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When Tokenization is Secretly Output Supervision

Tanja Baeumel, Josef van Genabith, Simon Ostermann

arXiv:2609.01386v1cs.CL

TL;DR

Tokenization is usually treated as input preprocessing, leaving the role of output granularity in defining the learning problem underexplained. The paper develops an output-supervision framework and tests it by decoupling input from output tokenization in numeric reasoning. Output tokenization predicts differences in task performance, training dynamics, and internal representations, while numeric-reasoning comparisons often fail to report this supervision regime.

  • Problem

    Tokenization is commonly viewed as input representation, but the paper identifies a missing account of how output granularity affects the task trained in autoregressive models.

  • Method

    The paper develops an output-supervision framework and uses controlled arithmetic experiments that decouple input from output tokenization, supplemented by probing and a survey of 120 numeric-reasoning papers.

  • Results

    Output tokenization drives differences in task performance, training dynamics, and model internals, largely independently of input tokenization; fewer than 10% report numeric granularity and 69% compare across unreported regimes.

  • Takeaways & Limitations

    Comparisons between language models may partly reflect differences in the output-supervision task defined by tokenization rather than differences in ability.

  • Takeaways & Limitations

    The experiments are limited to three-digit addition with small models, and the magnitude of tokenization effects in practical settings cannot be predicted from them.

Abstract

from arXiv · show

Tokenization in language models is treated by default as an input preprocessing decision. We argue that this framing is incomplete: in autoregressive models, tokenizer granularity determines what the model must resolve in a single forward pass, and therefore the supervision signal it receives. This affects both the difficulty of the learning problem and the representations that emerge inside the model. We test this in a controlled experiment on numeric reasoning with a novel decoupling of input and output tokenization. As the output supervision view predicts, differences in task performance, training dynamics, and model internals are induced by output tokenization and largely invariant to input tokenization. This may matter in practice, because models with different tokenization strategies differ not only in input representation but in the task they were trained on. Comparisons between models may thus partly reflect task definition rather than ability. A survey of 120 recent *CL papers on numeric reasoning confirms that this is rarely acknowledged: only about 10% report the numeric tokenization of the models they evaluate, while 69% compare across tokenization, and thus supervision, regimes without reporting it. While prior work documents that tokenization consistently affects model performance, there is no principled account of why. We argue that framing tokenization as output supervision provides that account.

1 Introduction

The paper reframes tokenization as output supervision: output granularity determines the task resolved per forward pass, affecting learning difficulty and internal representations. Controlled experiments and a survey of numeric-reasoning papers support this perspective.

  • Motivation: Tokenization is conventionally treated as input preprocessing, but output granularity determines the unit of supervision in autoregressive models.The loss is computed over the next output token, making token boundaries part of the learning problem.
  • Conceptual framing: Models trained with coarser output targets solve a different learning problem from models producing the same untokenized ground truth at finer granularity.The distinction parallels supervised-learning settings where word-level and character-level targets define different tasks and representations.
  • Contribution: Tokenization affects task performance, training dynamics, and model-internal representations, with the experimental effect driven primarily by output tokenization.The paper decouples input and output tokenization to distinguish input representation from output supervision.
  • Empirical motivation: Fewer than 10% of 120 surveyed numeric-reasoning papers report numeric tokenization granularity, while 69% compare models across regimes without noting it.Such comparisons may partly reflect differences in task definition rather than numeric reasoning ability.

2 A New Perspective: Tokenization Defines the Task to Solve

The paper defines output tokens as computational and supervisory units in autoregressive models, using integer tokenization to show how granularity changes the task. It further predicts that models resolve what their output supervision requires, while acknowledging a gap between rewarded computation and task requirements.

  • Tokenization Regimes: Holistic tokenization represents a multi-component unit as one token, whereas fragmented tokenization decomposes it into sub-components.For integers, 578 can be represented as [578] or [5, 7, 8]; fragmentation is defined by compositional segmentation, not necessarily characters.
  • Output Tokens as Units of Computation: Autoregressive training supervises exactly one output token per position, so required computation must be completed within a single forward pass.Output token granularity therefore constrains the unit of computation and supervision.
  • Arithmetic Example: In three-digit addition, holistic output requires all result digits jointly, whereas fragmented output permits step-wise prediction with previously generated digits as context.The abstract arithmetic task is unchanged, but the learning problem and distribution of difficulty differ.
  • Arithmetic Example: A random valid-token baseline is 1/10 per pass with fragmented tokenization versus 1/1000 with holistic tokenization, while end-to-end success is 1/1000 in both regimes.The regimes distribute equivalent overall difficulty differently across forward passes.
  • Scope: Output tokenization constrains what models must resolve but is not the sole determinant of learned representations, which are also shaped by architecture, data, optimization, and scale.The paper presents this as a narrower claim about detectable signatures in performance and internal representations.
  • Minimal Computation Hypothesis: The minimal computation hypothesis predicts that fragmented supervision makes only the currently required sub-component directly rewarded, leaving later sub-components at chance when probed.Under holistic supervision, all result sub-components must be resolved simultaneously; the hypothesis concerns training pressure, not absolute representational capability.

3 Controlled Evidence for the Output Supervision View

Controlled arithmetic experiments separate input representation from output supervision, showing that output tokenization shapes performance, training dynamics, and internal representations. Fragmented outputs support sequential computation, whereas holistic outputs require joint resolution of all result digits.

  • Task performance: MF converges reliably and quickly across seeds, whereas MH converges unreliably and reaches lower accuracy.The comparison uses the best hyperparameter setting, lr := 0.0001 and wd := 0.01.
  • Task performance: A factorial decoupling of input and output tokenization tests whether performance follows the input or output axis.The design compares MF with MHin, Fout and MH with MFin, Hout while computing cross-entropy only over output tokens.
  • Task performance: Models sharing output tokenization show comparable task performance and training dynamics regardless of input encoding.The observed relationships are MFin, Hout ≃ MH and MHin, Fout ≃ MF.
  • Model internals: At Layer 3, holistic-output models encode all three result digits, while fragmented-output models encode only the units digit.The probing analysis examines residual-stream activations at the = position across layers and digit positions.
  • Model internals: Internal representations track output rather than input tokenization: fragmented outputs compute digits sequentially, while holistic outputs resolve them jointly.This pattern supports the minimal computation hypothesis and is reported as MF ≃ MHin, Fout and MH ≃ MFin, Hout.

4 Tokenization Goes Unreported: A Survey of Reporting Practice

A survey of 120 recent ACL-family papers on numeric reasoning finds that numeric tokenization is rarely reported and often differs across compared models. Consequently, reported arithmetic comparisons may conflate reasoning ability with output supervision regime.

  • Survey design: The survey retrieved 120 mathematical or numeric reasoning papers from ACL, EMNLP, NAACL, and EACL in 2024 and 2025.Papers were filtered for topical fit and manually assessed for numeric-tokenization reporting and cross-model comparisons.
  • Results: 11/120 papers (9.2%) explicitly report the numeric tokenization strategy of evaluated models.This is fewer than 1 in 10 papers.
  • Results: 83 papers compare fragmented and holistic tokenization without flagging or controlling for the supervision-regime difference.Among the remaining papers, 20 evaluate only one tokenization type and 6 are unresolvable because tokenizers are closed-source or undisclosed.
  • Implications: Arithmetic comparisons between models with different output tokenization do not isolate reasoning ability from supervision regime.The practical impact may range from small to decisive, but cannot be assessed without reporting tokenization strategy.

5 Related Work

Related work treats tokenization mainly as input representation, while evidence across domains shows that it affects performance and learned representations. Prior arithmetic work also reports digit-position-specific mechanisms, which this paper interprets through output supervision.

  • Internal mechanisms of arithmetic: Limited linear decodability of the units digit in MH may reflect both lower units-digit accuracy and nonlinear representations.The passage points to higher MLP-probe than linear-probe accuracy as supporting evidence for possible nonlinearity.
  • Tokenization and task performance: Subword tokenization is generally treated as input preprocessing, with prior work emphasizing compression and vocabulary design.Source and target segmentation have been separated in machine translation, but not primarily to explain what models learn.
  • Tokenization and task performance: Prior studies document tokenization effects in arithmetic, temporal reasoning, code analysis, genomics, and broader tokenization-bias research.Morphology remains contested, so the paper uses it as motivation for generality rather than direct evidence.
  • Supervision granularity: In supervised learning, coarser prediction targets yield coarser features, and auxiliary supervision granularity affects representation depth.These findings provide related evidence that target granularity can shape learned representations outside autoregressive tokenization.
  • Internal mechanisms of arithmetic: Prior arithmetic work finds three digit-position-specific processing pathways with coarse numeric tokenization but only one with digit-wise tokenization.The paper hypothesizes that this pattern results from differing output supervision regimes.

6 Discussion

The paper distinguishes gradient reward from task requirements: models may represent future information when the task requires it, even though loss directly supervises only the current output token. This gap can make lookahead-dependent tasks brittle and remains difficult to isolate at production scale.

  • Gradient Reward versus Task Requirement: Gradient reward supervises only the current output token, whereas task requirements may demand information about future tokens.The distinction separates what the loss directly rewards from what successful task completion requires.
  • Gradient Reward versus Task Requirement: Big-endian addition tests this distinction because the first result digit depends on a carry supervised only later.The experiment keeps one-token-at-a-time supervision while introducing a dependency on later-supervised information.
  • Gradient Reward versus Task Requirement: 0.69 final-layer linear-probe accuracy for the second result digit in MHin and Fout rises from 0.12 in little-endian conditions.For the third result digit, accuracy rises from 0.18 to 0.56 in those conditions.
  • Gradient Reward versus Task Requirement: Future result digits become decodable above chance in fragmented-output models that solve the big-endian task accurately.The results support task-forced lookahead representation despite the absence of direct gradient pressure for those future digits.
  • Implications and Scope: Output tokenization can create a gap between what training rewards and what task dependencies require, potentially affecting long-range dependencies beyond addition.Whether this gap predicts brittleness in lookahead-dependent tasks is left as a testable consequence for future work.
  • Implications and Scope: Direct isolation of output supervision at production scale remains unavailable because large language models share one tokenizer across input and output.The paper argues the core loss-based mechanism is scale-independent, but direct evidence at scale remains future work.
  • Implications and Scope: The output-supervision view is expected to extend to morphologically complex words, dates, identifiers, and code literals with internal compositional structure.These domains involve outputs whose token boundaries may align differently with the dependencies the task requires.

7 Conclusion

The paper reframes tokenization as output supervision rather than only input preprocessing. A controlled arithmetic experiment and a survey of 120 publications support reporting and stratifying output-tokenization regimes when interpreting model capabilities and internal representations.

  • Conclusion: Output-token granularity determines the supervision unit in autoregressive training and therefore the problem the model is trained to solve.This extends tokenization’s role beyond input representation.
  • Conclusion: A 2x2 factorial arithmetic experiment finds that output tokenization drives differences in task performance and training dynamics.The experiment decouples input and output tokenization to isolate the output-side effect.
  • Conclusion: Fewer than 10% of 120 surveyed publications report tokenization strategies, while many compare models across regimes without noting the potential task-definition confound.The survey concerns recent publications on mathematical reasoning in language models.
  • Practical Consequences: The paper recommends reporting task-relevant output tokenization, stratifying capability comparisons by supervision regime, and qualifying mechanistic claims accordingly.These recommendations treat output supervision as a model descriptor relevant to structured outputs.
  • Practical Consequences: Output supervision complements existing input-representation views and is presented as necessary for valid cross-model comparison when output tokens have internal compositional structure.The paper argues that benchmark-comparison validity is often assumed rather than established in such settings.

Limitations

The empirical study is narrow and uses a controlled training setup, while several aspects of the broader claim remain difficult to quantify or generalize. The paper also identifies boundaries involving training objectives, probing interpretation, and survey methodology.

  • Scope: The experiment is limited to three-digit addition with small models trained from scratch, so practical effect magnitudes cannot be predicted.The authors note that the cross-tokenizer confound may be small in some surveyed work and meaningful in other work.
  • Training and Inference Boundaries: Post-training objectives and inference protocols that provide intermediate or sequence-level signals change what is effectively supervised per forward pass.The paper’s argument specifically concerns standard next-token prediction training.
  • Interpretation: Probe accuracy measures decodability rather than proving that information is present or absent in model representations.MLP probes are reported alongside linear probes as a partial check on nonlinear accessibility.
  • Survey Method: The survey’s keyword search and manual annotation may introduce errors.This limitation concerns the procedure used to identify and classify surveyed papers.
  • Experimental Setting: The training data consist of three-digit, two-operand addition problems with operands constrained to x + y ≤ 999.Results are evaluated on a fixed held-out set of 500 problems, with all integers zero-padded to three digits.
  • Experimental Setting: The study varies input and output tokenization independently across fragmented and holistic regimes in four factorial conditions.Fragmented numbers use one token per digit, while holistic numbers use one token per operand or result.
  • Experimental Setting: All models are identical decoder-only transformers trained from scratch, with cross-entropy loss computed only over output token positions.The architecture uses approximately 3.4M parameters and a shared 1003-token vocabulary.

A.4 Optimization and Compute

The optimization study trains models across tokenizer conditions, learning rates, weight decays, and random seeds, with results averaged across seeds and training curves reported across hyperparameters.

  • Optimization and Compute: 720 models are trained from four tokenizer conditions, three learning rates, six weight decays, and ten random seeds.Each run lasts up to 200,000 steps.
  • Optimization and Compute: Training uses AdamW with β1 = 0.9, β2 = 0.98, batch size 256, and a ten-step linear learning-rate warmup.Results are averaged across ten seeds per condition.
  • Optimization and Compute: The total training budget is roughly 360 GPU hours, using Nvidia RTX 3090, RTX A6000, and H100 GPUs.Each run takes approximately 30 minutes.
  • Optimization and Compute: Training-loss and evaluation-accuracy curves are provided for all hyperparameters in Figures 5–12.These figures cover the optimization and evaluation trajectories across the reported settings.

C Probing Classifiers

The probing analysis tests whether result digits are represented internally under different output-tokenization regimes. Across probe types, holistic-output models encode all result digits, whereas fragmented-output models primarily encode only the units digit, with probe-capacity and representational-format caveats.

  • Probe setup: Probes read residual-stream activations at the '=' position after each of four transformer blocks.They use 5,000 addition problems disjoint from evaluation and train probes separately for hundreds, tens, and units digits.
  • Probe setup: Three probe families measure digit decodability: linear, one-hidden-layer MLP, and circular sine/cosine probes.The MLP has 64 ReLU units, while the circular probe decodes digits by nearest-class angle.
  • Linear probes: At Layer 3, holistic-output models encode all three result digits, while fragmented-output models encode only the first, units digit.For fragmented-output models, later digit positions remain near chance across layers.
  • MLP probes: MLP probes reproduce the same qualitative pattern but show transient above-chance tens and hundreds accuracy for MHin, Fout at layers 1 and 2.Because the pattern disappears by Layer 3, the authors attribute it to probe capacity rather than genuine representational content.
  • Circular probes: Circular probes likewise recover all three digits in holistic-output models but only the units digit in fragmented-output models.For MH, poor circular-probe recovery despite good task performance is attributed to non-circular digit encoding rather than absent information.

D Big-Endian Ablation

The big-endian ablation reverses digit order so future result information must be resolved during generation. Fragmented-output models consequently encode future digits above chance, with stronger decodability for nearer future positions.

  • Motivation: Little-endian generation aligns with carry propagation, so each digit can be computed without information from future result digits.The big-endian ablation tests how internal representations change when future information must be resolved.
  • Setup: Big-endian training changes only digit order, and probing labels the generated positions as hundreds, tens, and units.Four highest-accuracy checkpoints per input-output condition are selected for probing.
  • Results: In big-endian models, fragmented-output systems show above-chance Layer 3 decodability for future result digits.This indicates that solving the task requires resolving at least some future information without direct gradient pressure on those digits.
  • Results: Decodability is higher for the immediately following digit than for the third digit.The authors relate this pattern to carry propagation: adjacent carries affect the current digit more often than carries traveling two positions.

E.2 Results

The survey finds that numeric tokenization is rarely reported in recent numeric-reasoning papers, even when models with different tokenization regimes are compared. Consequently, the potential effect of differing supervision regimes cannot be assessed from the published record.

  • Reporting: 11 of 120 papers (9.2%) explicitly mention the numeric tokenization strategy of evaluated models.The remaining 109 papers do not mention numeric tokenization granularity.
  • Cross-tokenization comparisons: 83 papers compare holistic and fragmented tokenization families without flagging or controlling for the difference.These comparisons treat models operating under structurally different supervision regimes as interchangeable baselines.
  • Framing: None of the 11 papers that mention tokenization frames the distinction as output supervision.Tokenization is instead consistently treated as an input representation choice.
  • Caveat: The survey does not claim that the supervision-regime confound is decisive in every comparison.Its potential impact ranges from negligible to decisive, but cannot be assessed when tokenization strategy is unreported.
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