N$-Grams Features

We reconsider the theory of probabilistic formal languages generated by n-gram models and by probabilistic context-free grammars (PCFGs). The expected hierarchy of probabilistic grammars is established by proving that every probabilistic language generated by an n-gram model is also generated by some PCFG, while some probabilistic languages generated by PCFGs cannot be generated by any $n$-gram model. We introduce the notion of fully connected PCFGs, namely PCFGs in Chomsky normal form where every production rule only involving non-terminals has non-zero probability. Our main result shows that any probabilistic language generated by an $n$-gram model differs from any probabilistic language generated by a fully connected PCFG. Therefore, the class of probabilistic languages generated by $n$-gram models is not a subset of the class generated by fully connected PCFGs.

Large language models trained recursively on their own or other models' outputs undergo model collapse, in which distributional tails and factual accuracy deteriorate while fluency survives. Prior work diagnoses collapse after training; the actionable problem is screening a corpus of unknown provenance before training. We introduce SynthSentry, a corpus-level, model-agnostic contamination signal requiring no access to the generating model, no generation history, and no synthetic labels. The score is a distributional divergence over three statistics: lexical diversity collapse, n-gram tail truncation, and perplexity variance across reference models. We evaluate on corpora contaminated by small open-weight generators and an instruction-tuned open-weight model under a leave-one-generator-out protocol. A domain-stratified study measures false positives on naturally repetitive human text (legal, clinical, source code). The score ranks corpora by severity with little loss when whole generator families are held out. Per-domain calibration holds near its nominal false-positive budget once covariance shrinkage and a bootstrap threshold replace a naive quantile, which runs four times over budget. A downstream fine-tuning check showed no contamination-driven accuracy deficit at our scale, so whether pruning recovers one remains open; the same run shows over-pruning risk once pruning exceeds the true contamination fraction. We frame screening as a data-curation defense rather than a post-hoc diagnosis and release the scoring toolkit. All results are small-scale; scope is English-language, batch-mode corpus screening. Contamination sources are single-generation or hand-authored rather than recursively generated, so results speak to synthetic contamination generally and not to recursion depth.

A deployed language model may refuse a harmful request in English yet comply with its faithful translation, revealing a cross-lingual safety failure that cannot be characterized reliably by output behavior alone. We formalize this phenomenon through an audited equivalence relation and show that, for a declared quotient, representation, metric, feature dictionary, scoring head, threshold, and contrast model, the resulting safety drift admits an exact linear-algebraic characterization. Specifically, the drift is a cross-Gram functional of the within-fiber contrast; its worst admissible value is a support function, while margin invariance is characterized by an annihilator condition. We introduce an intrinsic calibrated exposure measure, governed by the leverage duality $χ^2=1/\ell-1$, which separates observed drift into three diagnostically distinct regimes: a reader fault removable by recalibration, an exact correction that is too ill-conditioned to be reliable, and a representation-level collision that no readout-only intervention can remove. Thus, identical observed exposure can lead to fundamentally different remediation verdicts. The framework also extends to cone-valued safety heads. An untied order-swap identity provides a diagnostic for the linear control interface; its calibration-state residual predicts a distinct three-control composition error on unseen states and targets, achieving median Spearman correlation $0.964$, compared with $0.269$ for a static cross-Gram baseline. etc.....

Transformers lack a native lookup mechanism, requiring repeated dense computation to recognize and reuse local static patterns. Lngram v1 introduces tokenizer-independent conditional memory through discrete latent n-gram addressing, but its memory capacity is coupled with the backbone width, limiting scalability due to high parameter and activation costs. We propose Lngram v2, which decouples the number of routes, memory dimension, and backbone width, and introduces a context-aware grouped-query attention readout to scale memory capacity independently. A zero-value Sink and counterfactual surrogate gradients further improve readout selectivity and routing trainability while preserving hard discrete addressing. Experiments across vision--language models (VLMs) of different scales show consistent improvements, including successful scaling to a 30B-parameter model. Compared with Lngram v1, Lngram v2 substantially reduces both total and activated memory parameters while maintaining or improving language modeling performance. Further analysis shows that its discrete IDs preserve substantial semantic structure of continuous hidden states, enabling semantic recovery from IDs alone and stable ID--semantic associations across datasets. These results establish Lngram v2 as an efficient and scalable latent conditional memory mechanism whose discrete addresses also provide a structured interface for analyzing internal model representations.

We describe the architecture and ablations of Qwen3.8-Flash-Next, a sparse mixture-of-experts model with 125B parameters, 6B activated per token, and additional 51B parameters of n-gram embedding tables held off the accelerator. On fourteen pre-training benchmarks the model leads the 397B-A17B predecessor on eight and trails it on the rest by at most 2.6 points, at 1/3 the activated parameters, 1/3 the training tokens, and roughly 1/9 the training FLOPs. Token mixing uses a layer-wise hybrid of Gated DeltaNet (GDN) and global attention, with one full-attention layer in every four; at continued-pretraining time those full-attention layers are replaced by Qwen Sparse Attention (QSA), which scores context at micro-block granularity with a compressed lightweight indexer. The residual stream is widened to four branches and read through an elementwise gate, a design we call the Gated Residual (GR). Capacity is added outside the backbone by a single n-gram embedding layer whose tables are prefetched from host memory. We evaluate every candidate change along three axes: loss together with downstream benchmarks; the cost of the change in training, prefill and decode; and its effect on the optimal hyperparameters and training stability. Loss and downstream accuracy do not always move together: enlarging the n-gram vocabulary lowers loss monotonically while downstream accuracy saturates. The architecture and the Muon optimizer together shift the optimal learning rate and batch size upwards, render batch-size warmup unnecessary, and substantially improve stability under stress tests. Loss, benchmarks, efficiency and stability form one design problem. Solved jointly, they yield a recipe that is simultaneously more efficient, more capable and more stable.

Benchmark contamination is diagnosed today with n-gram overlap, with likelihood-based membership inference, or with canary strings, and each needs something usually unavailable: the training corpus, a well-chosen test statistic, or foresight at dataset release. A recent alternative reads contamination off a linear probe on internal activations. We show that the natural way to do this does not work, and specify one that survives measurement. The protocol reports a zero-sum contrast on the depth profile of probe accuracy, recentred on a level-matched placebo baseline, tested against a label-permutation null, with the reference set twice the size of the suspect set. Each choice replaces a simpler alternative we measured and rejected. Reporting the level of excess separability rather than its shape makes the false positive rate track the size of the analyst's own control set, from 0.03 to 0.99 under a true null. Contrasting against a flat depth profile fails in both directions, rejecting a true null 0.72 of the time when surface decodability rises with depth and losing all power when it falls. An item bootstrap holds the fitted probe fixed and rejects up to 0.09 of the time where a permutation null that refits it holds 0.02. A half-size baseline triples the error rate. On real transformers, baseline depth profiles are measurably not flat, spanning up to 29.1 accuracy points on a temporal split, and their non-flatness tracks the surface difference between the item sets (correlation 0.87 over 6 audits), so the correction is largest exactly where it is needed. All 4 well-matched Pile arms return null, and the protocol refuses a verdict on the temporal split rather than reporting one. What this does not establish is whether transformers carry a familiarity direction at all: the only positive sits on the split where exchangeability fails. Implementation, tests and audits are released.

Prior work on LLM-generated text has demonstrated quantitative and qualitative departures from text produced by humans. LLM-generated texts differ from human writing in style, resulting in a characteristic textual "feel," while the semantic range of LLMs is much restricted compared to that of humans. In this contribution, I note simple but consistent patterns in the statistical distribution of n-grams within LLM-generated text. Via qualitative analysis of these n-grams, I reveal deficiencies in LLM style. Because higher-order n-grams correlate to semantic content, I conclude that questions of style and semantics are not cleanly separable.

Dzongkha, being the national language of Bhutan, is a common and widely spoken language in the country. Official documents, scriptures and other literature products are written in Dzongkha in order to retain the cultural value. However, documenting Dzongkha writing is a challenging and time-consuming process, largely due to the complexity of the script, the need for multiple keystrokes per syllable, and the limited availability of efficient typing tools. An immediate system that can predict and display a list of probable words for Dzongkha is the solution for this problem. The project is mainly aimed to make Dzongkha typing as convenient as possible by reducing the number of keystrokes. Our dataset is acquired from DCDD and has a total of 100000 sentences, 1331282 words and 28344 unique words. The data preprocessing was done by removing all the alphanumeric characters, tokenization, generating N-gram sequences and padding. Three models selected for training are LSTM, Bi-LSTM and GRU. The training process included fine-tuning of the model's hyperparameters. GRU being lightweight and able to handle larger datasets performed best with 74.03% accuracy and also solved the problem of overfitting.

Cross-lingual retrieval-augmented generation (RAG) is often deployed in an English-evidence regime, where users query in diverse languages but retrieved passages remain English. In this setting, generation can fail despite strong base models: English evidence induces language drift (English or code-switching outputs) and models use evidence unreliably when producing non-English answers. We attribute these failures to two post-training challenges: (i) errors are prefix-dependent, so fixed-trajectory supervision suffers from prefix mismatch; and (ii) sequence-level (partly discrete / judge-based) rewards yield noisy credit assignment and high-variance updates. We propose TR-RAG, a teacher-regularized RL recipe that couples reward optimization with on-policy distillation on student-visited prefixes. A compact student samples on-policy answers, while a stronger frozen teacher is queried only on those prefixes and provides a prefix-wise student-to-teacher reverse-KL anchor. We further introduce a reward decomposition for English-evidence multilingual generation, combining language consistency, character 3-gram recall, and an LLM-judge score for evidence-grounded correctness. Across three benchmarks (BioASQ-ENKB5, Hotpot-ENKB5, and naturally multilingual MKQA) and two backbones, TR-RAG improves the composite of language adherence and evidence-grounded correctness over strong baselines. Crucially, the teacher anchor acts as a safety net: on in-domain languages it prevents the large language-consistency collapses (up to ~27 percentage points) that reward-only RL can suffer by drifting below even the base model, while on distant out-of-distribution languages, where reward-only RL stalls at the base model's ceiling, it still improves evidence grounding; and on character 3-gram recall the compact student sometimes surpasses its 70B teacher.

Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive. We study transformers trained on order-$k$ Markov chains and identify two complementary smoothing mechanisms. First, at finite attention-weight scale, the circuit implements a soft context-matching estimator: it aggregates contributions from exact and partial context matches, weighted exponentially by their overlap, and induces a data-dependent interpolation across context orders analogous to Jelinek-Mercer smoothing. Second, a beginning-of-sequence (BOS) token induces additive pseudo-counts, recovering Dirichlet-style smoothing. We construct a disentangled transformer implementing both mechanisms and show that trained transformers recover the predicted attention patterns. Across settings where pseudo-count smoothing is optimal or lower-order contexts provide structured evidence, trained transformers match or outperform classical count-based baselines. Our results bridge mechanistic interpretability of induction heads with classical statistical smoothing, revealing that transformers learn to regularize in-context estimation rather than simply count.

Malware poses a critical and ever-evolving threat, and robust and effective systems for detecting and classifying malware are of essential importance. $n$-grams features are among the common static features used in effective machine learning systems for malware, but these features are inherently brittle. We propose an algorithm for constructing more robust features, hamm-grams, which are a special class of regular expressions having a fixed length and single-character wildcards. We devise an efficient algorithm for finding common hamm-grams using a new locality-sensitive hash designed to produce collisions among pairs of small Hamming distance and a clustering within hash buckets to place wildcards. We then demonstrate the advantages of these features in malware classification and detection tasks.

A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes. In a parameter-neutral replacement, each hidden unit is an explicit fuzzy set operation on sigmoid-bounded [0,1] memberships: intersection AB and set-difference A(1-B), the latter a bounded positive negation ("A but not B") that gated/bilinear units lack -- a negation-capable FFN (NC-FFN). On N-bit parity they are the most parameter-efficient reasoning basis at shallow depth; at scale (125M, OpenWebText) NC-FFN ties the GELU baseline's perplexity, every unit carrying explicit logical form. Two limits share one cause: two-operand logic localizes to layer 0 and erodes under training, and the one robust grammatical deficit concentrates in licensing and quantifiers, beyond within-token operators. We resolve both with a small block of sequence quantifiers: a soft existential and a soft proportion, each with a per-unit learned forgetting rate from a sticky init. This recovers the deficit at epoch one (halving the wider epoch-two gap), modestly leads on LAMBADA, and makes the FFN legible: the structure now holds and migrates into depth; the decay un-learns its stickiness (median half-life ~1.5 tokens; zero latch units); and at the semantic layers the units read, without dictionary learning, as grammatical licensing detectors: each fires on a licensor (a comparative, a passive participle, a negative-polarity item) and carries its memory forward to predict the licensed word (than, by, nor). This legibility is localized and free only up to a partition (a fully Boolean FFN diverges in training), but the result is a parameter-neutral, language-model-quality transformer with a readable, interpretable-by-construction grammatical mechanism -- an account not just of what a feed-forward layer represents but how it licenses.

Accurate phoneme recognition is pivotal for mispronunciation detection and diagnosis (MDD) in modern standard Arabic (MSA), yet remains constrained by data scarcity and the synthetic-real domain gap. This work proposes a two-stage end-to-end framework. It integrates a pre-trained encoder with causal dilated temporal convolutional networks to preserve fine-grained phonetic variations. A hierarchical two-stage strategy first learns general mappings from native/synthetic corpora, then adapts to scarce real learner data to mitigate domain shift without over-correction. Prediction stability is further enhanced via multi-checkpoint ensemble inference with N-gram rescoring. Evaluated on the QuranMB.v2 test set, our system achieves an F1-score of $0.7201$, a $63.1$% relative improvement over baseline ($0.4414$). This performance ranks at the top of the IqraEval.2 Challenge, establishing a new state-of-the-art for low-resource MSA in MDD.

Variable-order Markov models preserve local symbolic syntax by adapting context length, but long continuations can enter recurring high-order "tunnels": repeated suffixes, locally periodic passages, or copied fragments longer than the formal Markov order. This paper introduces signed pattern control for variable-order Markov generation with BP-Regular sampling. A weighted recurrence automaton computes an activation R for a chosen family of target patterns, and belief propagation samples exactly from P_beta(x) proportional to P_0(x) exp(beta R(x)). Negative coupling makes the target patterns costly during sampling; positive coupling rewards the same patterns and turns them into controlled attractors. The target family may be mined online from overactive generated material, supplied by a score or style vocabulary, or designed as an experimental probe. The main experiments use the online homeostatic case, choosing patterns that become overactive in the sampling history. On six duration-bearing monophonic sources, including Bach and Telemann material, the negative branch reduces generated 8-gram self-reuse, increases the effective number of generated 8-grams, and increases coverage of training-supported 4-gram contexts while preserving substantial lower-order support. A pitch-sequence replication on five Weimar Jazz Database solos gives the same anti-reuse signature outside Baroque material. The same signed mechanism also provides a positive branch for probing attractor basins, phase transitions, and hysteresis in the underlying variable-order model.

Transformer-based language models for SMILES strings suffer from a locality gap: standard character-level tokenization fragments chemically meaningful motifs, forcing models to repeatedly learn local syntax at the expense of long-range dependencies. To address this without disrupting standard tokenizers, we propose MolGram, which integrates a conditional $n$-gram memory module into molecular language models. MolGram maps local string patterns to learned embeddings via scalable hash lookups and dynamically injects this regional context into hidden states. Evaluations across three tasks, including unconditional molecule generation, forward reaction prediction, and single-step retrosynthesis, show that MolGram consistently improves performance. Crucially, our analyses demonstrate that MolGram outperforms baselines with 3$\times$ more parameters, establishing explicit local pattern memory as a highly efficient inductive bias.

We present a method for automatic Chinese web neologism detection that operationalizes traditional linguistic identification principles as prompt-engineering skills. The method has four stages: tokenizer-independent character n-gram candidate generation; dictionary anchoring with a Pointwise Mutual Information pre-filter; a well-formedness skill based on Chinese word-formation principles; and a combined rule and three-way classification skill that distinguishes neologism, entity, and none. Applied to the BAAI CCI 3.0 corpus (267M documents), the method produces 226,959 classified candidates including 4,853 labeled neologisms. To evaluate the method, we develop a per-stage conditional recall decomposition in which the pipeline's strict recall factors mathematically into the product of stage conditional recalls. Applied to Hou (2023) (4,199 entries), the decomposition exposes Stage 1 candidate coverage and Stage 4B LLM semantic judgment as the two bottlenecks (R=41.5% and 60.0% respectively), while intermediate stages are near-lossless. A length-stratified analysis further reveals that the structural well-formedness skill is length-invariant (>= 96.9%) whereas the semantic novelty-classification skill is length-dependent (65.6%/59.0%/44.1% across 2/3/4-character candidates), mapping a current boundary of skill-based linguistic operationalization. We release the method, pipeline outputs, and evaluation protocol as public resources.

Remote sensing applications for environmental monitoring and disaster management are frequently constrained by a spatial--temporal trade-off: imagery with fine spatial detail is often acquired less frequently, whereas more temporally available observations are typically coarser. Single-image super-resolution provides a practical means to enhance coarse imagery without changing acquisition schedules, yet many Transformer-based SR models remain computationally expensive and can be sensitive to limited or geographically biased training data, which degrades robustness under out-of-distribution conditions. This paper presents NGram-MoSE, a lightweight Transformer architecture designed to improve both efficiency and texture continuity. NGram-MoSE introduces N-Gram Context Injection to strengthen cross-window local consistency and mitigate window-boundary artifacts, and incorporates a Mixture-of-Experts (MoE) feed-forward design to scale capacity through sparse activation without proportional growth in inference cost. Experiments on a geographically disjoint OOD test set show that NGram-MoSE achieves 31.68,dB PSNR while reducing FLOPs by $14\times$ relative to a heavyweight Transformer reference. Downstream evaluation on a landslide segmentation benchmark further demonstrates that restoring degraded inputs to the detector training scale improves performance, yielding a 4.47% absolute gain in mAP@50 over bicubic upsampling, and exhibits stronger cross-scale consistency under scale extrapolation. These results indicate that NGram-MoSE provides an effective SR module for resource-constrained remote sensing pipelines requiring robust generalization.

Modern language models represent text using discrete token-level embeddings, which forces recurring multi-token patterns to be learned implicitly across Transformer layers. Both Over-tokenized Transformers and Engram attempt to address this limitation by explicitly incorporating multi-token (n-gram) memories. However, they rely on separate hash tables for each n-gram order, which introduces hash collisions and prevents nested n-grams from sharing the underlying latent structures. To address these issues, we propose Tensorized Engram (TN-gram), a compact memory module that represents tensorized n-gram embeddings through shared factors in the Canonical Polyadic (CP) form. TN-gram learns shared token-position factors together with order-absorption vectors to encode the embeddings of different n-gram order. Comprehensive experiments demonstrate that TN-gram matches or even outperforms Engram-style n-gram modules while requiring much fewer parameters.

Speculative decoding has become a crucial component of large language model (LLM) inference, enabling faster generation by drafting multiple tokens and verifying them in parallel. However, small draft models tend to suffer from disproportionately poor multilingual capabilities. Thus, when generating text in a non-English language, speculative decoding is far less effective. We compare three strategies to improve speculative decoding efficiency for eleven languages: finetuning the draft model on task-specific data (translation); finetuning the draft model on unlabeled monolingual corpora; and training simple n-gram draft models on the same monolingual corpora. We evaluate efficiency on translation (from English into the target language) and the held-out task of story generation. We find that while task-specific distillation can significantly improve efficiency, distilled models generalize poorly to a new task. Meanwhile, n-gram draft models, despite lower acceptance rates, consistently provide large speed-ups due to much faster draft generation.

Sequence modeling requires both compositional reasoning and local static knowledge retrieval, yet standard Transformers handle both through dense computation. Engram partially decouples retrieval from the backbone, but its token-based keys remain tied to text tokenization and hash compression. We propose Lngram, a latent-space conditional memory module that learns discrete symbols directly from hidden states and performs N-gram lookup over these symbols. This design removes the dependence on tokenizer IDs and naturally extends to non-text modalities. In our evaluated settings, Lngram outperforms Transformer and Engram baselines, consistently reduces perplexity in long-context language modeling, and effectively injects domain knowledge when added post hoc to pretrained models. Joint training with the backbone further surpasses full fine-tuning, while experiments on vision-language and vision-language-action tasks show overall gains. Analyses with LogitLens and CKA suggest that Lngram enables prediction-relevant information to emerge earlier, increasing effective depth with limited inference and memory overhead. Code is available at https://github.com/zyaaa-ux/Lngram.

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.

Scaling conditional memory offers a promising way to increase language-model capacity, but existing methods such as Engram learn large memory tables from scratch during pre-training, making memory scaling expensive and sometimes ineffective. We propose Memory Grafting, a conditional memory scaling method that utilizes frozen hidden states from a grafting model as conditional n-gram memory. Given frequent local n-grams, we run the grafting model offline, store final-token hidden representations as memory values, and let the recipient model retrieve them through exact longest-match suffix lookup. Retrieved memories are adapted by lightweight projections and gates, while a hash-based Engram fallback preserves coverage for unmatched contexts. Since the grafting model is only run offline and exact lookup has expected O(1) complexity with respect to memory-bank size, Memory Grafting expands external latent capacity with limited training and inference overhead. Experiments under matched recipient architectures and pre-training budgets show that Memory Grafting improves over both MoE and vanilla Engram baselines. In the 2.8B-scale setting, it improves the average benchmark score from 51.95 for MoE and 52.43 for vanilla Engram to 53.86. In the 0.92B-scale setting, all grafting-model variants improve over the baselines, with Qwen3.5-35B-A3B giving the strongest gains. These results suggest that pretrained models can serve as reusable constructors of external latent memory, providing a practical step toward scaling future language models beyond trainable parameters alone.

Reasoning systems increasingly separate intermediate computation into private and public channels, creating evaluation cases that look similar in transcripts: independent co-derivation, direct access to private content, and indirect influence through public communication. This paper presents a counterfactual likelihood test for measuring influence between private reasoning channels. The method replaces an upstream private block with a length-matched donor block, holds the public token sequence and downstream target fixed, and measures the downstream target's negative-log-likelihood shift. On a 7B role-channel reasoning model used for validation, textual probes are unreliable: raw n-gram overlap overstates leakage, corrected overlap remains noisy, and canary reproduction reports no discrimination. Counterfactual likelihood separates unmasked and masked conditions, while length matching controls a RoPE positional confound. In the hardened masked validation, reverse B-to-A influence is near zero, while A-to-B influence persists through public-speech hidden states. A multi-checkpoint validation across three checkpoints, five seeds, and 13,734 valid directional contrasts replicates this asymmetry. A graph-separation control that blocks private-to-public carrier edges produces bit-identical natural and counterfactual scores across all 13,734 control evaluations, identifying the tested public-channel pathway as the complete carrier of the measured counterfactual signal under the implemented role-visibility mask. The results show that private-channel evaluation should report direct and indirect influence separately, and that counterfactual likelihood probes provide a practical default for measuring these boundaries.

Recent studies introduce conditional memory modules that decouple knowledge storage from neural computation, enabling more direct knowledge access. Compared to MoE, which relies on dynamic computation paths, explicit lookup provides a more efficient knowledge retrieval mechanism. However, these approaches still depend on learned memory embeddings, requiring additional training and limiting flexibility. To address this, we propose N-gram Memory (NGM), a training-free, plug-and-play module composed of a Causal N-Gram Encoder and a Cosine-Gated Memory Injector. The Causal N-Gram Encoder directly averages the pretrained token embeddings of the backbone model to construct N-gram representations, thereby eliminating the need to train separate N-gram embeddings from scratch. This design requires neither an additional memory table nor a retrieval pipeline. The Cosine-Gated Memory Injector then uses a non-parametric cosine gate with ReLU to modulate the retrieved embeddings into the contextual representations. We evaluate NGM on the Qwen3 series from 0.6B to 14B across eight benchmarks. NGM improves average performance by 0.5 to 1.2 points, with particularly clear gains on code generation and knowledge-intensive tasks (e.g., +3.0 on LiveCodeBench and +3.03 on GPQA for Qwen3-14B). Moreover, NGM also improves performance in multimodal benchmarks (e.g., MMStar +1.53 on Qwen3-VL-2B).

Adaptations of features commonly applied in the field of visual computing, co-occurrence matrix (COM) and run-length matrix (RLM), are proposed for the similarity computation of strings in general (words, phrases, codes and texts). The proposed features are not sensitive to language related information. These are purely statistical and can be used in any context with any language or grammatical structure. Other statistical measures that are commonly employed in the field such as longest common subsequence, maximal consecutive longest common subsequence, mutual information and edit distances are evaluated and compared. In the first synthetic set of experiments, the COM and RLM features outperform the remaining state-of-the-art statistical features. In 3 out of 4 cases, the RLM and COM features were statistically more significant than the second best group based on distances (P-value < 0.001). When it comes to a real text plagiarism dataset, the RLM features obtained the best results.

A method is presented for reducing the cost of representative token selection in transformer attention layers by exploiting the coherence of the representative set across depth. Activation Decorrelation Attention (ADA) selects $r \ll T$ representative tokens at each layer via a Gram threshold and computes attention on the compressed $r \times r$ problem, but the selection requires a $T \times T$ Gram matrix at every layer. The cascade mechanism introduced here inherits the representative set from layer $l$ to layer $l+1$, validates it via a $(T - r) \times r$ cross-Gram computation, and updates it with a small number of additions and removals. The cost of the selection step drops from $O(T^2 d)$ to $O(T r d)$ per layer. Validation on three model families (GPT-2 124M, GPT-J 6B, OPT 6.7B) on AMD MI300X demonstrates Gram operation savings of $22\%$ to $63\%$ with mean Jaccard overlap of $0.83$ to $0.94$ between consecutive layers. The cascade reveals that the set of informative tokens is a structural property of the input that propagates coherently through the depth of the network: the same tokens carry the non-redundant information at layer $l$ and at layer $l+1$.

Large token-indexed lookup tables provide a compute-decoupled scaling path, but their practical gains are often limited by poor parameter efficiency and rapid memory growth. We attribute these limitations to Zipfian under-training of the long tail, heterogeneous demand across layers, and "slot collapse" that produces redundant embeddings. To address this, we propose X-GRAM, a frequency-aware dynamic token-injection framework. X-GRAM employs hybrid hashing and alias mixing to compress the tail while preserving head capacity, and refines retrieved vectors via normalized SwiGLU ShortConv to extract diverse local n-gram features. These signals are integrated into attention value streams and inter-layer residuals using depth-aware gating, effectively aligning static memory with dynamic context. This design introduces a memory-centric scaling axis that decouples model capacity from FLOPs. Extensive evaluations at the 0.73B and 1.15B scales show that X-GRAM improves average accuracy by as much as 4.4 points over the vanilla backbone and 3.2 points over strong retrieval baselines, while using substantially smaller tables in the 50% configuration. Overall, by decoupling capacity from compute through efficient memory management, X-GRAM offers a scalable and practical paradigm for future memory-augmented architectures. Code aviliable in https://github.com/Longyichen/X-gram.

We compare lightweight automata-based models (n-grams) with neural architectures (LSTM, Transformer) for next-activity prediction in streaming event logs. Experiments on synthetic patterns and five real-world process mining datasets show that n-grams with appropriate context windows achieve comparable accuracy to neural models while requiring substantially fewer resources. Unlike windowed neural architectures, which show unstable performance patterns, n-grams provide stable and consistent accuracy. While we demonstrate that classical ensemble methods like voting improve n-gram performance, they require running many agents in parallel during inference, increasing memory consumption and latency. We propose an ensemble method, the promotion algorithm, that dynamically selects between two active models during inference, reducing overhead compared to classical voting schemes. On real-world datasets, these ensembles match or exceed the accuracy of non-windowed neural models with lower computational cost.

We define a multi-scale metric $d_ρ$ on strings by aggregating angle distances between all $n$-gram count vectors with exponential weights $ρ^n$. We benchmark $d_ρ$ in DBSCAN clustering against edit and $n$-gram baselines, give a linear-time suffix-tree algorithm for evaluation, prove metric and stability properties (including robustness under tandem-repeat stutters), and characterize isometries.

We present a methodological framework to discover linguistic and discursive patterns associated to different social groups through contrastive synthetic text generation and statistical analysis. In contrast with previous approaches, we aim to characterize subtle expressions of bias, instead of diagnosing bias through a pre-determined list of words or expressions. We are also working with contextualized data instead of isolated words or sentences. Our methodology applies to textual productions in any genre, encompassing narrative, task-oriented or dialogic. Contextualized data are generated using controlled combinations of situational scenarios and group markers, creating minimal pairs of texts that differ only in the referenced group while maintaining comparable narrative conditions. To facilitate robust analysis, linguistic forms are generalized and associations between linguistic abstractions and groups are quantified using a variant of pointwise mutual information to detect expressions that appear disproportionately across groups. A fragment-ranking strategy then prioritizes text segments with a high concentration of biased linguistic signals, which allows for experts to assess the harmful potential of linguistic expressions in context, bridging quantitative analysis and qualitative interpretation.

FastText remains a practical choice for industrial word representation because it can synthesize vectors for out-of-vocabulary words from character n-grams. Its original hash-bucket implementation, however, couples two engineering compromises that become painful at large scale: unrelated n-grams collide into the same row, while increasing the bucket count quickly turns the input matrix into the dominant memory cost. This paper presents a memory-efficient FastText variant based on an exact-then-compress principle: first give every observed word and n-gram an explicit identity, then compress only those rows whose learned vectors and lexical structure justify sharing. Concretely, we replace hash buckets with collision-free double-array trie indexes and compress the resulting n-gram matrix through structurally constrained prefix and suffix merging followed by mark-compact row reorganization. Unlike arbitrary hashing, the proposed method shares rows only after a high cosine-similarity test, preserving interpretable n-gram identities while reducing the number of live rows. We describe the full training and serving pipeline, including UTF-8 aware n-gram enumeration, double-array trie lookup, memory-mapped model loading, and vector reconstruction for words and sentences. On a large Chinese vocabulary benchmark with 30.1M words and 287.4M extracted n-grams, the compressed model reduces memory from 145.2GB to 28.9GB, improves load time from 12.3 minutes to 3.2 minutes, and preserves downstream quality within 0.3 points of a hash-free model. We position the result as a compact lexical memory layer for LLM-era retrieval systems and release the implementation as an extended FastText prototype.