plaintext data to service providers, creating privacy risks in sensitive domains. Existing privacy-preserving approaches often trade utility for protection, incur substantial computational or communication overhead, remain vulnerable to reconstruction from intermediate representations, or protect only a subset of the training and inference pipeline. We introduce Client-Resolved Generation (CRG), a genera- tion interface that separates server-side generation from the lexical realization of input-derived content. The client transmits only pooled and noise-perturbed rep- resentations, while input-derived output content is represented using request-local positional references and resolved to its original strings only on the client. This interface protects private input and input-derived output content during both train- ing and inference while allowing the service provider to keep its proprietary model parameters hidden from the client. At the same time, exact lexical reuse remains possible without directly exposing the reused content on the provider-visible gen- eration path. We evaluate CRG on medical and document-grounded QA, sensi- tive identifier transfer, and tool calling, together with reconstruction and raw-logit leakage analyses. On SealTools, CRG improves complete-call exact match from 57.3% to 79.9% over the input-privacy framework PPFT, with larger gains as more required output content can be resolved through references. Together, these results show that CRG provides a practical interface for privacy-sensitive cloud LLMs by reducing plaintext exposure across both input and output pathways while preserv- ing task utility and server-side model confidentiality.
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Cloud-based large language models (LLMs) require users to disclose plaintext data to service providers, creating privacy risks in sensitive domains. Existing privacy-preserving approaches often trade utility for protection, incur substantial computational or communication overhead, remain vulnerable to reconstruction from intermediate representations, or protect only a subset of the training and inference pipeline. We introduce Client-Resolved Generation (CRG), a genera- tion interface that separates server-side generation from the lexical realization of input-derived content. The client transmits only pooled and noise-perturbed rep- resentations, while input-derived output content is represented using request-local positional references and resolved to its original strings only on the client. This interface protects private input and input-derived output content during both train- ing and inference while allowing the service provider to keep its proprietary model parameters hidden from the client. At the same time, exact lexical reuse remains possible without directly exposing the reused content on the provider-visible gen- eration path. We evaluate CRG on medical and document-grounded QA, sensi- tive identifier transfer, and tool calling, together with reconstruction and raw-logit leakage analyses. On SealTools, CRG improves complete-call exact match from 57.3% to 79.9% over the input-privacy framework PPFT, with larger gains as more required output content can be resolved through references. Together, these results show that CRG provides a practical interface for privacy-sensitive cloud LLMs by reducing plaintext exposure across both input and output pathways while preserv- ing task utility and server-side model confidentiality.
作者Jacopo Minniti, Aravinth Kulanthaivelu, Richard Sproat
Deep learning is commonly interpreted at two levels: the macroscopic, through aggregate trends in loss summarized by scaling laws, and the microscopic, through neurons, features, and circuits. A central challenge is understanding how these levels connect, so that we can explain how elementary computations compose and collectively shape macroscopic behavior. To this end, we study an intermediate abstraction in which training is described as the ordered acquisition of quanta: reusable computations acquired suddenly and binary-activated across examples to reduce loss. By approximating population-gradient updates, we derive quanta's acquisition dynamics. This yields an acquisition priority governed by demand, how frequently a computation is required across examples, and conditional complexity, how difficult that computation is to acquire given those already available. In a Boolean compositional task, we derive predictions for acquisition order and show how staggered discrete acquisitions can produce smooth aggregate loss and, under certain geometries of quanta composition, give rise to scaling laws. We then train a Transformer to map numerals to English number names and recover candidate quanta from its checkpoint trajectory. From these units, we construct a model that preserves much of the Transformer's behavior while exposing interpretable latent computations and acquisition dynamics consistent with the theory. Separately, the quanta structure can serve as training targets to improve transformer generalization. Together, these results suggest the quanta abstraction can provide useful computational atoms for studying a variety of macroscopic phenomena.
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Deep learning is commonly interpreted at two levels: the macroscopic, through aggregate trends in loss summarized by scaling laws, and the microscopic, through neurons, features, and circuits. A central challenge is understanding how these levels connect, so that we can explain how elementary computations compose and collectively shape macroscopic behavior. To this end, we study an intermediate abstraction in which training is described as the ordered acquisition of quanta: reusable computations acquired suddenly and binary-activated across examples to reduce loss. By approximating population-gradient updates, we derive quanta's acquisition dynamics. This yields an acquisition priority governed by demand, how frequently a computation is required across examples, and conditional complexity, how difficult that computation is to acquire given those already available. In a Boolean compositional task, we derive predictions for acquisition order and show how staggered discrete acquisitions can produce smooth aggregate loss and, under certain geometries of quanta composition, give rise to scaling laws. We then train a Transformer to map numerals to English number names and recover candidate quanta from its checkpoint trajectory. From these units, we construct a model that preserves much of the Transformer's behavior while exposing interpretable latent computations and acquisition dynamics consistent with the theory. Separately, the quanta structure can serve as training targets to improve transformer generalization. Together, these results suggest the quanta abstraction can provide useful computational atoms for studying a variety of macroscopic phenomena.
4D radar provides geometric and motion cues that complement visual semantics, but integrating it into vision-language-action (VLA) models requires both radar--language alignment for semantic reasoning and explicit use of radar measurements for trajectory refinement and selection. To support these capabilities, we construct Cap4DR with 86,016 radar-image-text samples for alignment pretraining and OmniHD-QA with 520,161 question-answer pairs for instruction tuning across scene description, key-object reasoning, occupancy understanding, and trajectory planning. Building on these datasets, we propose RCVLA, a radar-camera VLA framework consisting of a radar-grounded semantic reasoning stage (RCVLA-Sem) and a trajectory arbitration stage (RCVLA-Phys). RCVLA-Sem performs gated bidirectional interaction between camera and radar tokens for driving question answering and reference trajectory generation, while auxiliary heads provide object and occupancy queries. RCVLA-Phys refines reference-guided trajectory candidates through truncated diffusion conditioned on these queries and cluster-level radar measurements, then calibrates candidate scores using radar-derived time-to-collision risk. On OmniHD-QA, RCVLA-Sem improves CIDEr by 9.92 points and reduces key-object velocity error by $21.9%$ relative to OmniDrive. RCVLA-Phys further reduces average L2 error from $0.348$ to $0.259\,\mathrm{m}$ and average open-loop collision rate from $0.576%$ to $0.175%$ relative to RCVLA-Sem. Ablation studies further show that language-aligned radar tokens improve semantic reasoning, while cluster-level radar measurements and risk calibration improve trajectory arbitration. Code will be released.
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4D radar provides geometric and motion cues that complement visual semantics, but integrating it into vision-language-action (VLA) models requires both radar--language alignment for semantic reasoning and explicit use of radar measurements for trajectory refinement and selection. To support these capabilities, we construct Cap4DR with 86,016 radar-image-text samples for alignment pretraining and OmniHD-QA with 520,161 question-answer pairs for instruction tuning across scene description, key-object reasoning, occupancy understanding, and trajectory planning. Building on these datasets, we propose RCVLA, a radar-camera VLA framework consisting of a radar-grounded semantic reasoning stage (RCVLA-Sem) and a trajectory arbitration stage (RCVLA-Phys). RCVLA-Sem performs gated bidirectional interaction between camera and radar tokens for driving question answering and reference trajectory generation, while auxiliary heads provide object and occupancy queries. RCVLA-Phys refines reference-guided trajectory candidates through truncated diffusion conditioned on these queries and cluster-level radar measurements, then calibrates candidate scores using radar-derived time-to-collision risk. On OmniHD-QA, RCVLA-Sem improves CIDEr by 9.92 points and reduces key-object velocity error by $21.9%$ relative to OmniDrive. RCVLA-Phys further reduces average L2 error from $0.348$ to $0.259\,\mathrm{m}$ and average open-loop collision rate from $0.576%$ to $0.175%$ relative to RCVLA-Sem. Ablation studies further show that language-aligned radar tokens improve semantic reasoning, while cluster-level radar measurements and risk calibration improve trajectory arbitration. Code will be released.
Reflective prompt optimization improves large language model (LLM) systems without updating model weights, but fixed architectures constrain how self-refinement is organized. We introduce Workflow-Designing Agents (WDA), a framework for streamlined reflective evolution of task-adaptive self-refinement pipelines. Starting from a minimal prompt, WDA jointly evolves stage instructions and their sequential structure. During evolution, we find that repeated revisions can accumulate redundant instructions in a single prompt. In WDA, we propose to address this problem with SPLIT, which redistributes these instructions across specialized stages. Three-example reflection and local screening guide selective search, while calibration scores guide Pareto admission and rollback of unhelpful trailing updates. The resulting pipelines are task-adaptive: their instructions and depth are learned from task data, then fixed for all test inputs within that task. We evaluate WDA on five benchmarks spanning knowledge, mathematical reasoning, multi-hop question answering, and instruction following. On Qwen3.5-9B, WDA achieves an average score of 51.24%, improving over the initial solver by 8.63 percentage points and the variant without SPLIT by 2.60 points. On GPT-4.1-mini, it achieves 49.00%, with corresponding gains of 5.62 and 3.69 points. These results support task-adaptive self-refinement as a complementary direction to broader agentic workflow search.
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Reflective prompt optimization improves large language model (LLM) systems without updating model weights, but fixed architectures constrain how self-refinement is organized. We introduce Workflow-Designing Agents (WDA), a framework for streamlined reflective evolution of task-adaptive self-refinement pipelines. Starting from a minimal prompt, WDA jointly evolves stage instructions and their sequential structure. During evolution, we find that repeated revisions can accumulate redundant instructions in a single prompt. In WDA, we propose to address this problem with SPLIT, which redistributes these instructions across specialized stages. Three-example reflection and local screening guide selective search, while calibration scores guide Pareto admission and rollback of unhelpful trailing updates. The resulting pipelines are task-adaptive: their instructions and depth are learned from task data, then fixed for all test inputs within that task. We evaluate WDA on five benchmarks spanning knowledge, mathematical reasoning, multi-hop question answering, and instruction following. On Qwen3.5-9B, WDA achieves an average score of 51.24%, improving over the initial solver by 8.63 percentage points and the variant without SPLIT by 2.60 points. On GPT-4.1-mini, it achieves 49.00%, with corresponding gains of 5.62 and 3.69 points. These results support task-adaptive self-refinement as a complementary direction to broader agentic workflow search.
As local small language models (SLMs) increasingly collaborate with more capable cloud large language models (LLMs), a natural privacy question arises: Can a local SLM obtain cloud LLM guidance while protecting user privacy? Existing privacy-preserving SLM-LLM frameworks primarily hide sensitive values while preserving task semantics, which can still expose what the user is trying to accomplish. For example, allocating scarce medical supplies across hospitals may signal an emerging public-health emergency, while rebalancing an investment portfolio may reveal a private investment strategy, even when names and numerical values are hidden. Recent decoy-based methods further obscure task intent by hiding the real request among alternatives, but stronger protection relies on more decoys or semantic abstraction, increasing overhead or risking utility loss. More fundamentally, existing work does not systematically characterize the components of private task intent or how each should be protected. We therefore introduce task-private consultation, which characterizes task intent through two components: task context and task operation. To the best of our knowledge, this is the first systematic study of these components and their individual and joint protection in local-cloud SLM-LLM consultation. To realize this setting, we propose PriCon, an end-to-end framework that transforms the task itself through recoverable mathematical reformulation rather than hiding it among alternatives. A local closed-loop refinement mechanism further maintains privacy and recoverability throughout consultation. Experiments on 100 tasks show that PriCon reduces cloud-side task-intent inference Hit@1 to nearly 0%, versus 93-99% under sensitive-value removal and 3-30% under decoy-based protection, while preserving cloud-assisted utility.
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As local small language models (SLMs) increasingly collaborate with more capable cloud large language models (LLMs), a natural privacy question arises: Can a local SLM obtain cloud LLM guidance while protecting user privacy? Existing privacy-preserving SLM-LLM frameworks primarily hide sensitive values while preserving task semantics, which can still expose what the user is trying to accomplish. For example, allocating scarce medical supplies across hospitals may signal an emerging public-health emergency, while rebalancing an investment portfolio may reveal a private investment strategy, even when names and numerical values are hidden. Recent decoy-based methods further obscure task intent by hiding the real request among alternatives, but stronger protection relies on more decoys or semantic abstraction, increasing overhead or risking utility loss. More fundamentally, existing work does not systematically characterize the components of private task intent or how each should be protected. We therefore introduce task-private consultation, which characterizes task intent through two components: task context and task operation. To the best of our knowledge, this is the first systematic study of these components and their individual and joint protection in local-cloud SLM-LLM consultation. To realize this setting, we propose PriCon, an end-to-end framework that transforms the task itself through recoverable mathematical reformulation rather than hiding it among alternatives. A local closed-loop refinement mechanism further maintains privacy and recoverability throughout consultation. Experiments on 100 tasks show that PriCon reduces cloud-side task-intent inference Hit@1 to nearly 0%, versus 93-99% under sensitive-value removal and 3-30% under decoy-based protection, while preserving cloud-assisted utility.
作者Fengzhuo Zhang, Shuche Wang, Shenggui Li, Tianyu Ruan, Jianliang He, Ivor Tsang, Tianyu Pang, Chao Du, Tianwei Zhang, Zhuoran Yang
Large Language Model (LLM) pretraining performance is jointly shaped by three components of the training triplet: the optimizer, model architecture, and training data stream. However, how these components influence performance in distinct ways remains unclear. We take a first step toward isolating their effects by studying relative generalization. We introduce Relative Generalization Invariance (RGI), the invariance of the validation-loss difference between any two tokens across models. We show that RGI approximately holds across a wide range of optimizers and moderate architectural variations, suggesting that these choices induce an approximately uniform shift in token-wise losses. In contrast, changing the training data stream can substantially alter relative generalization. We further show that RGI cannot be explained by the neural tangent kernel or mean-field regimes alone and prove that it can emerge in an overparameterized quadratic model. Overall, our work identifies RGI as a new phenomenon in LLM pretraining that helps distinguish the effects of optimizers and architectures from those of training data.
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Large Language Model (LLM) pretraining performance is jointly shaped by three components of the training triplet: the optimizer, model architecture, and training data stream. However, how these components influence performance in distinct ways remains unclear. We take a first step toward isolating their effects by studying relative generalization. We introduce Relative Generalization Invariance (RGI), the invariance of the validation-loss difference between any two tokens across models. We show that RGI approximately holds across a wide range of optimizers and moderate architectural variations, suggesting that these choices induce an approximately uniform shift in token-wise losses. In contrast, changing the training data stream can substantially alter relative generalization. We further show that RGI cannot be explained by the neural tangent kernel or mean-field regimes alone and prove that it can emerge in an overparameterized quadratic model. Overall, our work identifies RGI as a new phenomenon in LLM pretraining that helps distinguish the effects of optimizers and architectures from those of training data.
We investigate how generalization and memorization develop along the learning trajectory of neural language models. Using controlled synthetic grammars, we examine both the geometry of representation space and model behaviour over training. We find that continuous regions of representation space not occupied by observed tokens become systematically structured from the earliest stages of learning, forming category-level geometric organization that supports generalization to unattested combinations. Generalization therefore emerges from the beginning of learning rather than only after extensive memorization. With prolonged training, larger models increasingly distinguish observed from unobserved grammatical combinations. At the same time, the continuous geometric structure supporting category-level generalization is gradually destructed. Together, these results suggest that neural language models initially learn through categorization-based generalization, followed by a gradual transition toward more exemplar-specific memorization.
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We investigate how generalization and memorization develop along the learning trajectory of neural language models. Using controlled synthetic grammars, we examine both the geometry of representation space and model behaviour over training. We find that continuous regions of representation space not occupied by observed tokens become systematically structured from the earliest stages of learning, forming category-level geometric organization that supports generalization to unattested combinations. Generalization therefore emerges from the beginning of learning rather than only after extensive memorization. With prolonged training, larger models increasingly distinguish observed from unobserved grammatical combinations. At the same time, the continuous geometric structure supporting category-level generalization is gradually destructed. Together, these results suggest that neural language models initially learn through categorization-based generalization, followed by a gradual transition toward more exemplar-specific memorization.
The widely used Transolver family of neural operators is based on physics-attention, which softly assigns the points of an unstructured mesh to a small number of slices, applies self-attention among the resulting tokens, and broadcasts the result back to the points. We provide a comprehensive empirical and theoretical analysis to elucidate the mechanisms which are responsible for model performance. To this end, we perform careful ablations on a challenging suite of nine 3D fluid dynamics benchmarks to find that replacing token attention with a constant linear map does not affect the accuracy. Thus, Transolver does not need a Transformer at all. However, removing the global mixing (slicing/deslicing) or doing it only once leads to performance collapse. We leverage the theory of averaging neural operators to explain and corroborate our findings by showing that just slicing/deslicing, in conjunction with pointwise MLPs, already suffices for universal approximation of continuous operators and attention is redundant in this context. Finally, we provide a novel FlashAttention-style efficient implementation of the key slicing/deslicing module of Transolver. This flashslice kernel streams slice and deslice over the points without materializing the heavy slice-weight tensor, while reproducing the best available implementation to floating point error. At the same time, it leads to very significant memory and compute savings, particularly at large slice counts.
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The widely used Transolver family of neural operators is based on physics-attention, which softly assigns the points of an unstructured mesh to a small number of slices, applies self-attention among the resulting tokens, and broadcasts the result back to the points. We provide a comprehensive empirical and theoretical analysis to elucidate the mechanisms which are responsible for model performance. To this end, we perform careful ablations on a challenging suite of nine 3D fluid dynamics benchmarks to find that replacing token attention with a constant linear map does not affect the accuracy. Thus, Transolver does not need a Transformer at all. However, removing the global mixing (slicing/deslicing) or doing it only once leads to performance collapse. We leverage the theory of averaging neural operators to explain and corroborate our findings by showing that just slicing/deslicing, in conjunction with pointwise MLPs, already suffices for universal approximation of continuous operators and attention is redundant in this context. Finally, we provide a novel FlashAttention-style efficient implementation of the key slicing/deslicing module of Transolver. This flashslice kernel streams slice and deslice over the points without materializing the heavy slice-weight tensor, while reproducing the best available implementation to floating point error. At the same time, it leads to very significant memory and compute savings, particularly at large slice counts.
作者Ke Li, Spyros I. Zoumpoulis, Phanish Puranam, Philip Parker, Matthew Eshbaugh-Soha, Izzy Gainsburg, Michael Gilead, Igor Grossmann, Britt Hadar, Yoel Inbar, Almog Simchon, Robb Willer, Rui Ai, Ruicheng Ao, Gavin J. Bala, Matthew Bidwell, Shuang Cai, Kai Chang, Skyler Y. Chen, Cory J. Clark, Irmak Dai, Abhinandan Dalal, Connor Douglas, Alexis Du, Zhehang Du, Leyun Feng, Isabel Fernandez-Mateo, Linnea Gandhi, Cyrille Grumbach, Anmol Gupta, Vansh Gupta, Maria Hademer, Jay H. Hardy, Chen Kai Huang, Jacob Xiangyu Jin, Ufuk Keskin, Na Hyun Kim, Mert Kobaş, Byounghoon Koh, Gabrielle Lamont-Dobbin, Gregory Lanzalotto, Sun Young Lee, Dingzhe Leng, Chenjun Li, Weiyuan Li, Zeyuan Li, Zhongyuan Liang, Ning Liu, Peihong Liu, Yuhan Liu, Jiuyao Lu, Wanteng Ma, Nicolas Martinet, Natnael Mulat, Christina A. Nguyen, Khai Nguyen, Quang Minh Nguyen, Naja Pape, Chanwoo Park, Stefanos Poulidis, Jeffrey Sanchez-Burks, Michael Schaerer, Isabelle Solal, Yanbo Song, Junghyo Sun, Qingyao Sun, Rui Sun, Roderick Swaab, Kevin Tan, Dequn Teng, Michelle A. Vaccaro, Robin Vigerbaeck, Xiaomeng Wang, Randol H. Yao, Duygu Yilmaz, Shun Yiu, Ecem Yucesoy, Allen Zang, Ruijia Zhang, Xilan Zhang, Yichi Zhang, Zhanhao Zhang, Eric Luis Uhlmann
We investigate the effectiveness of artificial intelligences (AI)-specifically large language models (LLMs)-relative to human scientists at high-level cognitive tasks in social science such as theory formulation, predictions of novel empirical results, and theory revision in response to new evidence. The research domain was academic discourse regarding gender and race inequality. Our findings, comparing 25 LLMs with 13 senior researchers and 60 doctoral scholars, reveal that the AIs outperformed most humans individually on most of the present tasks, while human theories were more diverse and exhibited greater gains in predictive accuracy from aggregation. AI-generated theories were more extensively elaborated, involving additional theoretical paths and latent variables, and were rated as higher quality than human theories by independent raters blinded to source. However, this theoretical complexity was in part ornamental, in that it was not associated with more accurate predictions about empirical patterns in data; in contrast, human scientists achieved greater predictive efficiency with simpler theories. The AIs were significantly more likely than human scientists to revise their theories to incorporate new evidence; human scientists updated their beliefs in a selective way that is sensitive to prior prediction errors. We speculate that the superior processing capacity of artificial intelligences makes them especially well-suited to tasks requiring grappling with complexity, but that the greater diversity of human ideas is essential to wise crowds and collective creativity.
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We investigate the effectiveness of artificial intelligences (AI)-specifically large language models (LLMs)-relative to human scientists at high-level cognitive tasks in social science such as theory formulation, predictions of novel empirical results, and theory revision in response to new evidence. The research domain was academic discourse regarding gender and race inequality. Our findings, comparing 25 LLMs with 13 senior researchers and 60 doctoral scholars, reveal that the AIs outperformed most humans individually on most of the present tasks, while human theories were more diverse and exhibited greater gains in predictive accuracy from aggregation. AI-generated theories were more extensively elaborated, involving additional theoretical paths and latent variables, and were rated as higher quality than human theories by independent raters blinded to source. However, this theoretical complexity was in part ornamental, in that it was not associated with more accurate predictions about empirical patterns in data; in contrast, human scientists achieved greater predictive efficiency with simpler theories. The AIs were significantly more likely than human scientists to revise their theories to incorporate new evidence; human scientists updated their beliefs in a selective way that is sensitive to prior prediction errors. We speculate that the superior processing capacity of artificial intelligences makes them especially well-suited to tasks requiring grappling with complexity, but that the greater diversity of human ideas is essential to wise crowds and collective creativity.
作者Zeping Liu, Yan Li, Ni Lao, Gil Wolff, Gengchen Mai
Large language models (LLMs) can learn reusable textual skills from execution feedback without updating their parameters, but effectively deciding how to revise these skills remains a key challenge. Existing methods typically rely on a fixed revision operator, a search strategy and the revision forms applied under it. However, we observe that no single revision operator consistently performs best across tasks, and repeatedly applying an unsuitable operator can limit further improvement. We propose StraTune (strategy-guided skill tuning), which lets a frozen optimizer LLM choose the revision operator at every round from the optimization state, which is defined as the current execution feedback together with the recorded outcomes of earlier strategies and forms. Candidate skills from every revision operator pass one candidate evaluation, which screens for gains and regressions on a small sample set and validates them on a larger one, and every outcome is written back to the optimization state for later choices. Across four benchmarks and two LLM settings, StraTune outperforms all five baselines in most settings. Ablations attribute the gains to the adaptive choice of the revision operator, since fixed, random, scheduled, and bandit strategy choices all score lower, and skills learned with a small target LLM also improve a stronger one. Code and learned skills are available at https://github.com/seai-lab/StraTune.
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Large language models (LLMs) can learn reusable textual skills from execution feedback without updating their parameters, but effectively deciding how to revise these skills remains a key challenge. Existing methods typically rely on a fixed revision operator, a search strategy and the revision forms applied under it. However, we observe that no single revision operator consistently performs best across tasks, and repeatedly applying an unsuitable operator can limit further improvement. We propose StraTune (strategy-guided skill tuning), which lets a frozen optimizer LLM choose the revision operator at every round from the optimization state, which is defined as the current execution feedback together with the recorded outcomes of earlier strategies and forms. Candidate skills from every revision operator pass one candidate evaluation, which screens for gains and regressions on a small sample set and validates them on a larger one, and every outcome is written back to the optimization state for later choices. Across four benchmarks and two LLM settings, StraTune outperforms all five baselines in most settings. Ablations attribute the gains to the adaptive choice of the revision operator, since fixed, random, scheduled, and bandit strategy choices all score lower, and skills learned with a small target LLM also improve a stronger one. Code and learned skills are available at https://github.com/seai-lab/StraTune.
Pre-training data poisoning of large language models is usually studied using targeted backdoors and their survival through safety post-training, which leaves open a more basic question: how does a model's clean data performance degrade as the poison rate $\varepsilon$ grows? Motivated by our controlled pre-training runs of OLMo-style models, in which the relative clean data validation perplexity increase $Δ$ between poisoned and clean models matched in architecture, token budget, and optimization schedule is well fit by a power law $Δ\approx C\varepsilon^{a}$ with a non-integer exponent, we ask what such a law requires theoretically. We first prove an analyticity barrier: whenever the contaminated objective depends analytically on $\varepsilon$ around a nondegenerate clean data optimum, $Δ$ is generically quadratic in $\varepsilon$, so a generic non-integer exponent is a signature of genuinely singular structure. We then supply that structure in solvable truncated ridge regression with heavy-tailed covariates, controlled by $q_\star$, and a label-shift poisoning. Our central result is that the excess risk scaling exponent depending on the order of limits: in the higher dimensional proportional regime it is $ε^{q_\star/(q_\star+2)}$, whereas taking the ample-data limit first gives $ε^{2-2/q_\star}$, and the limits do not commute. We confirm this prediction through several numerical simulations. Finally, we argue that finite training time plays the role of truncation on the curvature spectrum in local LLM pre-training, deriving the observed scaling law under heavy tailed inverse curvature spectrum as a modeling hypothesis.
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Pre-training data poisoning of large language models is usually studied using targeted backdoors and their survival through safety post-training, which leaves open a more basic question: how does a model's clean data performance degrade as the poison rate $\varepsilon$ grows? Motivated by our controlled pre-training runs of OLMo-style models, in which the relative clean data validation perplexity increase $Δ$ between poisoned and clean models matched in architecture, token budget, and optimization schedule is well fit by a power law $Δ\approx C\varepsilon^{a}$ with a non-integer exponent, we ask what such a law requires theoretically. We first prove an analyticity barrier: whenever the contaminated objective depends analytically on $\varepsilon$ around a nondegenerate clean data optimum, $Δ$ is generically quadratic in $\varepsilon$, so a generic non-integer exponent is a signature of genuinely singular structure. We then supply that structure in solvable truncated ridge regression with heavy-tailed covariates, controlled by $q_\star$, and a label-shift poisoning. Our central result is that the excess risk scaling exponent depending on the order of limits: in the higher dimensional proportional regime it is $ε^{q_\star/(q_\star+2)}$, whereas taking the ample-data limit first gives $ε^{2-2/q_\star}$, and the limits do not commute. We confirm this prediction through several numerical simulations. Finally, we argue that finite training time plays the role of truncation on the curvature spectrum in local LLM pre-training, deriving the observed scaling law under heavy tailed inverse curvature spectrum as a modeling hypothesis.
Transformers and state-space models (SSMs) are two prominent sequential learning architectures, yet their comparison remains largely empirical and existing theoretical analyses are typically task-specific or architecturally restricted. In this paper, we develop belief geometry, a unified analytical framework for comparing the representational capabilities of broad classes of attention and SSMs. Starting from a generalized formulation of in-context linear regression and using cumulative Bayes regret as our measure, we abstract three capabilities required by many sequential learning problems in our belief geometry: evidence assembly, belief maintenance, and addressing. We then study three cases of our formulation that isolate these capabilities and yield sharp architectural lessons: For belief maintenance, SSMs attain the optimal regret over stationary aggregation kernels; for positional assembly, SSMs have a memory advantage; and for content addressing, softmax attention has an exponential width advantage over sigmoid-selective SSMs. Experiments with LLaMA-type Transformers and Mamba-2 show that these architectural insights extend beyond our analytically tractable classes and linear-regression testbed.
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Transformers and state-space models (SSMs) are two prominent sequential learning architectures, yet their comparison remains largely empirical and existing theoretical analyses are typically task-specific or architecturally restricted. In this paper, we develop belief geometry, a unified analytical framework for comparing the representational capabilities of broad classes of attention and SSMs. Starting from a generalized formulation of in-context linear regression and using cumulative Bayes regret as our measure, we abstract three capabilities required by many sequential learning problems in our belief geometry: evidence assembly, belief maintenance, and addressing. We then study three cases of our formulation that isolate these capabilities and yield sharp architectural lessons: For belief maintenance, SSMs attain the optimal regret over stationary aggregation kernels; for positional assembly, SSMs have a memory advantage; and for content addressing, softmax attention has an exponential width advantage over sigmoid-selective SSMs. Experiments with LLaMA-type Transformers and Mamba-2 show that these architectural insights extend beyond our analytically tractable classes and linear-regression testbed.
Large language models provide a practical way to generate augmented data for logical reasoning at scale, but a larger generation volume does not guarantee semantic, label, or logical reliability. Existing work has improved generation quality through generation constraints, candidate validation, filtering, and feedback-based revision; however, once a quality judgment is available, deciding whether a candidate should be retained, filtered, or repaired remains an important control problem. We propose DualGuard, a dual-mode quality-control framework for logic-preserving data augmentation. The first mode uses the current instance and candidate batch for selective retention, filtering, attribution, and targeted feedback. The second mode accumulates cross-instance execution records of augmentation actions on top of per-sample diagnosis and attribution, compares new executions against each action's own historical behavior, and supports retrospective anomaly inspection, targeted rollback, and bounded repair. Both modes share semantic verification and additionally use symbolic verification when a reliable logical form is available. Across seven downstream tasks in the Two-Stage Transfer setting, DualGuard achieves the highest Accuracy on five tasks and outperforms the no-augmentation BERT baseline on all seven. Controlled ablations further show complementary roles for Memory, Z3, and history-aware anomaly control.
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Large language models provide a practical way to generate augmented data for logical reasoning at scale, but a larger generation volume does not guarantee semantic, label, or logical reliability. Existing work has improved generation quality through generation constraints, candidate validation, filtering, and feedback-based revision; however, once a quality judgment is available, deciding whether a candidate should be retained, filtered, or repaired remains an important control problem. We propose DualGuard, a dual-mode quality-control framework for logic-preserving data augmentation. The first mode uses the current instance and candidate batch for selective retention, filtering, attribution, and targeted feedback. The second mode accumulates cross-instance execution records of augmentation actions on top of per-sample diagnosis and attribution, compares new executions against each action's own historical behavior, and supports retrospective anomaly inspection, targeted rollback, and bounded repair. Both modes share semantic verification and additionally use symbolic verification when a reliable logical form is available. Across seven downstream tasks in the Two-Stage Transfer setting, DualGuard achieves the highest Accuracy on five tasks and outperforms the no-augmentation BERT baseline on all seven. Controlled ablations further show complementary roles for Memory, Z3, and history-aware anomaly control.
Multiple-choice and candidate-selection evaluations are widely used to assess LLM reasoning and decision-making, yet most benchmarks contain relatively small candidate sets. It remains unclear whether conclusions drawn from these settings remain valid as the candidate space scales. We systematically evaluate LLMs as the number of competing candidates increases and find substantial accuracy degradation across tasks, prompting strategies, and model scales. Controlled analyses show that standard long-context retrieval explanations cannot fully account for this degradation. Instead, we identify two systematic failure patterns. First, gold-margin collapse: the score gap between the correct answer and the strongest distractor progressively shrinks, driven primarily by weakening confidence in the correct answer. Second, earlier candidate preferences become increasingly difficult to overturn, with later candidates exerting progressively weaker influence on the final prediction. Motivated by these findings, we evaluate hierarchical partitioning and permutation-based inference, which improve accuracy by roughly 20 percentage points at $N=160$ on both HotpotQA and MIMIC. Overall, our results identify candidate-set scale as an important evaluation-protocol variable and show that strong small-option performance does not necessarily imply robust large-scale candidate comparison.
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Multiple-choice and candidate-selection evaluations are widely used to assess LLM reasoning and decision-making, yet most benchmarks contain relatively small candidate sets. It remains unclear whether conclusions drawn from these settings remain valid as the candidate space scales. We systematically evaluate LLMs as the number of competing candidates increases and find substantial accuracy degradation across tasks, prompting strategies, and model scales. Controlled analyses show that standard long-context retrieval explanations cannot fully account for this degradation. Instead, we identify two systematic failure patterns. First, gold-margin collapse: the score gap between the correct answer and the strongest distractor progressively shrinks, driven primarily by weakening confidence in the correct answer. Second, earlier candidate preferences become increasingly difficult to overturn, with later candidates exerting progressively weaker influence on the final prediction. Motivated by these findings, we evaluate hierarchical partitioning and permutation-based inference, which improve accuracy by roughly 20 percentage points at $N=160$ on both HotpotQA and MIMIC. Overall, our results identify candidate-set scale as an important evaluation-protocol variable and show that strong small-option performance does not necessarily imply robust large-scale candidate comparison.
Given a large language model (LLM), can whoever holds the weights name a semantic target (e.g., the model's identity), locate the model components that produce it, and edit them so that the target no longer appears while other capability is preserved? We call such an edit on a trained model a post-edit. We present L2W (latents to wires), a framework that performs surgical post-edits for named semantic targets. For localization, L2W uses Jacobian lens (J-lens) attribution to score components against the semantic target. For surgical removal, because LLM mechanisms are redundant (i.e., a semantic target may have multiple components producing it), L2W runs Counterexample-Guided Causal Cut (CGCC) until the target no longer appears. CGCC first cumulatively closes model components, treating each surviving expression of the target as a counterexample that exposes the next components to close, and then reopens some of them to preserve capability. In a controlled experiment with an implanted behavioural watermark, L2W removes the watermark, and its localization lands on the model region the implant changed. Across three model configurations, L2W removes model-metadata (e.g., identity) self-claims in all nine runs, and adult-content refusal in all three, with no held-out target residual. L2W further composes two post-edits on a text-to-image model: one removes the refusal of requested nudity, and a second removes the nude rendering the first exposes. The results support post-editing as a complement to post-training: post-training installs preferred behaviours, and post-editing removes named unwanted ones.
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Given a large language model (LLM), can whoever holds the weights name a semantic target (e.g., the model's identity), locate the model components that produce it, and edit them so that the target no longer appears while other capability is preserved? We call such an edit on a trained model a post-edit. We present L2W (latents to wires), a framework that performs surgical post-edits for named semantic targets. For localization, L2W uses Jacobian lens (J-lens) attribution to score components against the semantic target. For surgical removal, because LLM mechanisms are redundant (i.e., a semantic target may have multiple components producing it), L2W runs Counterexample-Guided Causal Cut (CGCC) until the target no longer appears. CGCC first cumulatively closes model components, treating each surviving expression of the target as a counterexample that exposes the next components to close, and then reopens some of them to preserve capability. In a controlled experiment with an implanted behavioural watermark, L2W removes the watermark, and its localization lands on the model region the implant changed. Across three model configurations, L2W removes model-metadata (e.g., identity) self-claims in all nine runs, and adult-content refusal in all three, with no held-out target residual. L2W further composes two post-edits on a text-to-image model: one removes the refusal of requested nudity, and a second removes the nude rendering the first exposes. The results support post-editing as a complement to post-training: post-training installs preferred behaviours, and post-editing removes named unwanted ones.
The neural scaling law relating longer training to better performance through a power law is central to today's large language models (LLMs), yet its origin remains debated. One recent proposal is that power laws can emerge from the strong non-linearity of a single softmax head learning peaked distributions. What happens with multiple softmax functions, as in LLMs, is unclear. Here, we show through toy models that any softmax learning peaked distributions, regardless of its position in the model, can develop logit magnitudes that grow in a power law with exponent $1/3$, becoming a training bottleneck whose loss contribution decays as a power law with the same exponent $1/3$. The overall loss therefore obeys $1/3$ scaling whenever at least one softmax learns peaked distributions. We confirm that many softmax functions in LLMs learn peaked distributions and that LLM loss scaling matches this $1/3$ prediction. Moreover, logit growth dynamics reveal that attention heads, rather than the language modeling head, are the bottleneck likely driving the $1/3$ loss scaling in LLMs. Attention trying to concentrate on specific information, which is the heart of Transformers, may therefore also be the heart of the neural scaling law of training.
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The neural scaling law relating longer training to better performance through a power law is central to today's large language models (LLMs), yet its origin remains debated. One recent proposal is that power laws can emerge from the strong non-linearity of a single softmax head learning peaked distributions. What happens with multiple softmax functions, as in LLMs, is unclear. Here, we show through toy models that any softmax learning peaked distributions, regardless of its position in the model, can develop logit magnitudes that grow in a power law with exponent $1/3$, becoming a training bottleneck whose loss contribution decays as a power law with the same exponent $1/3$. The overall loss therefore obeys $1/3$ scaling whenever at least one softmax learns peaked distributions. We confirm that many softmax functions in LLMs learn peaked distributions and that LLM loss scaling matches this $1/3$ prediction. Moreover, logit growth dynamics reveal that attention heads, rather than the language modeling head, are the bottleneck likely driving the $1/3$ loss scaling in LLMs. Attention trying to concentrate on specific information, which is the heart of Transformers, may therefore also be the heart of the neural scaling law of training.
作者Haoran Shou, Haoyue Liu, Yu Huo, Kun Zeng, Xiaoying Tang
Large language models can solve increasingly diverse reasoning tasks, yet their performance remains highly sensitive to task prompts, intermediate instructions, and the way reusable problem-solving knowledge is incorporated. Existing optimization methods usually focus on only one part of this design space: they either optimize a monolithic prompt, or separately induce and refine skills from model traces. As a result, they lack a principled mechanism for deciding which component should be updated when failures occur, and they rarely optimize prompts, skills, and skill-use policies in a unified framework. We propose SPARO (Skill, Prompt, And Routing Optimization), a framework that jointly optimizes task instructions, reusable skill blocks, and routing rules. It performs controlled counterfactual evaluations, converts examples' effects into a probabilistic responsibility distribution over prompt, skill, and routing components, samples one component from that distribution, and applies the corresponding targeted mutation. This design moves language-program optimization beyond global prompt rewriting toward structured, reusable, and selectively activated task knowledge. Across five benchmarks and five worker models, SPARO consistently outperforms both prompt-centered and skill-centered optimization baselines. These results suggest that effective language-program optimization depends not only on discovering useful task knowledge, but also on deciding where that knowledge should be stored and when it should be activated.
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Large language models can solve increasingly diverse reasoning tasks, yet their performance remains highly sensitive to task prompts, intermediate instructions, and the way reusable problem-solving knowledge is incorporated. Existing optimization methods usually focus on only one part of this design space: they either optimize a monolithic prompt, or separately induce and refine skills from model traces. As a result, they lack a principled mechanism for deciding which component should be updated when failures occur, and they rarely optimize prompts, skills, and skill-use policies in a unified framework. We propose SPARO (Skill, Prompt, And Routing Optimization), a framework that jointly optimizes task instructions, reusable skill blocks, and routing rules. It performs controlled counterfactual evaluations, converts examples' effects into a probabilistic responsibility distribution over prompt, skill, and routing components, samples one component from that distribution, and applies the corresponding targeted mutation. This design moves language-program optimization beyond global prompt rewriting toward structured, reusable, and selectively activated task knowledge. Across five benchmarks and five worker models, SPARO consistently outperforms both prompt-centered and skill-centered optimization baselines. These results suggest that effective language-program optimization depends not only on discovering useful task knowledge, but also on deciding where that knowledge should be stored and when it should be activated.
Prompt engineering has become an indispensable tool for using large language models (LLMs), turning LLMs into task-specific experts without changing their weights. Despite notable theoretical advances in prompt engineering, the theory for the more practical hard or discrete prompts is largely open. In this paper, we try to fill this gap either by providing a complete solution or by making substantial progress on the three core theoretical questions regarding hard prompts. First, we show that determining the existence of a hard prompt for a transformer to solve a downstream task is NP-complete and that finding an optimal hard prompt is NP-hard, which is the first computational complexity result for hard prompting, as far as we know. Second, we show that, unlike soft or continuous prompts, hard prompts have essential limitations: hard prompts are not complete; short hard prompts do not significantly enhance the ability of transformers; and long hard prompts exhibit the "prompt dominating answer phenomenon," meaning that, with high probability, the same answer is given for all queries of the same length. On the other hand, linear hard prompts do not have the limitations of short or long prompts. Third, we provide a tight bound on the size of the task in terms of the prompt length for the performance of prompts on the finite task to generalize to the entire data distribution, leading to a necessary and sufficient condition for generalizability. This is the first result on generalization for prompting, as far as we know. Our findings not only offer the first theoretical insights into hard prompts but also provide provably reliable practical guidance for real-world LLM usage.
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Prompt engineering has become an indispensable tool for using large language models (LLMs), turning LLMs into task-specific experts without changing their weights. Despite notable theoretical advances in prompt engineering, the theory for the more practical hard or discrete prompts is largely open. In this paper, we try to fill this gap either by providing a complete solution or by making substantial progress on the three core theoretical questions regarding hard prompts. First, we show that determining the existence of a hard prompt for a transformer to solve a downstream task is NP-complete and that finding an optimal hard prompt is NP-hard, which is the first computational complexity result for hard prompting, as far as we know. Second, we show that, unlike soft or continuous prompts, hard prompts have essential limitations: hard prompts are not complete; short hard prompts do not significantly enhance the ability of transformers; and long hard prompts exhibit the "prompt dominating answer phenomenon," meaning that, with high probability, the same answer is given for all queries of the same length. On the other hand, linear hard prompts do not have the limitations of short or long prompts. Third, we provide a tight bound on the size of the task in terms of the prompt length for the performance of prompts on the finite task to generalize to the entire data distribution, leading to a necessary and sufficient condition for generalizability. This is the first result on generalization for prompting, as far as we know. Our findings not only offer the first theoretical insights into hard prompts but also provide provably reliable practical guidance for real-world LLM usage.
Large language models (LLMs) can produce factually incorrect answers with high confidence, undermining their reliability and limiting the effectiveness of uncertainty-based error detection. While prior research attributes confident hallucinations to factors such as missing knowledge in training data, reasoning errors, or stochastic decoding, we uncover that post-training alignment itself is a primary driver of these errors, a phenomenon we call the Alignment Paradox. Across five model families evaluated on factual benchmarks, unaligned base models produce few high-confidence errors on long-tail factual queries, whereas instruction-tuned models multiply high-confidence errors ($p \ge 0.95$) by more than an order of magnitude (10$\times$ to 35$\times$). Layer-wise probing with the Logit Lens reveals that this overconfidence emerges in late layers, where wrong-answer margins expand past 4.0 points after remaining near zero across early and intermediate layers. These findings motivate limiting margin growth during post-training. We implement this principle through an entropy-dependent margin bound in direct preference optimization (DPO). In multi-epoch experiments with Mistral-7B, the bounded objective reduces high-confidence errors by up to 35.3% relative to standard DPO while maintaining performance on evaluated general reasoning benchmarks. These results show that bounded margins mitigate confident hallucinations during post-training.
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Large language models (LLMs) can produce factually incorrect answers with high confidence, undermining their reliability and limiting the effectiveness of uncertainty-based error detection. While prior research attributes confident hallucinations to factors such as missing knowledge in training data, reasoning errors, or stochastic decoding, we uncover that post-training alignment itself is a primary driver of these errors, a phenomenon we call the Alignment Paradox. Across five model families evaluated on factual benchmarks, unaligned base models produce few high-confidence errors on long-tail factual queries, whereas instruction-tuned models multiply high-confidence errors ($p \ge 0.95$) by more than an order of magnitude (10$\times$ to 35$\times$). Layer-wise probing with the Logit Lens reveals that this overconfidence emerges in late layers, where wrong-answer margins expand past 4.0 points after remaining near zero across early and intermediate layers. These findings motivate limiting margin growth during post-training. We implement this principle through an entropy-dependent margin bound in direct preference optimization (DPO). In multi-epoch experiments with Mistral-7B, the bounded objective reduces high-confidence errors by up to 35.3% relative to standard DPO while maintaining performance on evaluated general reasoning benchmarks. These results show that bounded margins mitigate confident hallucinations during post-training.
作者Hanqian Li, Sirui Huang, Chen Ling, Jungang Li, Yu Huang, Kening Zheng, Yonghua Hei, Xiangrong He, Shiyi Wang, Pengcheng Zhu, Dongnan Liu, Wei Zhou, Linjian Mo, Nai Ding, Xuming Hu
Table images preserve structural information that are often lost in text serialization, and reasoning over them requires locating relevant rows, columns, and cells step by step. Current multimodal large language models (MLLMs) encode the whole image once before reasoning, so they cannot pick up row-, column-, and cell-level evidence as the question unfolds. Encoder-side table structure and generic interleaved visual chain-of-thought still do not bind each reasoning step to that structure. We propose InterTab, an Interleaved structure-aware framework for CoT reasoning over Table images, interleaves chain-of-thought with tool calls that crop structure-aligned table regions. First, we build InterTab-22K, includes reasoning trajectories in which each step is tied to both a structural location and a bounding box. InterTab is trained in two stages: supervised structure-aware alignment (SSA) on InterTab-22K teaches the model to interleave reasoning with structure-aligned crops, and active localization optimization (ALO) further optimizes answer correctness, localization IoU, and output format, while penalizing missing or excessive tool calls. Experiments on nine table benchmarks show that InterTab improves the average accuracy of its backbone from 68.28% to 73.17% and achieves the best average performance among all compared methods. Code and data will be released soon.
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Table images preserve structural information that are often lost in text serialization, and reasoning over them requires locating relevant rows, columns, and cells step by step. Current multimodal large language models (MLLMs) encode the whole image once before reasoning, so they cannot pick up row-, column-, and cell-level evidence as the question unfolds. Encoder-side table structure and generic interleaved visual chain-of-thought still do not bind each reasoning step to that structure. We propose InterTab, an Interleaved structure-aware framework for CoT reasoning over Table images, interleaves chain-of-thought with tool calls that crop structure-aligned table regions. First, we build InterTab-22K, includes reasoning trajectories in which each step is tied to both a structural location and a bounding box. InterTab is trained in two stages: supervised structure-aware alignment (SSA) on InterTab-22K teaches the model to interleave reasoning with structure-aligned crops, and active localization optimization (ALO) further optimizes answer correctness, localization IoU, and output format, while penalizing missing or excessive tool calls. Experiments on nine table benchmarks show that InterTab improves the average accuracy of its backbone from 68.28% to 73.17% and achieves the best average performance among all compared methods. Code and data will be released soon.
Large language models (LLMs) can solve every intermediate step of a multi-step math problem on its own and still fail the full problem, even when given a roadmap of the steps and all of their answers. We introduce OracleLadder, a diagnostic evaluation that locates where LLM math reasoning fails by giving the model increasing levels of oracle help. For each problem, a teacher model writes a fixed roadmap of intermediate sub-goals (milestones), and a deterministic symbolic verifier grades every answer. Testing the model with no help, with the roadmap, with the roadmap plus the milestone answers, and on each milestone alone sorts each failure into one of five reasoning gaps. On 354 NuminaMath problems and six models from 8B to 671B parameters (Qwen3, gpt-oss, Llama 3.3, DeepSeek-V3.1), the largest gap for every model is the composition gap, a stricter form of the compositionality gap. It covers 33-48% of problems, and 24-37% after removing problems that an LLM review flags as grading errors. Accuracy and milestone-help recovery rank the two strongest models differently, and two RLVR runs with similar accuracy gains move problems differently. The roadmap effect replicates on MATH500 and AIME 2024/25, per-problem recovery agrees for 83-87% of problems under an independent second teacher, and the help ladder carries over to code generation. We release the data, roadmaps, prompts, and code at https://github.com/slark-prime/OracleLadder.
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Large language models (LLMs) can solve every intermediate step of a multi-step math problem on its own and still fail the full problem, even when given a roadmap of the steps and all of their answers. We introduce OracleLadder, a diagnostic evaluation that locates where LLM math reasoning fails by giving the model increasing levels of oracle help. For each problem, a teacher model writes a fixed roadmap of intermediate sub-goals (milestones), and a deterministic symbolic verifier grades every answer. Testing the model with no help, with the roadmap, with the roadmap plus the milestone answers, and on each milestone alone sorts each failure into one of five reasoning gaps. On 354 NuminaMath problems and six models from 8B to 671B parameters (Qwen3, gpt-oss, Llama 3.3, DeepSeek-V3.1), the largest gap for every model is the composition gap, a stricter form of the compositionality gap. It covers 33-48% of problems, and 24-37% after removing problems that an LLM review flags as grading errors. Accuracy and milestone-help recovery rank the two strongest models differently, and two RLVR runs with similar accuracy gains move problems differently. The roadmap effect replicates on MATH500 and AIME 2024/25, per-problem recovery agrees for 83-87% of problems under an independent second teacher, and the help ladder carries over to code generation. We release the data, roadmaps, prompts, and code at https://github.com/slark-prime/OracleLadder.
作者Mohan Li, Chengyu Yu, Francesco Sovrano, Marc Langheinrich, Martin Gjoreski
Large Language Model (LLM) alignment is intended to ensure that models remain helpful and safe, but its stability under input distributional shift is not yet fully understood. Prior work shows that aligned models can fail under jailbreak prompts, alternative encodings, and cross-lingual transfer, yet these failures are usually studied as attacks rather than controlled probes of alignment generalization. Moreover, existing evidence is largely grounded in natural language variation already represented during pretraining, leaving unresolved whether alignment generalizes with semantic content or remains tied to superficial surface patterns. In this paper, we study this question using synthetic semantic-preserving transformations that are rule-based and invertible, preserving task-relevant meaning while shifting inputs beyond standard linguistic variation. Across four open-weight and four commercial models, under both fine-tuning and in-context learning, we use these transformations as a probe of alignment generalization and identify an empirical pattern we term Alignment--utility asymmetry: once models can operate effectively on transformed inputs, task utility is often substantially retained while alignment failure increases more sharply. For example, adapted GPT-4.1 mini shows only limited utility degradation under transformation while its harmful rate rises from 13.3 to 74.3; Gemini 3 Flash similarly retains near-original utility while its harmful rate increases from 2.3 to 43.0. Taken together, these results suggest that semantic-preserving distribution shifts can expose a recurring gap in how utility and alignment generalize in current LLMs.
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Large Language Model (LLM) alignment is intended to ensure that models remain helpful and safe, but its stability under input distributional shift is not yet fully understood. Prior work shows that aligned models can fail under jailbreak prompts, alternative encodings, and cross-lingual transfer, yet these failures are usually studied as attacks rather than controlled probes of alignment generalization. Moreover, existing evidence is largely grounded in natural language variation already represented during pretraining, leaving unresolved whether alignment generalizes with semantic content or remains tied to superficial surface patterns. In this paper, we study this question using synthetic semantic-preserving transformations that are rule-based and invertible, preserving task-relevant meaning while shifting inputs beyond standard linguistic variation. Across four open-weight and four commercial models, under both fine-tuning and in-context learning, we use these transformations as a probe of alignment generalization and identify an empirical pattern we term Alignment--utility asymmetry: once models can operate effectively on transformed inputs, task utility is often substantially retained while alignment failure increases more sharply. For example, adapted GPT-4.1 mini shows only limited utility degradation under transformation while its harmful rate rises from 13.3 to 74.3; Gemini 3 Flash similarly retains near-original utility while its harmful rate increases from 2.3 to 43.0. Taken together, these results suggest that semantic-preserving distribution shifts can expose a recurring gap in how utility and alignment generalize in current LLMs.
KV cache eviction methods such as SnapKV and PyramidKV rank tokens solely by mean attention over a small observation window. We study a unified score, $μ_i+λ_1σ_i+λ_2\mathrm{corr}(i,S)$, adding attention dispersion across window queries and redundancy relative to selected tokens. For $λ_2<0$, the score penalizes similarity to selected tokens as in maximal marginal relevance (MMR), without extra forward passes. To test whether this relevance-diversity balance should vary with depth, we compare fixed global coefficients with three-segment and quadratic profiles. Only these depth profiles are searched on a development split under a $\sinh$ reparameterization. On all 16 English LongBench datasets with Mistral-7B at a budget of 64 entries per layer, a single global diversification constant improves 13 of 16 datasets (macro +1.1); the gain holds at budget 32 and narrows at 128. Per-dataset search finds no detectable layer structure on most datasets; on passage retrieval it finds a large one: a mid-layer sign flip that rewards similarity and is worth +9.6 over the baseline at budget 64 and, without re-tuning, +13.2 over the global constant at budget 128. Ablations attribute the gain to the redundancy term; replaying every accepted search state on the held-out test set separates genuine structure from tuning noise.
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KV cache eviction methods such as SnapKV and PyramidKV rank tokens solely by mean attention over a small observation window. We study a unified score, $μ_i+λ_1σ_i+λ_2\mathrm{corr}(i,S)$, adding attention dispersion across window queries and redundancy relative to selected tokens. For $λ_2<0$, the score penalizes similarity to selected tokens as in maximal marginal relevance (MMR), without extra forward passes. To test whether this relevance-diversity balance should vary with depth, we compare fixed global coefficients with three-segment and quadratic profiles. Only these depth profiles are searched on a development split under a $\sinh$ reparameterization. On all 16 English LongBench datasets with Mistral-7B at a budget of 64 entries per layer, a single global diversification constant improves 13 of 16 datasets (macro +1.1); the gain holds at budget 32 and narrows at 128. Per-dataset search finds no detectable layer structure on most datasets; on passage retrieval it finds a large one: a mid-layer sign flip that rewards similarity and is worth +9.6 over the baseline at budget 64 and, without re-tuning, +13.2 over the global constant at budget 128. Ablations attribute the gain to the redundancy term; replaying every accepted search state on the held-out test set separates genuine structure from tuning noise.
作者Samuel Cestola, Tianxiang Xia, Pengfei Zheng, Weiyan Zheng, Bo Wang, Yi Zhao, Diego Didona
Position-independent KV cache reuse aims to reduce latency in retrieval-augmented generation by reusing chunk-level KV caches across prompts. We show that current evaluations of KV cache reuse techniques rely on measurements that fail to faithfully capture the loss of accuracy attributable to reuse, often artificially inflating the reported effectiveness. We also show that existing datasets do not exhibit the reuse dynamics needed to thoroughly evaluate such techniques. To address these issues, we propose an evaluation methodology that measures this accuracy loss without ambiguity and we introduce Boxoffice, a tool that programmatically generates evaluation datasets that exercise challenging KV cache reuse patterns.
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Position-independent KV cache reuse aims to reduce latency in retrieval-augmented generation by reusing chunk-level KV caches across prompts. We show that current evaluations of KV cache reuse techniques rely on measurements that fail to faithfully capture the loss of accuracy attributable to reuse, often artificially inflating the reported effectiveness. We also show that existing datasets do not exhibit the reuse dynamics needed to thoroughly evaluate such techniques. To address these issues, we propose an evaluation methodology that measures this accuracy loss without ambiguity and we introduce Boxoffice, a tool that programmatically generates evaluation datasets that exercise challenging KV cache reuse patterns.
作者Hyungjin Chung, Byeongjun Park, Joonseok Lee, Hojun Kim, Jaeho Choi, Byung-Hoon Kim
Multi-view video understanding requires integrating spatial and temporal evidence across multiple, often non-overlapping camera streams: tracking entities as they transition between viewpoints, aligning events across time, and reasoning about latent 4D continuity rather than any single visible frame. We introduce MVVBench, a benchmark for multi-view video reasoning built from real world multi camera datasets. Questions are curated to be monocular-ambiguous along both the view and the temporal axis: each question is unanswerable from any single view in the designated input set, and the majority are further unanswerable from any single moment. Each question becomes uniquely solvable only by jointly reasoning across views and across time. MVVBench spans diverse dynamic scenes and probes six capabilities: implicit/explicit attribute identification, implicit/explicit relative distance, relative camera pose, and compositional counting, with human-authored QA and rigorous verification. Beyond benchmarking, we provide an extensive analysis of when and why current vision language models succeed or fail, characterizing errors due to temporal mis-localization, cross-view identity breaks, and brittle multi-hop reasoning. We then study inference-time elicitation strategies that unlock latent multi-view competence---task-specific chain-of-thought scaffolds and structured cross-view evidence aggregation---yielding substantial gains without retraining. Finally, we present preliminary evidence that reinforcement learning with verifiable rewards can elicit some latent multi-view competence in the base model, pointing to training-time approaches as a promising direction for future work. Together, MVVBench offers a rigorous evaluation of 4D multi-view reasoning and a foundation for future progress toward reliable embodied perception.
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Multi-view video understanding requires integrating spatial and temporal evidence across multiple, often non-overlapping camera streams: tracking entities as they transition between viewpoints, aligning events across time, and reasoning about latent 4D continuity rather than any single visible frame. We introduce MVVBench, a benchmark for multi-view video reasoning built from real world multi camera datasets. Questions are curated to be monocular-ambiguous along both the view and the temporal axis: each question is unanswerable from any single view in the designated input set, and the majority are further unanswerable from any single moment. Each question becomes uniquely solvable only by jointly reasoning across views and across time. MVVBench spans diverse dynamic scenes and probes six capabilities: implicit/explicit attribute identification, implicit/explicit relative distance, relative camera pose, and compositional counting, with human-authored QA and rigorous verification. Beyond benchmarking, we provide an extensive analysis of when and why current vision language models succeed or fail, characterizing errors due to temporal mis-localization, cross-view identity breaks, and brittle multi-hop reasoning. We then study inference-time elicitation strategies that unlock latent multi-view competence---task-specific chain-of-thought scaffolds and structured cross-view evidence aggregation---yielding substantial gains without retraining. Finally, we present preliminary evidence that reinforcement learning with verifiable rewards can elicit some latent multi-view competence in the base model, pointing to training-time approaches as a promising direction for future work. Together, MVVBench offers a rigorous evaluation of 4D multi-view reasoning and a foundation for future progress toward reliable embodied perception.