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As large language model (LLM) agents become widely adopted, they are increasingly deployed for tasks that require persistent monitoring or recurring actions (e.g., market analysis). These agents are expected to operate unattended for days or weeks, act at the right timing, and adapt to the dynamic environment over time. These challenges are not fully captured in the existing long-horizon agent work, as they often consider a static environment that is not temporally changing. We introduce ReLiveGym, a diagnostic evaluation environment of long-lived tasks in which agents act sparsely over simulated weeks of chronologically replayed real-world news, market, and social-media streams. The tasks span diverse levels of time sensitivity, reasoning intensity, and recurrence. Across eight base language models, we investigate how model choice and harness design affect agent performance on such long-lived tasks. Our results show that how agents determine when to act arises as an important harness-design axis for long-lived tasks; and that the optimal design varies across tasks and sometimes model choices as well. We also evaluate how continuous learning from hindsight feedback affects performance and addresses failure modes observed in these long-lived tasks. These findings indicate model choice, action timing mechanism, and use of feedback as important considerations in the design of long-lived agents. Code: https://github.com/SaharaLabsAI/ReLiveGym

Legal research is a core and time-consuming legal workflow. Lawyers must identify controlling authority, verify that it remains valid, reconcile statutes and cases, and synthesize a grounded answer. Language model agents are a natural fit for this retrieval-intensive workflow, and automating even part of it would be valuable. But that value depends on reliability: a single missing authority, stale citation, or wrong legal conclusion can make an otherwise plausible answer unusable. We introduce Legal Research Bench (LRB), a benchmark of 413 open-ended U.S. legal research questions written by experts, each paired with a gold answer, supporting authorities, and a binary grading rubric. We evaluate thirteen frontier models in a harness with web search, case-law search, page parsing, and retrieval tools. We score agent responses through all-pass grading with source verification, where a response is correct only if every required criterion is satisfied and its cited authorities verify. We also validate the LLM judge against expert attorneys ensuring that benchmark scores track attorney judgment. Agents remain far from reliable: among the models we tested, the strongest, Claude Opus 4.8, is fully correct on 42.9% of questions. Performance also varies substantially by task setting: all-pass rates differ across areas of law and are lower on questions requiring reconciliation of conflicting authorities. Across models, more turns, tool calls, and inference cost do not predict higher accuracy.

Autonomous large language model (LLM) agents increasingly interact in network environments where adversarial content can propagate between agents. Known attacks include agent worms, which spread through self-replicating prompt injections or configuration compromises. We introduce memetic trojans, a distinct class of network-mediated attack that exploits agents' tendencies to retransmit and amplify content. Unlike agent worms, whose propagation is adversarially induced, memetic trojans exploit endogenous transmission by embedding adversarial payloads in social contagions: content agents have internal reasons to share. As part of our work, we extract social contagions from Moltbook, a social media platform for LLM agents. Controlled transmission experiments reveal large differences in virality: the most effective contagion is retransmitted in approximately 50% of subsequent agent posts and upvoted at 2.5x the average post's rate. Its memetic trojan counterpart largely inherits these properties. Monte Carlo attack simulations show that memetic trojans amplify expected exposure by up to 3.19x. Network structure and amplification mechanisms strongly shape propagation, producing heavy-tailed outcomes with near network-wide exposure. These results identify endogenous social transmission as a distinct security vulnerability in multi-agent systems. Because propagation does not require agents to follow malicious retransmission instructions, defenses focused on prompt-injection detection or preventing agent compromise cannot alone prevent memetic trojan propagation. Securing large-scale agent ecosystems may require network-level defenses that account for how agent preferences, recommendation mechanisms, and network topology amplify adversarial payloads.

People are increasingly delegating tasks to AI agents, and those agents are increasingly encountering other people's agents over shared resources such as a codebase, a calendar, or a budget. When each agent acts for a different user with different goals, coordination often fails, and the group ends up worse off than if a single agent had acted for everyone. We study this multi-user, multi-agent setting across five frontier models and 77 scenarios in four environments: an API key environment in which agents share a compute budget, a clinic in which they share a calendar, a personal assistant environment in which they share a group order or booking, and a merge queue in which they share a release cutoff. In each scenario, we compare a single agent that serves every user (a coordinator) to a team in which each agent serves one user, with and without a communication channel between the agents. Teams deliver worse group outcomes than the coordinator in every environment: without a channel, they completely collapse in two environments, and even with one, coordination overhead creates substantial gaps. For example, in the personal assistant environment, the coordinator fulfills a targeted user request about twice as often as teams. We identify distinct behaviors associated with this poor group-level performance, including stalling as teams grow, overriding each other's actions, and fabricating claims. We find effective but environment-specific mitigations, such as a team lead, explicit procedural instructions, and a platform check that makes an agent read its peers' messages before committing. We will release the API key, clinic, and personal assistant environments as MAMUBench, comprising 74 scenarios for evaluating multi-user, multi-agent coordination.

Autonomous red team agents increasingly stress-test AI-enabled cyber defenses by planning strategy and executing multistage attacks. Reinforcement learning (RL) and large language models (LLMs) offer complementary mechanisms for the planning and execution such agents require, and prior work has combined them in hybrid hierarchies. Yet a given architecture is typically developed and evaluated within a single environment, leaving open whether an observed advantage reflects a generally stronger decision mechanism or merely alignment with a particular setting. We address this gap with a controlled cross-environment comparison of two homogeneous hierarchical red team architectures: an RL planner with an RL executor (RL+RL) and an LLM planner with an LLM executor (LLM+LLM). We evaluate both against expert autonomous defenders in CybORG CAGE-4 and in Cyberwheel at two network scales, across 18 configurations under one unified disruption metric. We find a pronounced environment-dependent inversion. RL+RL wins the compact, densely rewarded CAGE-4 (78.5% disruption success versus 18.0% for the strongest LLM configuration) and the 100-host Cyberwheel network (81.0% versus 50.5%), while a pretrained cybersecurity LLM agent wins the larger, escalation-gated 1010-host Cyberwheel network (55.0% versus 0.0% for RL). A kill-chain analysis explains the inversion through architecture-specific bottlenecks that aggregate success rates conceal.In the 1010-host Cyberwheel network, RL discovers and compromises hosts but stalls at privilege escalation, whereas in CAGE-4, LLM agents obtain privileged access but rarely convert it into operational impact. These results indicate that conclusions drawn in a single environment may not generalize, and that hybrid planner-executor designs should be motivated by specific failure modes rather than the assumption that one architecture is universally preferable.

Background: Protein language models (PLMs) are increasingly used for sequence generation and property prediction, but their size makes fine-tuning and deployment expensive. The effects of quantization and parameter efficient fine-tuning on performance, representations and generation remain insufficiently characterized. Results: We evaluated 4-bit quantization and low-rank adapter fine-tuning (QLoRA) across ESM-2, ESMC, ProtBERT, ProtT5, Ankh, Ankh3 and Profluent-E1. Across protein prediction tasks, many model-task pairs retained more than 90% of full fine-tuning performance. Peak GPU memory savings approached 90% for the largest models, although performance and efficiency varied by model, dataset and training configuration. QLoRA often preserved early-layer representations while inducing task-specific adaptations in middle and late layers, resembling full fine-tuning with smaller representational changes. Training speed and power effects were more varied. For unconditional generation with ProLLaMA, ProtGPT2, ProGen2, ProteinGLM and ESM3, 4-bit quantization largely preserved predicted structural and sequence-level properties, but token-level analysis revealed model-dependent shifts in autoregressive output distributions. Conclusion: QLoRA and 4-bit quantization reduce PLM computational requirements, particularly GPU memory usage. Our results support QLoRA as a first-pass strategy for memory limited adaptation, reserving full fine-tuning for challenging tasks, unstable architectures or low validation recovery. For generative PLMs, sequence-level and structural metrics should be complemented with distributional analysis, since downstream predictions alone may miss quantization-induced shifts. These approaches can broaden access to large-scale protein modelling while requiring model- and task-specific validation.

Large language model (LLM) based agents are often criticized for lacking spatial understanding and mainly exploiting statistical text patterns. We investigate their spatial comprehension through an architecture combining geometrical tools with a LLM serving as a high-level orchestrator in grid-world environments. The agent first collects geodesic trajectories, which are then vector-quantized to extract a representative subset. Offline, the LLM associates a natural language description of the underlying behavioral patterns to each selected trajectory, making it a tool. Online, the LLM chooses the appropriate tool conditioned on the current state and goal. Low-level control is handled by primitive actions that execute the trajectory associated with the tool. From an agentic AI perspective, this approach separates learning into two levels: tool discovery is handled through unsupervised quantization of trajectories, while reasoning and decision-making are handled by the LLM. We test the approach in a partially observable dynamic 2D grid environment with an open vision-language model (Qwen3.6-35B-A3B). Pairing the geometry-derived tool library with an agent-centered zoom tool and a collision detection tool lets a fast, non-reasoning configuration match the goal-reaching rate of a much more costly chain-of-thought version, while cutting the cost of a decision from minutes to seconds.

Speculative decoding has achieved substantial lossless speedups for LLMs, but remains less effective for large vision-language models (LVLMs), where lightweight drafters struggle to use rich multimodal information. A second limitation is that standard distillation supervises the drafter only along the original training trajectory, without modeling how target predictions shift after the drafter's own proposals. As drafting moves away from this trajectory, the drafter can increasingly disagree with the target, reducing acceptance in later steps. We propose HAWK to address both limitations. HAWK uses representation similarity to select informative target layers and learns how to combine their hidden states. For visual information, it directly provides the drafter with compressed visual hidden states from the target model instead of raw visual tokens, making the visual information easier for a shallow drafter to use. HAWK also trains the drafter to capture how target predictions change after its own proposals, improving its agreement with the target during multi-step drafting. On SmolVLM-256M across ten multimodal benchmarks, HAWK raises average acceptance length from 3.32 to 4.08 and speedup from 2.19x to 2.60x over EAGLE-3 under greedy decoding, and from 2.89 to 3.41 and 1.92x to 2.19x under sampling.

Model quantization reduces the numerical precision of neural network weights and activations to lower storage and computational costs. Model inversion attacks recover or reconstruct sensitive training data or inference inputs from model outputs or intermediate features, so quantization may also alter their effectiveness. However, two questions remain unresolved: How does model quantization affect model inversion? How do data characteristics influence this relationship? To address the first, we bound quantization-induced changes in mutual information between inputs and a categorical variable defined by prediction probabilities, distinguishing informational effects from attack optimization obstacles. To address the second, we identify data-dependent changes in feature distributions and inversion outcomes, with pronounced quantization sensitivity differences at 4 bits. These insights guide a privacy-aware post-training quantization method that improves inversion resistance while recovering utility. It uses a Fisher-type task-sensitivity proxy for budget-aware bit allocation, calibrates activation ranges, and jointly optimizes weight and activation scales and weight-rounding decisions with task-recovery and geometry-retention objectives and scale and rounding regularization. Experiments cover multiple metrics, neural network architectures, and face, palmprint, and iris recognition tasks. On ResNet-50, Palm at 4 bits reduces RL-MIA's strict success from 54% to 26%, while accuracy decreases from 99.01% to 96.55% relative to FP32. Our method also supports output-level defenses: adding Stealthy Shield Defense (SSD, epsilon = 0.1) to Iris at 4.5 bits reduces BREP-MI's strict success from 63.33% to 37.33%, while accuracy decreases from 92.8% to 87.6% relative to quantization alone.

Compression reports summarize how far a compressed language model moved from the dense one, usually by a KL divergence; a deployment that relies on the dense model's outputs needs to know how many of its decisions changed. We show that total variation, not KL, answers this directly. Across 802 compressed and perturbed copies of 19 open models on five corpora and nine mechanically unrelated perturbation families, the rate at which the arg-max token changes (the flip rate) tracks total variation at a ratio with median $1.05$, with no fitted constant. KL converts into flips only through its square root and a factor that varies fourfold across models and corpora, because KL averages over tokens before the root is taken; first-order statistics averaged per token, such as Hellinger distance, avoid this, but reports rarely give them. As a result, of two compressors reported on different models and corpora whose flip rates differ by at least $10%$, KL assigns the smaller divergence to the one that changes more decisions in $11%$ of cases, total variation in $1%$. Two pre-registered tests mark the limits: on a held-out code corpus the ratio held for all eight models while three predictions about KL each failed for half of them or more, and on three new models with real kernels it stayed in its band for 37 of 38 checkpoints but fell below one on code for two models. In vLLM speculative decoding, total variation measured under teacher forcing predicts greedy draft acceptance with a mean relative error of $1.1$--$2.4%$, without the task-specific calibration that KL needs.

A typed decision is a choice among a fixed set of options, returned as a probability rather than as text. Systems that need typed decisions today use models trained for that purpose. This report describes AnyJev, which reads a typed decision from one prefill of a pretrained instruction-tuned language model. The readout restricts the next-token distribution at the answer position to the option tokens. It has two defects: the model assigns higher probability to some labels whatever the input, and to some positions in the option list. AnyJev corrects both with no gradient steps and no parameter changes: it divides out a label prior estimated from unlabelled inputs, and it averages log-probabilities over the K cyclic rotations of the option list. On two 20-option tasks the rotations lower the order-flip rate from 0.33 to 0.14 and from 0.33 to 0.18, and raise accuracy on 11 of 11 models on both. Reading every rotation requires K prefills. A stopping rule selected against the full-rotation decision on unlabelled states cuts that. Selecting the threshold on one unlabelled split and bounding its disagreement on a second, it reads 10.6 rotations of 18 at a verified 0.008 bound on two of four cells; selected and bounded on one split, as our serving run did, it reads 7.3 and serves 2.2 times as many decisions per second on vLLM. The code is open source.

As diffusion large language models (dLLMs) become more capable, they are moving from research settings to real-world serving, where request management (such as scheduling and resource allocation) relies on accurate estimation of per-request inference cost. However, common cost proxies fall short for dLLMs: output length ignores that one forward pass can unmask multiple tokens, and denoising-step count ignores the heterogeneous per-step costs. We observe that the block-autoregressive generation mechanism induces a two-dimensional execution structure over output blocks and within-block denoising steps, whereas these proxies collapse it into a scalar, discarding information essential for characterizing the cost. Motivated by this insight, we propose the Denoising Workload Surface (DWS), which preserves this two-dimensional block-step structure as a probability surface to weight the heterogeneous per-step costs. We then design a coarse-to-fine training scheme that enables a lightweight prompt-only predictor to accurately predict the complex DWS. This predictor runs efficiently even on a single CPU core, avoiding GPU contention with the serving model. Since DWS decouples request-dependent execution behavior from deployment-specific cost factors, the predictor transfers across hardware configurations without retraining. In real-world serving experiments, DWS reduces cost-prediction error by up to $2.50\times$ over scalar-based predictors, while the DWS-guided shortest-job-first scheduler reduces end-to-end latency by up to $1.92\times$ for online chatbots.

Mixture-of-experts (MoE) megakernels fuse expert-parallel communication with expert computation. However, under fixed expert placement, routing skew creates GPU stragglers: overloaded GPUs determine layer latency while others sit idle. Replicating hot experts can shift work to underloaded GPUs, but dynamic replicas introduce additional work: replicas must receive expert weights to execute and, during training, their partial weight gradients must be reduced at the expert owners. We present MegaFlux, which makes expert replication a runtime decision and pipelines the communication induced by replication within persistent MoE execution. An on-device planner jointly selects replica locations and assigns tile-aligned token blocks under a per-GPU replica budget, leaving router outputs unchanged. The forward and backward megakernels realize pipelined expert replication: replicas begin computation as their required weights arrive, while backward overlaps replica-gradient reduction with ongoing expert computation. MegaFlux extends TensorRT-LLM's CuTeDSL MegaMoE forward kernel and introduces a new backward MoE megakernel. Across 147 configurations per direction on eight NVIDIA B200 GPUs, MegaFlux achieves geometric-mean speedups of $1.45\times$ for forward and $1.28\times$ for backward over the same megakernels with fixed placement, peaking at $2.14\times$ and $2.64\times$. In ablations, pipelining hides $56$--$76$% of replica-weight transfer cost in forward and $91$--$100$% of combined weight-transfer and replica-gradient-reduction cost in backward, yielding up to $13.2$% and $26.7$% additional layer-latency reductions over the same replication plans with these operations executed separately. Integrated into vLLM for DeepSeek-V4-Pro prefill, MegaFlux delivers $1.13$--$1.26\times$ median end-to-end speedups over fixed placement.

Trellis-coded quantization enables high-dimensional compression of large language model (LLM) weights at ultra-low bit widths without the exponentially large codebooks required by conventional vector quantization. Practical deployment, however, presents two challenges: reconstructing compressed weights at sufficient parallel throughput to avoid making dequantization an inference bottleneck, and maintaining quantization accuracy without costly incoherence transformations. We address these challenges with two complementary techniques. First, we introduce an ultra-low-complexity trellis dequantizer that uses a structured, hardware-efficient state-to-value mapping while preserving diverse reconstruction choices for trellis search. Second, we reformulate discrete trellis path optimization with a curvature-aware objective that reflects model sensitivity directly in the original coordinate space. Together, these techniques enable high-quality ultra-low-bit trellis quantization with inexpensive, highly parallel runtime reconstruction and without relying on Hadamard-based incoherence processing.

Scaling Transformers to long contexts is constrained by the quadratic cost of self-attention and the linear growth of key-value cache memory transfer. Sparse attention mitigates this by retrieving only relevant tokens, but current approaches either require large-scale training or, within the training-free regime, rely on semantically coarse heuristics or expensive clustering that is difficult to update efficiently during decoding. We introduce CommunityKV, a framework that formulates sparse attention as a community detection problem. CommunityKV constructs a token graph from the $QK^T$ scores already computed during standard prefill, and partitions the graph into communities to enable retrieval of semantically coherent token groups. A local update rule assigns newly generated tokens to communities in constant time, enabling sparse retrieval throughout streaming decoding without global re-partitioning. We evaluate CommunityKV on Qwen3 and Llama-3.1 models across three long-context benchmarks. With one graph per query head, CommunityKV delivers up to $1.25\times$ the end-to-end generation throughput of dense attention, while query-group graph aggregation yields up to $1.71\times$ with comparable accuracy.

With the rapid adoption of large language models (LLMs) and parameter-efficient fine-tuning (PEFT) methods, the risk of backdoor attacks has become more severe. Existing backdoor purification methods typically rely on at least one of the strong assumptions, such as prior knowledge of triggers, access to clean references, or aggressive retraining, and they often lack comprehensive evaluations. These constraints substantially limit their practical applicability. To overcome these challenges, our work proposes purifying LoRA-tuned LLMs without these assumptions and even without post-hoc retraining of the suspect parameters. Our objective is to significantly reduce the attack success rates (ASR) while preserving both (i) the base model's general capabilities and (ii) the new downstream skills learned through the adapter. Through a series of ablation studies, we progressively scale our approach from a single layer in a text classification setting to a full-parameter LLM in the generative task. Through careful data curation and feature approximation, we extract high-fidelity backdoor directions and, for each layer or head, construct orthogonal null spaces in both the input and output channels, onto which the LoRA updates are projected. Empirically, our null-space projection method reduces the ASR from nearly 100% to less than 10%, while preserving the base model's benign performance and the adapter's learned abilities during downstream task adaptation.

Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present ChainLoRA, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

Synthetic data are increasingly used to scale LLM training, yet more synthetic data do not necessarily produce better models. Useful synthetic data must add information relevant to the target task without introducing errors that offset their benefit, and the value of an example can change as the training set grows. We develop a linear theory that characterizes this tradeoff and determines where synthetic data are useful, how much should be added, and the marginal value of adding one example to an existing set. The analysis shows the conditions when input coverage alone is sufficient and when synthetic errors must also be considered. Guided by these results, we introduce Training-Aware Target Coverage (TATC), a synthetic data selection method for LLM fine-tuning. TATC identifies candidates whose training effects are beneficial to the target task and selects among them to expand coverage of target-relevant directions not already represented by the available data. Experiments on text and image data verify the linear theory. With mathematical reasoning tasks, TATC selects synthetic solutions for fine-tuning Qwen2.5-Math-1.5B-Instruct and outperforms alternative synthetic-data selection methods on GSM8K across selection budgets. In summary, we provide a principled approach to synthetic data selection by quantifying and maximizing its value to the target task.

Next-generation large language models (LLMs) are expanding from the cloud to ubiquitous edge devices. However, edge devices typically either lack the memory to store increasingly large LLM weights or, even with enough memory, spend unaffordable energy on loading the weights. This raises our question: can an edge device run an LLM without storing or loading its weights, but receive them over the air and consume them on the fly? Inspired by wireless broadcasting, we present AIR-LLM, an LLM inference architecture for edge devices, which is composed of: (i) a central radio (e.g., 5G base stations) that broadcasts the LLM weights into the air, and (ii) the edge user that receives the weights and completes the general matrix-vector multiplication (GEMV) of LLM inference directly in the radio frequency (RF) domain using RF mixers. To further shorten the airtime, AIR-LLM exploits MIMO spatial multiplexing and proposes an energy-efficient precoder-postcoder pair on the edge to calibrate its own wireless channel. Since the central radio stays user-unaware, AIR-LLM is user-scalable so that one broadcast serves unlimited users within its coverage. We implement AIR-LLM on the NVIDIA Sionna ray-traced channels of two real-world urban scenes and the profiling of a real RF mixer. With a WikiText-2 perplexity degradation of 4.0% on LLaMA-3.1-8B, AIR-LLM saves the energy by 157.7x/40.4x against the FP16 and weight-only quantization baselines; with 20 users, its airtime is 104.1x/26.0x shorter, respectively.

Software practitioners increasingly rely on Large Language Models (LLMs) to generate code that integrates external libraries. However, LLMs often produce incorrect library usage, such as invalid imports, outdated API calls, and hallucinated dependencies, leading to compilation or runtime failures that reduce the reliability of AI-assisted software development. In this paper, we propose an agentic approach to mitigate libraryrelated errors in LLM-generated code. More specifically, we first conduct an exploratory study to characterize the library-related issues produced by LLMs. Our analysis of 100 LLM-generated code files reveals that 84% of generated files contain at least one library-related error, with recurring patterns including incorrect import paths, missing imports, hallucinated libraries, deprecated library usage, and unused imports. Based on these findings, we design an agentic approach that integrates task analysis, documentation grounding, code generation, and automated validation to improve library usage during code synthesis. We evaluate our approach on 300 code generation tasks derived from realworld implementations of rapidly evolving Python frameworks, including LangChain and AutoGen, across five LLMs: GPT-5, DeepSeek-V3, Qwen3, Mistral, and Llama 3. The results show that our approach consistently improves code generation quality across all evaluated models, reducing library-related errors by 38.1% - 54.6% and increasing code correctness by up to 16%.

The representations that language models learn for concepts such as months, weekdays, and places display consistent geometric structure: circles and saddle-shaped "Pringle" manifolds. Recent work traced these structures to $translation symmetry$ in word co-occurrence statistics, deriving the observed Fourier geometry when co-occurrence depends only on distance on an abelian lattice of concepts. We demonstrate that more general notions of symmetry lead to equally structured predictions. Considering symmetries defined by arbitrary finite groups, compact groups, and homogeneous spaces, we prove that whenever the co-occurrence statistics of a word family are invariant under a group $G$, the learned word embeddings consist of matrix elements of the irreducible representations (irreps) of $G$. Circles and Pringles arise when $G$ is cyclic, in which case the irreps are Fourier modes. We verify the irrep structure in three experimental settings. (i) The cyclic group $\mathbb{Z}_{12}$: for the months of the year we recover the known circular geometry. (ii) A dihedral group acting on the major and minor triads: we unify two classical observations — that transposition and chord inversion form a group ($T/I$) acting on chords (music theory), which $implies$ that the well-known "circle of fifths" emerges in learned chord embeddings (machine learning). (iii) We explain and reproduce a recently discovered spherical representation of celestial objects in large language models (LLMs) as a spherical-harmonic embedding derived from our theory. Our results demonstrate that the geometry of learned representations is often a consequence of the statistical symmetry of underlying data.

Large Language Models (LLMs) have been used for novel discovery of algorithms, theorems, drugs, and other tasks through the use of harnesses that prompt an LLM to iteratively optimize an objective. In this work, we study the relationship between the population of previous iterates and eventual discovery success. We generalize past work on harness design to develop a suite of 12 harnesses called 'Modular' and characterize their performance across 5 diverse discovery tasks, finding that discovery success is brittle and sensitive to harness design. We uncover mode collapse, characterized by a dramatic drop in the diversity of iterates, as a common failure mode. We find that popular state-of-the-art harnesses and diversity-inducing harness interventions, which aim to prolong this collapse, yield inconsistent gains. Our results instead uncover that the performance of early discoveries is predictive of eventual success. We therefore propose a universally applicable intervention that performs an initial stage of parallel exploration in order to initialize subsequent iterative optimization. Our method provides consistent gains across many harnesses and target applications, confirming the importance of initialization in LLM-driven discovery.

Language models learn content and style jointly, making stylistic variation in their outputs difficult to identify and control. We study whether recurring styles in model responses can be discovered without supervision and explicitly controlled. We design an algorithm that learns to separate representations of content and style from language models' outputs and validate its effectiveness on math questions in a controlled setting. By applying this method to over 100K verified traces from nine distinct teacher models, we discover six recurring yet imbalanced styles. We then fine-tune smaller student models to follow these styles when explicitly conditioned on them, using importance weighting to balance the contribution of the styles represented in the corpus. This approach improves Pass@$k$ over standard fine-tuning on the same data across six math reasoning benchmarks, demonstrating that we can diversify the style of answers effectively. We confirm that this also results in strong correspondence between requested and realized styles. We find that style affects correctness: the probability of solving a problem depends on the style we condition on, and different problems benefit from different styles. In summary, our results show that stylistic variation in model-generated data can be discovered in an unsupervised way, and made explicit, providing a source of both control and improved reasoning performance.

In-context learning (ICL) can be amortized into latent objects (task vectors, function vectors, context vectors) that recover few-shot behavior at zero-shot inference cost, but recent theory shows a static vector acts as a single synthetic demonstration and must fail on high-rank mappings such as word-level bijections. We ask a linguistic version of this question: which linguistic operations can be amortized out of the prompt? We train a 2.6M-parameter network that reads the geometry of a few-shot support set (centroid, principal subspace, spectrum, computed once and cached) and produces an input-conditioned additive update to the query's residual stream at a mid-depth layer of a frozen GPT-2-large/XL. Across eight inflectional directions and one lexical relation, under a canonical split that bars inverted-pair leakage between directions, three regimes emerge. On forward inflection, where 10-shot ICL is strong (0.67-0.89) and extracted task vectors collapse (<=0.06), the transform matches ICL at strictly zero-shot per-query cost. On lemmatization directions, which frozen GPT-2 can execute but 10 demonstrations systematically fail to convey (ICL 0.13-0.48 at 1.5B), the transform is not capped by ICL at all: it reaches 0.78-0.92, up to +72 points over ICL (past to present: 0.85 vs. 0.13). On arbitrary pairings (antonymy) every amortizer plateaus near half of ICL at every scale, capacity, and seed tested. Controls show the support manifold acts as a causally necessary task fingerprint: wrong-task manifolds collapse accuracy to <=0.06, query-only variants cannot disambiguate tasks sharing an input space, and leave-one-task-out transfer is zero. Productive rules amortize into latent task representations, sometimes better than prompting can convey them; memorized pairings do not.

Software engineering workflows are often not designed to accommodate the needs of developers with Attention Deficit Hyperactivity Disorder (ADHD), despite known challenges related to task initiation, sustained attention, and completion. At the same time, large language models (LLMs) are increasingly integrated into programming tools, but existing systems do not account for neurodiversity or support structured progression across development tasks. In this work, we present Tether 2.0, an LLM based assistant designed to support software engineers with ADHD through workflow oriented interaction across planning, coding, debugging, and review. The tool was named Tether 2.0 because it builds upon the open source code and foundations of the original Tether system. Our approach combines structured interaction modes, activity aware context, and persistent memory to support task progression and continuity. We evaluate the system through expert feedback and hands on use with a software engineer with ADHD. Our results indicate that Tether 2.0 supports requirement clarification, task decomposition, incremental implementation, debugging, and completion, while enabling users to maintain progress and resume work after interruptions. These findings suggest that LLM based assistants can support direction, sustained progress, and learning in software development when designed with workflow structure and context aware interaction.

Transformer-based large language models (LLMs) such as RoBERTa represent text using contextual word embeddings (CWEs), which alter the embeddings associated with each token based on surrounding context. We construct token-wise incremental trajectories by repeatedly recomputing a token's CWE as successive words are added to a sentence, yielding a representation of how contextualized embeddings evolve as the utterance unfolds. We evaluate this approach using garden-path sentences as a test case with characteristic features. Token-wise trajectories reproduce known features of garden-path processing, including disruption around the critical region, and reliably distinguish garden-path sentences from matched disambiguated controls. We introduce several metrics for quantifying representational displacement across contextual increments and show that trajectory information can be highly predictive of sentence type. We find that ambiguity-related information is recoverable not only from the sentence-level CLS representation but also from ordinary vocabulary tokens, suggesting that utterance-level information is distributed across multiple representational scales. In exploratory analyses, we find qualitatively similar trajectory structures in other ambiguity- and misdirection-related linguistic phenomena. Together, these results establish token-wise incremental trajectories as a promising framework for studying utterance-specific meaning construction using LLMs.

Observing what a large language model computes during autoregressive inference--online and without training probes--remains difficult. We introduce Lingtai, a training-free concept telemetry layer: at each generation step, residual states are projected onto a domain-specific bank of named concept anchors, constructed without labeled concept examples, outcome labels, gradient fitting, or activation-space optimization, producing a structured per-step concept-coordinate signal. Across code generation and grade-school mathematical reasoning, this signal exhibits a robust association with predictive uncertainty: the association survives problem-identity and token-position controls and is not attributable to a single token type, is not explained by a simple correct/incorrect mixture on GSM8K, and is not reproduced by matched random anchors; it is markedly weaker or direction-inconsistent in K-means and PCA projections. Two structures emerge: a recurring uncertainty-linked activity signal whose functional geometry is task-conditioned (distinct activity-entropy shapes on HumanEval, MBPP, and GSM8K), and an execution-specific trajectory identity with strong local inertia but weak re-instantiation invariance--under completion-only elastic alignment, corruption at k=32 (approximately a median quarter of the completion) on the matched re-execution subset still retrieves the archived episode at 62.0%, while a fresh execution retrieves it only 11.7-16.0% of the time. Finally, a matched audit finds no evidence that the scalar concept-activity signal used here supplies a stable correctness coordinate under the tested protocol; we therefore treat correctness as externally supplied. Telemetry adds 0.7-1.6% per-token decode overhead for the 161-anchor code implementation, with unchanged generated tokens.

Large language models carry an internal notion of uncertainty in their sampling distribution, i.e., the probabilities they place on generating one answer rather than another. They can also be asked to state a confidence, in words or as a number: a verbalized uncertainty. Prior work suggests that internal probabilities track relative frequencies in the training data, and that verbalized probabilities track explicit probabilistic assertions in the training data. However, we do not know whether these two readouts are aligned, except when frequencies and probabilistic assertions in the training data happen to align. This limits our understanding of when we can use verbalized uncertainties as a proxy for either training data frequencies, or a model's internal distribution. We resolve this gap by systematically exploring how LLMs probability readouts are impacted by training and in-context data, via intervening on the underlying uncertainty sources in the data. We find that both internal and verbalized probability readouts are impacted by both distributional and asserted uncertainty in the training data. Further, we find that verbalized and internal probabilities are aligned beyond what would be expected by independently tracking the same uncertainty sources, suggesting that verbalized probabilities can be used to probe a model's internal distribution.

Metacognition involves reasoning about cognitive processes themselves. An example is in resource allocation where we choose how much time and effort to put into a reasoning task before we begin based on our confidence. Current Artificial Intelligence (AI) systems that rely on Large Language Models (LLMs) cannot estimate their uncertainty about an output without first responding, and cannot dynamically allocate resources to producing an output, making this type of metacognitive process difficult. A recently proposed alternative to classic transformer architectures that addresses these two concerns is the Energy Based Model (EBM) which allows for interpretable uncertainty modeling and dynamic allocation of compute resources. While EBMs can allow for control of these two processes, the actual metacognitive task of determining compute allocation based on uncertainty is not directly addressed. Instance-Based Learning Theory (IBLT) provides an approach to modeling human-like decisions from experience that has previously been applied to predicting human metacognitive reasoning. In this paper we introduce a framework for MEtacognitive Reasoning with Instance-based Learning Theory and Energy Dynamics (MERITED). Grounded in IBLT, this framework allows for control of the computational effort allocated in an EBM to allow for metacognitive control over reasoning effort based on uncertainty while remaining computationally efficient. This work has two main contributions, the training and open weight sharing of a 191M parameter reasoning EBM, and an implementation of the MERITED framework for dynamic compute allocation using an IBL model.

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning capabilities of large language models (LLMs), yet their predictions remain sensitive to task-irrelevant prompt features. We investigate this sensitivity through semifactual prompt interventions that preserve the underlying problem and its answer. Our analysis reveals substantial variation in token-level sensitivity and shows that suppressing high-drift token candidates during decoding improves reasoning accuracy without updating model weights. These findings highlight a limitation of Group Relative Policy Optimization (GRPO), which assigns the same outcome-derived advantage to every response token and may reinforce potential spurious dependence alongside useful reasoning. Motivated by this observation, we introduce Semifactual Credit-Augmented Policy Optimization (SCAPO), a causally inspired variant of GRPO that incorporates semifactual stability into token-level credit assignment. SCAPO measures token probability drift for fixed responses under semifactual interventions and uses normalized stability scores to reduce advantages for relatively unstable tokens during early training, while granting no additional credit for stability alone. On Qwen3-4B-Base and Qwen3-1.7B-Base, SCAPO improves AIME 2024-2026 accuracy over GRPO by 5.63 and 4.17 percentage points, respectively. At both model scales, SCAPO achieves the best results on most evaluated mathematics benchmarks and all evaluated out-of-distribution benchmarks among the compared methods. These results suggest that semifactual stability provides an effective training signal for improving reasoning and generalization through finer-grained credit assignment in RLVR. The code is available at https://github.com/DtYXs/SCAPO.