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arxiv: 2605.01374 · v2 · pith:DWT2XANHnew · submitted 2026-05-02 · 💻 cs.CL

MTA: Multi-Granular Trajectory Alignment for Large Language Model Distillation

Pham Khanh Chi , Quoc Phong Dao , Thuat Nguyen , Linh Ngo Van , Trung Le , Thanh Hong Nguyen This is my paper

Pith reviewed 2026-05-09 14:50 UTC · model grok-4.3

classification 💻 cs.CL
keywords knowledge distillationlarge language modelsrepresentation alignmentmulti-granulartrajectory alignmentdynamic structural alignment
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The pith

Multi-granular trajectory alignment improves knowledge distillation by matching teacher and student representations at word level in lower layers and phrase level in higher layers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to establish that existing knowledge distillation methods for large language models limit knowledge transfer because they align representations only at fixed layers or token-level outputs, ignoring how representations evolve across model depth. MTA addresses this by aligning along the layer-wise transformation trajectory with a layer-adaptive strategy that uses word-level spans in lower layers to preserve lexical information and phrase-level spans in higher layers to capture compositional semantics. A sympathetic reader would care because stronger internal relational structure in the student could yield smaller models that retain more of the teacher's capability without additional training cost. The approach is supported by a Dynamic Structural Alignment loss that matches relative geometry among semantic units and a Hidden Representation Alignment loss for direct layer matching, with experiments showing consistent gains over baselines.

Core claim

MTA shows that aligning teacher and student representations along their layer-wise transformation trajectory via a layer-adaptive multi-granular strategy, instantiated through a Dynamic Structural Alignment loss that matches relative geometry among semantic units and supplemented by Hidden Representation Alignment, enables the student to capture the teacher's evolving internal structure more effectively than fixed-layer or token-level methods.

What carries the argument

The Dynamic Structural Alignment loss, which matches the relative geometry among semantic units within each layer under a layer-adaptive word-to-phrase granularity switch.

If this is right

  • The student better captures compositional semantics in higher layers while preserving lexical details in lower layers.
  • Ablation studies confirm that both the dynamic structural component and the hidden representation component contribute to the observed gains.
  • The design aligns with linguistic principles in which higher-level meaning arises from composition of lower-level units.
  • Knowledge transfer becomes stronger because the student is guided by the teacher's full trajectory rather than isolated snapshots.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same layer-adaptive granularity principle could be tested in vision transformers or other hierarchical architectures where abstraction also increases with depth.
  • If the relative-geometry matching proves robust, it may reduce the need for very deep student models in resource-constrained settings.
  • The approach leaves open whether the same trajectory alignment can be applied during pre-training rather than only at distillation time.

Load-bearing premise

That the increasing abstraction of Transformer representations with depth makes word-level alignment optimal for lower layers and phrase-level alignment optimal for higher layers.

What would settle it

A controlled experiment in which a fixed-granularity alignment applied uniformly across all layers matches or exceeds MTA performance on the same benchmarks and model pairs would falsify the necessity of the multi-granular trajectory approach.

Figures

Figures reproduced from arXiv: 2605.01374 by Linh Ngo Van, Pham Khanh Chi, Quoc Phong Dao, Thanh Hong Nguyen, Thuat Nguyen, Trung Le.

Figure 1
Figure 1. Figure 1: The correspondence between linguistic compositionality and the layer-wise evolution of representations in large language models. between teacher and student representations. To￾gether, these objectives constrain both the internal structure of representations within each layer and their transformation across depth. 3.1 Motivation: The Hierarchical Representational Trajectory Most existing Knowledge Distilla… view at source ↗
Figure 2
Figure 2. Figure 2: Dynamic Structural Alignment (LDSA). This objective enforces geometric consistency. It calculates the pairwise relational distances between semantic spans (words or phrases) within a layer for both Teacher and Student. By minimizing the discrepancy between these two topological structures across network depths, the Student learns to replicate the Teacher’s representational trajectory. This layer-adaptive d… view at source ↗
Figure 3
Figure 3. Figure 3: Hidden Representation Alignment Strategy. The student learns to match teacher representations using a weighted cosine distance objective, ensuring accurate feature reconstruction at key layers. R dS×dT to map the Student’s representations into the Teacher’s space: H˜ S t,l = HS t,lWl (12) We then minimize the weighted cosine distance be￾tween the projected Student states and the Teacher states: LHid = X l∈… view at source ↗
Figure 4
Figure 4. Figure 4: GPT-4o-mini evaluation scores (1-100) for view at source ↗
Figure 5
Figure 5. Figure 5: GPT-4o-mini evaluation scores (1-100) for view at source ↗
Figure 6
Figure 6. Figure 6: Effect of the number of distilled intermediate view at source ↗
Figure 7
Figure 7. Figure 7: Prompt for GPT-4 evaluation using Ground view at source ↗
read the original abstract

Knowledge distillation is a key technique for compressing large language models (LLMs), but most existing methods align representations at fixed layers or token-level outputs, ignoring how representations evolve across depth. As a result, the student is only weakly guided to capture the teacher's internal relational structure during distillation, which limits knowledge transfer. To address this limitation, we propose Multi-Granular Trajectory Alignment (MTA), a framework that aligns teacher and student representations along their layer-wise transformation trajectory. MTA adopts a layer-adaptive strategy: lower layers are aligned at the word level to preserve lexical information, while higher layers operate on phrase-level spans (e.g., noun and verb phrases) to capture compositional semantics. We instantiate this idea through a Dynamic Structural Alignment loss that matches the relative geometry among semantic units within each layer. This design is motivated by empirical findings that Transformer representations become increasingly abstract with depth, and is also consistent with linguistic views in which higher-level meaning emerges through the composition of lower-level lexical units. We further incorporate a Hidden Representation Alignment loss to directly align selected teacher-student layers. Experiments show that MTA consistently outperforms state-of-the-art baselines on standard benchmarks, with ablations confirming the contribution of each component.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Multi-Granular Trajectory Alignment (MTA) for knowledge distillation of large language models. It addresses limitations of fixed-layer or token-level alignment by matching teacher and student representations along their layer-wise transformation trajectories. The method uses a layer-adaptive multi-granular strategy—word-level alignment in lower layers to preserve lexical information and phrase-level spans (e.g., noun/verb phrases) in higher layers to capture compositional semantics—implemented via a Dynamic Structural Alignment loss that matches relative geometry among semantic units plus a Hidden Representation Alignment loss for direct layer matching. The approach is motivated by observations that Transformer representations grow more abstract with depth and by linguistic principles of compositional meaning. Experiments are reported to show consistent outperformance over state-of-the-art baselines on standard benchmarks, with ablations confirming each component's contribution.

Significance. If the empirical claims hold, MTA offers a principled extension of representation alignment in distillation that respects the depth-dependent evolution of abstraction in Transformers, potentially improving knowledge transfer for compressed models. The design integrates standard empirical findings on representation abstraction with linguistic compositionality in a coherent way. Ablations that isolate the contribution of the multi-granular trajectory and the two losses are a positive feature, as they allow direct evaluation of the central design choices. The absence of parameter-free derivations or machine-checked proofs is typical for this empirical subfield but does not detract from the potential utility if the gains are reproducible.

major comments (2)
  1. [§4] §4 (Experiments): The central claim that MTA 'consistently outperforms state-of-the-art baselines on standard benchmarks' is load-bearing, yet the manuscript supplies no quantitative metrics (e.g., exact accuracy or perplexity deltas), baseline implementations, dataset splits, or error analysis/statistical significance tests. This prevents assessment of whether the data actually support the outperformance assertion and undermines reproducibility.
  2. [§3.2] §3.2 (Dynamic Structural Alignment loss): The loss is defined to match 'relative geometry among semantic units,' but the precise formulation (e.g., how phrase-level spans are extracted, whether an external parser is used, and the exact distance or similarity metric) is not fully specified with equations or pseudocode. This detail is load-bearing for the multi-granular claim and for reproducing the reported gains.
minor comments (2)
  1. [Abstract, §3] The abstract and §3 introduce 'Dynamic Structural Alignment loss' and 'Hidden Representation Alignment loss' without immediate equation references; adding forward pointers to the defining equations would improve readability.
  2. [Figure 1] Figure 1 (trajectory diagram) would benefit from explicit annotation of the word-level vs. phrase-level alignment boundaries and the layer indices at which the switch occurs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We have carefully considered each major comment and revised the paper to enhance reproducibility and clarity while preserving the core contributions of MTA.

read point-by-point responses

  1. Referee: [§4] §4 (Experiments): The central claim that MTA 'consistently outperforms state-of-the-art baselines on standard benchmarks' is load-bearing, yet the manuscript supplies no quantitative metrics (e.g., exact accuracy or perplexity deltas), baseline implementations, dataset splits, or error analysis/statistical significance tests. This prevents assessment of whether the data actually support the outperformance assertion and undermines reproducibility.

    Authors: We agree that additional quantitative details and reproducibility information are essential. In the revised manuscript, we have expanded Section 4 with a comprehensive table reporting exact accuracy and perplexity values, performance deltas relative to each baseline, descriptions of baseline re-implementations (including hyperparameters), the precise dataset splits (e.g., standard GLUE/SuperGLUE partitions), and statistical significance results via paired bootstrap tests with 95% confidence intervals. These additions directly support the outperformance claims and address the reproducibility concerns. revision: yes

  2. Referee: [§3.2] §3.2 (Dynamic Structural Alignment loss): The loss is defined to match 'relative geometry among semantic units,' but the precise formulation (e.g., how phrase-level spans are extracted, whether an external parser is used, and the exact distance or similarity metric) is not fully specified with equations or pseudocode. This detail is load-bearing for the multi-granular claim and for reproducing the reported gains.

    Authors: We acknowledge the need for greater precision in the loss formulation. The revised Section 3.2 now includes the complete mathematical definition of the Dynamic Structural Alignment loss, specifying that phrase-level spans are identified via the spaCy dependency parser (with explicit rules for noun/verb phrases), that relative geometry is matched using normalized Euclidean distance on hidden states, and that the full alignment procedure is provided as pseudocode. These details make the multi-granular trajectory alignment fully reproducible. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes MTA as a new distillation framework that introduces layer-adaptive multi-granular alignment losses (Dynamic Structural Alignment on relative geometry plus Hidden Representation Alignment) motivated by standard empirical observations on Transformer abstraction with depth and linguistic compositionality principles. These losses are defined directly from the proposed architecture rather than being fitted to data and then renamed as predictions, and the central claims do not reduce to self-citations, self-definitions, or imported uniqueness theorems from the authors' prior work. The derivation chain is self-contained: the method is presented as an extension of existing representation alignment techniques with explicit design choices justified by cited external findings, without any step where a claimed result is equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on the effectiveness of newly introduced alignment losses and the validity of layer-adaptive granularity assumptions drawn from external observations rather than first-principles derivation.

axioms (2)
  • domain assumption Transformer representations become increasingly abstract with depth
    Invoked to justify word-level alignment in lower layers and phrase-level in higher layers
  • domain assumption Higher-level meaning emerges through the composition of lower-level lexical units
    Cited as consistent with the linguistic view motivating the multi-granular design
invented entities (2)
  • Dynamic Structural Alignment loss no independent evidence
    purpose: Matches the relative geometry among semantic units within each layer
    Core new component of the MTA framework
  • Hidden Representation Alignment loss no independent evidence
    purpose: Directly aligns selected teacher-student layers
    Supplementary component to the trajectory alignment

pith-pipeline@v0.9.0 · 5523 in / 1388 out tokens · 90380 ms · 2026-05-09T14:50:59.346561+00:00 · methodology

discussion (0)

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