Repeating a small block of middle layers increases a language model's effective inference depth without adding parameters or generating extra tokens, and recent work shows that this latent recurrence improves reasoning. However, two design choices limit these gains. Each iteration sees only the previous output and cannot directly access earlier computations. Moreover, a fixed loop count wastes depth on easy inputs while leaving hard ones with too little computation. We introduce RecurTrace, which addresses both limitations using the loop's own trajectory. Specifically, Loop Memory Attention lets each looped layer attend to its own states from previous iterations along the loop-time axis, so the model can revisit earlier computations instead of relying on the latest state alone. A halting head then reads the loop state and predicts whether to continue, with supervision from an oracle that identifies when additional depth still reduces loss. In a controlled MathQA comparison on the same looped backbone, RecurTrace achieves 56.9% accuracy with an average of 2.0 loops, exceeding the best fixed loop depth by 2.2 points at matched compute. By comparison, ACT and PonderNet collapse to one loop, and CALM reaches only 54.1% with 5.6 loops, while the stronger LoopUS-Conf and TaH-Mismatch baselines reach 55.3% at 3.2 loops and 55.7% at 2.1 loops. Finally, RecurTrace improves generation accuracy over same-budget fine-tuned baselines at 0.6B, 1.7B, 4B, and 8B, with the gain growing with model size from 0.6 to 3.4 points.
Ziqi Zhang, Emmanuele Chersoni, Mohammad Momeniancs.CL
Information-theoretic measures derived from autoregressive language models are widely used to characterize the expectations that shape human reading, but whether language-variety-specific training improves such psycholinguistic alignment remains unclear. This question is still open for Cantonese, where recent NLP evaluations reported mixed benefits from Cantonese-specific training relative to Mandarin-oriented or general-purpose models. Using naturalistic Cantonese eye-tracking data, we compare two within-family adaptation contrasts: CKIP GPT-2 Tiny versus its lightly Cantonese-adapted JED351 derivative, and Qwen2.5-7B versus CantoneseLLM-7B, which underwent substantially more extensive Cantonese continued pretraining and instruction tuning. From each model, we derive lexical surprisal, POS surprisal, entropy before the target, and entropy reduction. Lexical surprisal and the joint four-metric model consistently favor CantoneseLLM-7B, followed by Qwen2.5-7B, CKIP, and JED351, whereas entropy reduction favors CKIP. These results suggest that more extensive Cantonese-specific training can be associated with stronger predictive fit, while model rankings also depend on the information-theoretic measure being evaluated.
Toni J. B. Liu, Jiajun Bao, Yizhou Liu +4cs.LG cs.AI cs.CL stat.ML
What does a language model predict when it has few clues? The answer lurks in its unembedding geometry: a single direction of the unembedding matrix encodes the unigram distribution of the training corpus, which serves as the Bayesian prior the model falls back on when uncertain. This structure --- which we term the \emph{direction of ignorance} --- appears in all four model families examined (\texttt{Llama}, \texttt{Qwen}, \texttt{Gemma}, and \texttt{Pythia}), ranging from 0.4B to 405B parameters. Projecting the final prediction state onto this direction yields a per-token \emph{prior loading factor} $λ$, which, empirically, declines steadily as the context becomes more informative. Formally, the same projection decomposes the prediction state into two orthogonal vectors that correspond exactly to the two factors of a tempered Bayesian update: a unigram prior raised to the exponent $λ$ and a context-driven likelihood. This geometric-probabilistic interpretation calibrates $λ$, making it meaningfully comparable across model sizes and families, with larger models generally exhibiting lower prior reliance in the high-context limit. Finally, we show that the direction of ignorance is causally active: raising or lowering $λ$ at the final prediction state steers the prediction toward or away from the unigram prior in KL divergence.
Moghis Fereidouni, Muhammad Umair Haider, Hassan Sajjad +1cs.CL
Activation steering suppresses undesired behaviors in language models by adding a steering vector to the hidden state during generation. Recent conditional methods such as CAST and DSAS improve the behavior-capability trade-off by deciding when to intervene, but once active, they apply the full dense vector to all hidden dimensions, regardless of whether a neuron carries concept information or already lies in the desired regime. We introduce dimension-level conditioning as a complementary axis of selectivity that also decides which neurons to intervene on. Our method, GAPS (Gated Activation steering via Posterior and Separability), combines two training-free gates: a static separability gate that restricts steering to neurons with statistically reliable concept information (via AUROC), and a dynamic posterior gate that steers a neuron only when its current activation is better explained by the undesired concept under a Gaussian model. The gates add O(D) overhead per token, and they plug into existing conditional methods. On toxicity mitigation (RealToxicityPrompts) and concept removal (OneSeC) with Gemma-3 (4B) and Qwen-3 (1.7B), GAPS consistently matches or improves the Pareto front of its token-level counterparts; under a fixed capability budget, DSAS+GAPS reduces Gemma-3's toxicity rate from 6.52% to 0.48%, versus 3.52% for DSAS alone. Ablations attribute most of the gain to the posterior gate.
Junjie Yao, Liangkai Hang, Zhi-Qin John Xucs.LG cs.CL
Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern language models learn embeddings from random initialization through gradient-based training, the dynamical mechanism by which meaningful embedding structures emerge remains unclear. In this work, we identify that the evolving embedding structures are closely related to token-conditioned label and contextual distributions, which we formalize as probability signatures. We observe a progressive learning process, which we term Context Staircase: embeddings learn the low-order statistic signatures of the data before the high-order ones. More specifically, we observe that early in training they align with the simplest, context-free signature linking a token to its label, and as training proceeds, they progressively reflect signatures involving more and more context tokens. We then analyze the gradient flow of embeddings under small initialization to explain this phenomenon, deriving embedding evolution equations for feed-forward and self-attention architectures. We further extend these observations to real language-model training. Finally, we show that these embedding structures play an important role in both task learning and the incorporation of semantic structure into the embedding space. Overall, our results provide a dynamic explanation of how data statistics and architecture jointly shape token embeddings in language models, and reveal an implicit bias in the space of data statistics: training proceeds from simpler, low-order statistical relations toward increasingly complex, context-dependent ones.
A token's representation is carried through the network layer by layer. The whole vocabulary carried together forms a flow. We fit this flow's equation of motion as a discrete Langevin model over corpus-mean trajectories of Pythia-160M and Pythia-410M, and score the predicted steps on held-out tokens. Linear maps are often used as cheap surrogates for a layer. The flow they summarize is not linear: a quadratic drift beats the linear linear map at every transition of both models, and the Kramers--Moyal estimator agrees wherever its neighborhoods stay local. We then characterize the flow further. First, we show that it does not descend its own log-density. The drift instead descends a potential that is not the density. Second, the rotational component is not negligible, $4$ to $45\%$ of the explainable drift, and the circulation shows in what the flow preserves: a token keeps its angular rank across all thirteen layers while its norm rank is shuffled and its concentration rank is reversed by the last block.
A wide range of methods have been proposed for interpreting language models, delivering important insights into their inner workings. However, different methods and their resulting insights stand in relative isolation: what could the underlying structure of language models be, such that they give rise to all our interpretations? In this work, we propose using Tensor Product Representations (TPRs) as a unifying hypothesis. TPRs give a concrete proposal for how compositional structure could be represented in vector space --- as filler-role bindings. We show, both mathematically and empirically, that TPRs can unify several prior interpretability methods: additive analogies, linear probing, sparse autoencoders, and activation patching. Mathematically, we show that these methods can all be derived from TPRs. Empirically, we apply the derivations to a range of different models --- from small toy models to LLMs --- to construct instances of each of the above interpretability methods; these constructed variants perform comparably to their standard variants. We view this work as a step toward what interpretability will ideally provide: a unified account of the nature of neural networks, corroborated not just by individual observations but also by an explanation of the connections between them.
Juan Pablo Vigneaux, Mary Kennedy, Khalil Iskarous +2cs.CL
Structural probes were introduced by Hewitt and Manning to reconstruct syntactic trees from a neural language model's latent representations. They are evaluated by calculating the proportion of syntactic tree edges correctly reconstructed over an annotated corpus (as measured by undirected unlabeled attachment score). Here, we disaggregate this measure, considering undirected attachment score by label (UASL), which assesses the reconstruction accuracy of each syntactic relation separately, establishing important differences among relations that overlap linguistic distinctions. Moreover, we identify two factors that predict most of UASL's variability across relations: (i) the mean and dispersion of the linear distance (on a log scale) between the related words, and (ii) the diversity (similarity-aware entropy) of the syntactic relation's head. These results, which hold across a range of model sizes and architectures, shed light on the degree of abstraction of the representation of syntax in language models and the dependence of such representation on geometric properties of the embedding space.
Block drafters propose several tokens in one forward pass, before earlier target tokens are realised. Their rejection mixes two losses: missing within-block path information and imperfect modelling of observable information. Accepted length cannot distinguish them. We separate the two with an information floor, the minimum expected rejection at a specified conditioning order; rejection above this floor is the model gap. Estimating both from target rollouts across four domains, four open-weight targets, and a frontier API target yields three findings. First, the all-parallel floor reaches $0.286$ at the final slot on Qwen3-4B, limiting even the best proposal to $71\%$ per-slot acceptance. Second, one realised token removes $86$--$100\%$ of this floor, a locality also recovered by an independent mutual-information analysis. Third, current drafters remain far above their floors: the final-slot model gap accounts for $43$--$64\%$ of DFlash rejection and $85$--$92\%$ of DSpark's oracle-conditioned rejection. These findings separate the value of short-range conditioning from proposal quality.
The Jacobian lens (J-lens) has been proposed as a way to read verbalizable representations from language models. However, its principle and meaning lack a detailed and theoretical discussion. We provide a mathematical view of this interpretation and of its assumed causal structure. Besides treating the J-lens as a heuristic probe, we further regard it as a first-order causal transfer operator from intermediate activations to expected future readouts. We study the Jacobian matrix as the optimal local linear approximation of the downstream mapping, analyze its global approximation behavior and bias, and identify its mathematical meaning as an expectation over anticipated future readouts. Further analysis of the Jacobian energy distribution reveals that its causal geometry is highly sparse. The energy decays with depth, concentrates in an extremely small proportion, and decomposes into diagonal pathways and specific critical positions. This decomposition further resolves the expectation of the J-lens over future outputs into short-horizon and sparse concept predictions, providing a more intuitive attribution and explanation for the ability of the J-lens to visualize concepts during the thinking process. Based on the theory, we propose a simple but effective improvement strategy and decoupling method for the J-lens, which significantly enhances the ability of the J-lens to read out correct intermediate concepts.
Order-dependent activation statistics are often interpreted as evidence of interaction, but that interpretation can be confounded by where interventions enter the network. We introduce a no-fit site-asymmetry audit. For a twice-differentiable readout, the open-path order-swap decomposes into a canonical additive response measured by single interventions and an antisymmetrized second difference free of first-order and pure self-curvature terms to second order. Across six open-weight language-model families, the single-intervention baseline explains 84.3-97.7 percent of the bracket norm (mean 93.7 percent), while the no-interaction self-curvature term is 1.8-5.2 times larger than the corrected residual in the two families with the plus/minus injection split. The corrected residual clears a generic-interaction null in three of six families under a confound-free prompt split and two of six after configuration robustness. A known-positive surrogate recovers planted mixed interaction, while a matched site-separation test changes the baseline share and a random architecture reproduces the first-order regime. The same estimator transfers to released non-language references: trained residual fractions fall below a fixed Gaussian-direction null in 11/12 contrasts (5/6 ViT-B/16, 6/6 ResNet-50), a portability check rather than pooled evidence. The contribution is a reusable measurement criterion: run the single-intervention baseline before reading an order-swap vector as interaction or geometric structure; if it explains the vector, form the second difference instead. All claims are scoped to activation-space interventions at distinct sites; we do not claim that representation geometry is globally Abelian.
As people adopt transformer-based language models (e.g., ChatGPT and Gemini) for an increasing number of use-cases, it is important to know how such models learn and represent the meaning of the language, and to be more informed about what language is. This document is an attempt to help the reader understand how linguistic meaning (i.e., semantics) is approached from different fields of scientific and philosophical examination. I also explain three primary semantic theories: formal semantics, grounded semantics, and distributional semantics then compare how transformer-based language models differ from how humans learn language.
That a prompt's effect is not a property of the prompt is established: prompts optimised for one model degrade on another, and rankings reorder under neutral reformatting. That evidence is about task accuracy, which cannot say whether the interaction is a fact about task machinery or about the conditional distribution itself. We ask on a readout with no task in it: the fixed-point structure of the short-window argmax map x_{t+1} = argmax_x p(x | x_{t-1}, x_t), censused from 96 starts. It is deterministic, so nothing can be helped or hurt, and it exists only at short windows -- four of six models lose it entirely by window 16 -- so everything here concerns how a model reads a fragment. Two results. First, the interaction reaches this readout at full magnitude: nine tokens of conditioning move the fixed-point fraction across most of its range, change a four-way structural class, and reorder models, while instruction tuning worth 60.5 IFEval points moves the class by zero. Second, nothing we proposed carries it. Prefix length fails: the effect is not monotone. Four phenomenological factors -- prose-versus-markup, a universal direction, bidirectionality, instruct-resistance -- were each withdrawn within one run of being proposed, dissolved by widening the sample. And the nearest mechanistic account, attention-sink dominance of early tokens, predicts the sign of the shift on 2 of 5 models -- chance -- while a length-by-content cross shows it holds on real text and fails on our probe's uniformly random input, so we are outside its regime, not against it. One fixed nine-token prefix drives four models toward 0 and two toward 1; the bidirectionality survives in-distribution starts. On this readout the unit of explanation is the prompt-model pair. The recurring error it caught in us has a name: a criterion with a shape applied to a quantity with no room to vary.
Are frontier models able to introspect about their internal states? Recent work suggests that under certain conditions a complex enough model can audit its own internals, call out what changed, and report back confidently about it. We tested that claim on eight open-weight models from seven families and found no such ability: asked whether their own computation had been altered, none answered better than chance. To test it we built Open-Weight Masked Introspection (OWMI), a framework that intervenes on residual-stream sites, attention heads and sparse-autoencoder features, then interrogates the model about the change against the null conditions an answer has to beat: sham runs where nothing was altered, impact-matched random perturbations, and a text-only observer that sees only the visible output. Over 78,000 measurements, no model's report discriminates a real intervention from a sham beyond chance (AUROC ~0.5007), and an equivalence test bounds the effect below 0.15 percentage points of AUROC. Surprisingly, all the information needed is in the models. A model fine-tuned to report this class of intervention reaches near-perfect recovery on held-out directions, and a linear probe recovers intervention presence from the same activations at 75% to 95.8% accuracy, sharpening to no held-out error at the last layer before the model speaks. In one model the signal surfaces in the confidence rather than the words: its yes-or-no report never varies, while the confidence attached to it separates intervention from sham at AUROC 0.647. The failure sits in the path from internal state to verbal report, so oversight that reads a model's own testimony needs validating against an internal reference. While our results show the inability of current open-weight models to introspect, the debate is not settled for future models.
Whether a language model has improved itself is increasingly judged not by mean accuracy but by which individual problems it gains and loses. Tracking these transitions means differencing two noisy estimates, leaving them vulnerable to measurement artifacts. Auditing three rounds of rank-$32$ LoRA self-training on Qwen3-8B against a frozen control pushed through the identical pipeline, we identify seven measurement failures, each of which inverts a reported finding when its control is absent. Several are standard practice. A ledger built on a single greedy decode manufactures capability changes on an untrained model, largely an artifact of inference batching; the expansion statistic separating acquisition from sharpening assigns that same model a rate of $0.280$. The natural threshold repair does not survive replication: estimated across the frozen comparisons such a design already contains, its null stays non-zero. We replace it with a per-problem exact test against a pooled baseline under false-discovery-rate control, which detects nothing on any held-out replicate and is unchanged under the multiple-testing rule, error rate and pool size. Applied to a ladder of arms matched in stream, volume and evaluation, the audit finds that external distillation improves problems the base model rarely reaches while three forms of self-training do not; a regression rejects this asymmetry as a by-product of distillation's larger overall gain ($p < 10^{-8}$). On the far smaller set of problems the base model never reaches, the evidence is inconclusive, while self-training corrupts problems solved at baseline at rates well above the measured floor. Transition-level auditing therefore requires a separately measured null for every statistic it reports: nulls that cost no new experiments, built from baseline replicates a multi-arm study already owns, though not from as few as most possess.
Looped language models improve reasoning and knowledge manipulation by applying shared computation repeatedly. Existing systems usually repeat an entire layer stack, although a mixer and a dense feed-forward network (FFN) perform different operations and have different costs. We ask a narrower question: what should loop? We view recurrence as repeated composition of a state update and argue that an application is valuable when it exposes a new cross-position influence direction that remains observable at the task readout. Iterative Transport Rank (ITR) describes the cumulative influence trajectory; marginal ITR describes the nonredundant influence contributed by successive applications. This view motivates MixerLoop, which repeats each Gated DeltaNet mixer while applying its dense FFN once. We compare MixerLoop with no recurrence and full-block recurrence at 15M and 110M parameters under the same data, initialization, and architecture. A finite context-off intervention tests whether later mixer applications produce distinct, non-negligible, and beneficial changes at the final language-model readout. MixerLoop surpasses FullLoop on aggregate CORE at 15M and retains 41.5% of its CORE improvement at 110M while reducing recurrent-backbone projection FLOPs by 45.9%. These results show that the benefits of recurrent depth can be retained without repeatedly executing the dense FFN.
Intrinsic dimensionality (ID) is widely used to probe the representational complexity of language models, but it remains unclear whether ID differences reflect properties of language itself or artefacts of how the underlying dataset was constructed. In this paper, we focus specifically on how lexical diversity, the number of unique last-token items present in a dataset, affects ID estimates of that dataset. We find a scale-dependent transition between two regimes: at low lexical diversity, conditions with fewer unique final words produce higher ID, while at high lexical diversity, this ordering reverses, and conditions with more unique words produce higher ID. We derive an exact, parameter-free formula for the point at which this reversal occurs, which matches the observed transition point at every scale tested. On the one hand, our results highlight how care must be taken when interpreting the intrinsic dimensionality of a set of representations as a straightforward cue of their complexity. On the other hand, our discovery of the two ID regimes reveals a general principle of organisation of linguistic data in LLMs that sheds new light on their inner manifold structures.
On-policy distillation (OPD) has emerged as an effective paradigm for transferring knowledge between language models, where a student is trained to align its next-token distribution with the teacher's along its own trajectories. To provide dense supervision at tractable cost, many works minimize the reverse Kullback-Leibler (KL) divergence between the student and teacher's normalized distributions over the teacher's top-$k$ tokens. However, this normalized objective discards the information about tail probability: the total probability outside the teacher's top-$k$ tokens. As a result, the optimization can steadily increase the student's tail probability and entropy, empirically degrading downstream accuracy. To address this issue, we propose Tail-Aware Top-$k$ OPD (\textbf{TA-OPD}), a novel distillation method that restores the missing tail probability signal. In particular, TA-OPD minimizes the reverse KL divergence over the top-$k$ tokens plus a tail token that carries the tail probability. In effect, TA-OPD better aligns the student's next-token distribution with the teacher's, preventing the increase in tail probability and entropy caused by top-$k$ normalization. Extensive experiments demonstrate the superiority of TA-OPD, improving Avg@8 by up to 8.05 points on common benchmarks. Our code is available at https://github.com/HuipengHuang/TA-OPD.
When a language model answers an interventional question, the computation it must perform depends on the type of evidence the query requires. We report a decoupling in how a transformer organizes causal knowledge: slot-by-type structure induced by type-level supervision organizes routing, yet remains functionally decoupled from answer readout. We establish this with a typed mechanism library -- discrete mechanism slots partitioned by evidence type, auditable at the state level -- on a causal-world benchmark with exact interventional ground truth, under a frozen protocol, at two scales (22.6M and 125M). Four preregistered findings. (i) Origin. Slot-by-type organization is induced by type-level supervision: absent in architecturally identical unsupervised controls, not buyable by content-free gating labels, and statistically attributable to the supervision signal, replicating at 125M under a powered preregistered protocol (all nine cells passed). (ii) Boundary. The induced structure is a typed routing index with a sharp routing/readout boundary: slot codes scaffold routing but do not drive answer readout ($|Δ\hat{y}| \le 3.4\times10^{-6}$, zero collateral, three seeds, stable across a 5.6x scale window) -- we therefore make no behavioral-editability claim. (iii) Cost. The structure is free: LM quality matches a parameter-matched monolith within 0.0082 nats. (iv) Trust. The library state is exactly local under edit and bit-exactly revertible -- 250 single-edit and 1,000 stacked reverts per seed, zero failures. We further find that the unsupervised null itself moves with scale, so comparisons reusing a null calibrated at one scale may be confounded at another. Every claim is tied to a preregistered, machine-checkable criterion archived before the data it governs; the full audit trail, including one criterion we failed and how the frozen protocol handled it, is released as an appendix.
Activation-based tools are usually tied to one model's native hidden space, requiring probes, sparse autoencoders, and natural-language interpreters to be rebuilt or rediscovered for each new language model. We present a Universal Activation Bus, a framework that provides a common activation interface across compatible language models. Using a small set of source models, we learn a shared dense space together with one lightweight linear encoder--decoder adapter pair per model. After source training, the interface is frozen; a new model joins by fitting only its adapter pair on unlabeled matched text. The resulting interface allows activation-based tools to be shared across connected models, including common probes and SAE features as well as access to an NLA originally trained for a different model. Across five models, semantically related texts form consistent neighborhoods in the shared space, and an onboarded model reuses these tools effectively without retraining them. We further show that an intermediate activation from one model can be used by another model's frozen upper layers to produce predictions. These results establish a stable, model-wise activation contract for reusable tools across compatible language models.
On-policy self-distillation (OPSD) adapts a language model by distilling guidance from a frozen teacher on trajectories sampled from the student. Its effectiveness, however, depends critically on the quality of those trajectories. We show that when student rollouts drift from target trajectories, conditioning the teacher on off-target prefixes substantially weakens its task-relevant supervision. Controlled prefix-corruption experiments expose this failure mode, which we term rollout-conditioned signal degradation. To address this problem, we propose a unified training framework that separates two complementary supervision pathways. The first retains rollout-conditioned distribution matching, providing guidance on states the student actually visits. The second applies supervised cross-entropy on canonical ground-truth contexts, avoiding the incompatibility of imposing target tokens on erroneous rollout prefixes. Token-level rollout-target alignment is used to adapt the strength of the canonical-context anchor, emphasizing it during cold start and relaxing it as rollout quality improves. Experiments across multiple model scales, two task families, and general-reasoning benchmarks show that the proposed approach improves task acquisition over OPSD while preserving general capabilities, resulting in a more favorable empirical plasticity-stability trade-off. These findings identify context quality as a central bottleneck in on-policy self-distillation and demonstrate the value of separating rollout-conditioned guidance from canonical supervision.
Removing the left context from a causal language model reveals a useful kind of boundary: an edge where the model processes the same right-hand tokens with little change. We turn this observation into prefix-removal probing and introduce Right Reset (RR), which measures preservation of the right-hand hidden-state trajectory. A dynamic program converts RR edge scores into variable-length chunks. On flattened text formed by concatenating topically similar records after deleting their separators and layout, RR recovers 47.7% of the original records as clean units, versus 25.9% for a BGE embedding boundary, the strongest tested conventional baseline without task-specific model training. The gain persists after rendering and OCR. Passive scores from the same Qwen3-4B layer and direct prompting of a same-scale instruction model perform substantially worse on flattened records. Across six language models, RR-selected cuts also undergo consistently less local output disruption than unselected candidate edges. An observed-token likelihood-ratio readout is competitive in some architectures, indicating that the central contribution is the intervention: context dependence itself can provide a boundary signal when surface structure is weak.
Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.
Timur Mudarisov, Mikhail Burtsev, Radu Statecs.LG cs.AI cs.CL
Feed-forward networks (FFNs) account for a large fraction of Transformer parameters, yet their hidden width is usually constant across depth. We ask whether this capacity can instead be allocated from a forward-pass measurement of layer behavior. We view each FFN as transporting a cloud of token representations and quantify the induced geometric change using correspondence-preserving shift, Gromov-Wasserstein distortion, and degree-one persistent homology under raw and scale-normalized metrics. A layerwise approximation surrogate yields an exact fixed-budget optimizer. Across seven pretrained language models, raw Euclidean work largely tracks residual-norm growth, whereas normalized work is predominantly front-loaded. Gromov-Wasserstein work is more consistently associated with perturbation-based layer sensitivity than the finite-sample topological estimate. In paired 128M and 256M training runs, several normalized-work schedules reduce mean validation loss relative to both uniform width and a hand-designed cosine taper. With the amplified paired differences at 440M, the best geometry-based allocations improve over uniform substantially larger than the cosine taper, while the anti-topological raw control is worse than uniform.
Post-training can substantially alter language-model behavior, yet aggregate behavior rates do not reveal whether training removes an existing mechanism, creates a new one, or changes how an inherited mechanism is used. We study this question through two mechanistically distinct failures, repetition as a decoding-attractor pathology and sycophancy as a preference-related alignment failure. We introduce behavioral manifold analysis, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts. We construct these charts in two complementary spaces. ACT captures runtime activation states, while NOC quantifies how strongly the model routes functional information flow through the shared behavior-associated subspace. Across multiple model families, the resulting charts are highly compressed and partially alignable across architectures. Contribution-space charts expose a more architecture-robust shared core, whereas activation-space charts retain stronger family-specific structure. Tracking these charts through controlled post-training reveals a consistent asymmetry. Supervised fine-tuning substantially alters the inherited behavioral geometry, whereas reward optimization changes behavior while largely preserving the underlying chart. This geometric perspective provides a unified framework for understanding the mechanistic distinction between the two objectives. SFT tends to rewrite behavioral geometry, whereas reward optimization primarily reweights it. Code is available at https://github.com/ronglingze/Manifold-Analysis
Taeyeong Kim, Ahhyun Kim, TaeHyeon Kim +1cs.CL cs.LG
Adapting a language model to a task no longer requires training all of its weights, and a line of parameter-efficient methods has driven the trainable count from billions down to a handful of scalars. Gradient-free adaptation, which samples random weight perturbations and keeps the ones that score well, has not followed that trajectory and still perturbs every entry of the weight tensor. It is unknown whether that full-weight search is necessary, and more fundamentally which property of a perturbation makes it work at all, because existing methods vary the search space, the perturbation scale, and the aggregation together. We resolve this by intervening on one factor at a time inside a fixed pipeline, holding candidate scoring and voting constant while we vary the search dimension, the subspace that carries the perturbation, and its norm. Perturbing a frozen frame of 12 to 16 scalars stays 1.8 accuracy points behind full-weight search on average across 49 model-benchmark cells, trailing it in 36 of them. Neither the dimension nor the choice of basis explains that performance. A random frame whose Grassmann overlap with the SVD frame is at chance level performs identically once a single scale factor is matched, and at large scales the SVD directions collapse first. What survives is the perturbation norm, whose usable range closes within a factor of five across seven models and stays flat inside. The perturbation norm is therefore the one factor with a failure mode, and its safe region transfers across scale and family. The design question narrows from which subspace to perturb to how hard to shake.
Heterogeneous model fusion seeks to combine models that differ in tasks, initializations, architectures, or scales. We study an underexplored cross-scale setting: improving a small recipient language model with a stronger donor despite substantial architectural mismatch. We ask whether useful capabilities can be transferred without explicit neuron-wise semantic alignment. Building on the observation that truncating a large model to a smaller architecture and injecting it with a tiny mixing weight can already improve the recipient, we propose Activation-Prune-Merge (APM), an activation-guided framework for cross-scale fusion. APM constructs task-conditioned activation maps on the donor, selects salient layers, hidden dimensions, attention heads, and MLP neurons to prune it to the recipient architecture, and injects the resulting donor slice into the original recipient using a micro interpolation coefficient. This formulation treats the donor as a source of concentrated functional components rather than requiring precise structural transplantation. Across 16 benchmarks spanning reasoning, mathematics, code generation, instruction following, and classification, APM improves the overall average accuracy from 55.5% to 60.6% over the original 3B recipient. RTE accuracy increases from 64.3% to 82.3%, QNLI from 52.3% to 65.7%, and BoolQ from 70.8% to 79.2%. Analyses of injection ratios and sequential multi-stage fusion further suggest that activation-guided extraction improves the quality of the transferable donor slice while preserving the small-ratio fusion regime. These results provide evidence that cross-scale heterogeneous fusion can succeed without explicit semantic alignment when the donor contribution is sufficiently concentrated and carefully selected.
Identical language-model answers can arise from hidden states that support different future computations, so current-answer probes do not establish a reusable internal interface. We introduce forked futures: future operations are sampled only after a prefix state has formed, and states are compared through the response distributions induced by those operations. This yields an empirical causal quotient over hidden states without requiring researcher-specified latent labels. Shared, Local, Mixture, and Distributed interfaces then compete under prequential causal description length subject to future-signature fidelity and matched capacity constraints. In the two detailed model evaluations, Shared has the lowest held-out description length, with gains of 0.216 nats on Qwen2.5-1.5B and 0.294 nats on Llama-3-8B, while maintaining tightly clustered mean future-signature distortion; a five-backbone sweep preserves the positive direction of Sharedness Gain. The figure-aligned transplantation analysis gives Shared the strongest joint target-correctness, locality, copy-preservation, and composite profile, and API-aligned paths mediate 0.749 of the target effect versus 0.150 for matched null paths. In the blind four-class model-organism test, 14/16 architectures are recovered, with one observed non-Shared to Shared error among 12 non-Shared organisms. These results support an economical reusable causal interface within the tested operation banks, while keeping the claim explicitly conditional on the candidate architectures, interventions, and held-out futures.
A known limitation of long-context language models is their increasingly unreliable performance in non-additive, set-based aggregation as context length grows. Examples include cardinality estimation, set relationships, and grouped statistics, which widely exist in logs, program outputs, tables, and multi-turn conversations. To provide the aggregation state required by these tasks, we introduce a model-side aggregation interface that maintains compact Hash-based HyperLogLog (HLL) sketch states alongside a frozen language model. While the model processes the context, an extractor maps each relevant record to a canonical identity. The identity is then hashed and updates the HLL state. These states can be merged across context segments and/or read out directly for downstream reasoning, avoiding an additional generate-execute-return cycle. We validate the proposed approach by setting the HLL state size as 2 KiB (2,048 registers), which does not increase with context length or set cardinality. In a distinct-count experiment involving one million records, the mean relative error was 1.6%. In a separate merge test, states built from as many as 256 segments produced exactly the same readout as a single pass over the same stream. On 3,969 aggregate-then-reason tasks from 174 source windows, the fixed-budget interface reached 99.2% accuracy on Gemma 4 (31B, BF16), compared with 100.0% under exact aggregation; the paired gap was 0.8 percentage points (95% window-cluster CI: 0.5-1.3 points). On a matched set of 174 items, our method improved over direct full-context reasoning by 63.2 points on Qwen and 56.3 points on Gemma. The corresponding gains over chain-of-thought (CoT) reasoning were 60.9 and 63.2 points, respectively. On a fixed 1,200-task Oolong-Synth subset, our method reached 91.1% on Qwen and 99.3% on Gemma. Code is available at https://github.com/songdc98/sketchops.
Multi-head Latent Attention (MLA), introduced in DeepSeek-V2, compresses key-value pairs through a shared low-rank bottleneck (cKV), achieving 81% KV-cache reduction during inference. Despite its adoption in massive production models, no prior work has studied what information this bottleneck preserves or discards, nor how it reshapes internal transformer circuits. We present the first comprehensive mechanistic interpretability study of MLA, training a 114M-parameter transformer (pretrained on a web/code/math mixture, fine-tuned on TinyStories) and analyzing its representations through SVD, attention head taxonomy, linear probing, and a disruption-attribution analysis. Our key findings are: (1) the cKV bottleneck learns a pure content representation, preserving entity identity (98% retention) while discarding positional information, validating MLA's separation of content from position via RoPE; (2) induction heads co-locate at a single layer (Layer 12), unlike their distributed formation in standard MHA; (3) a single "semantic hub" layer (Layer 15) simultaneously exhibits the highest SVD effective rank and strongest disruption-attribution score; and (4) the bottleneck is globally over-provisioned, using only 46% of its capacity on average. These findings suggest MLA does not merely compress attention passively, but reshapes how the model organizes content, position, and circuit structure. We view this as an initial data point and detail scope limitations in Section 5.