L-MTP: Leap Multi-Token Prediction Beyond Adjacent Context for Large Language Models
Authors: Xiaohao Liu
Xiaobo Xia
Weixiang Zhao
Manyi Zhang
Xianzhi Yu
Xiu Su
Shuo Yang
See-Kiong Ng
Tat-Seng Chua
Venue: NeurIPS 2025 poster ()
Keywords: large language models
multi-token prediction
inference acceleration
Primary area: deep_learning

Abstract: Large language models (LLMs) have achieved notable progress. Despite their success, next-token prediction (NTP), the dominant method for LLM training and inference, is constrained in both contextual coverage and inference efficiency due to its inherently sequential process. To overcome these challenges, we propose leap multi-token prediction~(L-MTP), an innovative token prediction method that extends the capabilities of multi-token prediction (MTP) by introducing a leap-based mechanism. Unlike conventional MTP, which generates multiple tokens at adjacent positions, L-MTP strategically skips over intermediate tokens, predicting non-sequential ones in a single forward pass. This structured leap not only enhances the model's ability to capture long-range dependencies but also enables a decoding strategy specially optimized for non-sequential leap token generation, effectively accelerating inference. We theoretically demonstrate the benefit of L-MTP in improving inference efficiency. Experiments across diverse benchmarks validate its merit in boosting both LLM performance and inference speed. The source code is available at https://github.com/Xiaohao-Liu/L-MTP.

L-MTP: Leap Multi-Token Prediction Beyond Adjacentt Context for Large Language Models
Xiaohao Liu'
Xiaobo Xia!*
Weixiang Zhao?
Manyi Zhang²
Xianzhi Yu
Xiu Su Shuo Yang²
See-Kiong Ng¹
Tat-Seng Chua
National University of Singapore
Harbin Institute of Technology
Huawei Noah's 's Ark Lab
CCnttrll South University
HHarbin Institute of Technology, Shenzhen
Abstract
Large language models (LLMs) have achieved notable progress. Despite their success, next-token prediction (NTP), the dominant method for LLM training and inference, constrained both contextual coverage and inference efficiency due its inherently sequential process. To overcome these challenges, propose leap multi-token prediction (L-MTP), an innovative token prediction method that extends the capabiliiies of multi-token prediction (MTP) by introducing leap- based mechanism. Unlike conventional MTP, which generates multiple tokens at adjacent positions, L-MTP strategically skips over intermediate tokens, predict- ing non-sequential ones single forward pass. This structured leap not only enhances the model's ability to capture long-range dependencies but also enables a decoding strategy specially optimized for non-sequential leap token generation, effectively accelerating inference. We theoretically demonstrate the benefit of L- MTP in improving inference efficiency. Experiments across diverse benchmarks validate its merit boosting both LLM performance and inference speed. The source code is available at https: / //ttthggttttttt//// com/ wataahhho-LlLL----
Introduction
Large language models (LLMs) have demonstrated rapid and remarkable progress, driven by data, computing, and architectural innovation advances [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. They exhibit strong capabilities in world knowledge acquisition [12, 13] and enable breakthroughs across a wide range of research domains, such chemistry [14, 15], biology [16, 17J, medicine [18, 19], and personalization [20, 21, 22, 23). As model scales and training data continue to increase, LLMs are attaining more powerful generalization and reasoning abilities [24, 25, 26, 27, 28, 29, 30].
Next-token prediction (NTP) remains the mainstream strategy for both training and inference in LLMs [31, 32, 33, 34, 35, 36, 37]. It generates tokens in autoregressive manner, where each token is predicted based only on the preceding context (see Figure (a)). However, despite its conceptual simplicity, NTP results in inefficient generation, and limits the model to focused yet short contex- tual horizon, and overlooks "hard" decisions [38, 39]. Intriguingly, LLMs are verified with inherent pre-planning capabilities, which indicates the potential of extending NTP to predict multiple tokens at once [39]. This gives rise to the multi-token prediction (MTP) paradigm [39] (see Figure 1(b)). Specifically, by incorporating additional language model heads, MTP enables the parallel prediction of a sequence of adjacent tokens and brings two key henefits. First, it provides a broader training
*Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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5
Training
Head
Head
Head
LLM Backbone
LLM Backbone
LLM Backbone
Inference
Look
One token time
Multiple takens per time
Backward
(a) Next-token prediction.
(b) Multi-token prediction
(c) Leap multi-token prediction
Figure 1: Illustrations of LLM architectures with three prediction paradigms, including NTP (a), MTP (b), and L-MTP (c). NTP utilizes a single output head for sequential token prediction. MTP employs multiple output heads for adjacent multi-token forecasting. As comparison, L- MTP reassigns prediction heads to leaping positions. For instance, given 4 heads, L-MTP predicts 31 5, 7] tokens instead of the adjacent sequence [1,2,3, 3, 4] in MTP with stride of 2 and the initial input token. The top depicts the training difference, while the bottom showcases the inference".
signal by supervising multiple upcoming tokens at each step, which can enhance performance in tasks requiring long-range reasoning planning [39, 40, 41]. Second, it enables faster inference by generating multiple tokens in a single forward pass, reducing latency and increasing throughput in applications with efficiency constraints [39].
In this paper, motivated by the philosophy of going broader and faster, we extend the MTP paradigm and propose leap multi-token prediction (L-MTP), which further amplifies both contextual coverage and inference efficiency LLMs. As illustrated in Figure I(c), L-MTP introduces leaping mech- anism that skips intermediate tokens and directly predicts -on-adjacent future tokens. Structurally, L-MTP retains the core architecture of MTP, where multiple prediction heads are applied in par- allel. Nevertheless, instead of targeting consecutive positions, each head in L-MTP is reassigned to predict tokens at leaping intervals (e.g., positions 1, 3, 5, and 7). This yields a broader training signal than MTP, the model learns to capture longer-range dependencies beyond adjacent-token contexts. During inference, L-MTP further improves generation speed by reusing overlapping con- text across decoding steps. By jointly predicting multiple and strategically spaced tokens, L-MTP enables each forward pass to generate more tokens per step, which helps reduce the total number of decoding iterations required. This leads faster inference compared standard MTP, while maintaining consistency in the generated outputs.
The study of L-MTP can be justified from both human thinking and recent trends in language model reasoning. In human thinking, we rarely reason in a strictly sequential fashion. Instead, we often skip over intermediate elements complete reasoning more efficiently [42, 43, 44]. This leap-wise reasoning aligns naturally with L-MTP's mechanism of skipping intermediate tokens and predicting non-adjacent ones. Similarly, in language model reasoning, recent advances in efficient reasoning have revealed that many intermediate reasoning steps can be compressed or abstracted without loss of correctness [45, 46, 47]. By predicting tokens leaping positions, L-MTP mimics this abstraction process, not by explicitly modeling token importance, but by altering the prediction pattern to skip intermediate positions, to accelerate LLM inference.
We provide theoretical analysis to demonstrate the inference acceleration of our L-MTP, by focus- ing on the attenuation and consistency of output token probabilities. Besides, through comprehen- sive experiments, we show that L-MTP can improve the performance of LLMs in series of tasks
"To avoid dense confusing presentation, we here omit prediction, verification, and acceptance sub- procedures during the inference of MTP and L-MTP. More details can be checked in Section 2.

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(e.g., math and code tasks) and meanwhile improve inference speed. For instance, L-MTP achieves competitive performance and outperforms MTP most tasks. L-MTP also boosts existing MTP models with 22% more inference speed-up with the same number of heads. Furthermore, we pro- vide experimental evidence that L.MTP extendable to speculative decoding techniques, making models up to 4 times faster at inference time across a wide range of settings.
2 Preliminaries
In this section, we formulate and detail the training and inference procedures of next-token predic- tion (NTP) and multi-token prediction (MTP) for large language models (LLMs).
NTP. Given input tokens Xç1, where I t in the subscript represents the abbreviation {1, 2........ ...,., t), the LLM with parameters predicts the next token X441 and is optimized via the following objective:
CTTP
log p( Σ T
(1)
where 7' denotes the number of tokens. The decoding process of NTP in inference also follows an autoregressive manner, which generates tokens one by one. The next token is sampled from p(xe+1/x<<
MTP. A natural extension for NTP is MTP [39] that predicts multiple tokens at once. Given input tokens Xgt, the LLM with parameters 0, predicts the following tokens, by involving more output heads (e.g., output heads totally). Therefore, the optimization objective is derived from Eq. (l) to:
CMTP = Σ log (12244//.....22244)/30030
(2)
In this case, the LLM is requested to pre-plan the adjacent context rather than the single next token. For MTP, during decoding, the next tokens can be sampled independently. following p(xetr\x<r:0), E (1, Recent research [39, 48] disentangles the LLM with the LLM backbone and output heads, where the former yields hidden states and the latter maps them into a vocabulary distribution. Therefore, the LIM backbone can equipped with multiple heads to predict the tokens independently according to the shared hidden states. To this end, we have
II (p(sttlagg))) ( p(asalxzs;00))
(3)
where z denotes the hidden states, 0' represents the parameters for the L.M backbone, and 0 the parameters for the i-th output head. Following token predictions, MTP typically incorporates ver- ification and acceptance sub- nub-procedures to determine which tokens are eligible for output (cf., Figure 2). Specifically, the verification sub-procedure invokes LLMS evaluate the predictions in parallel and records their probabilities for determining the acceptance. Ac- cepted token will be used to update the KV cache, and the process proceeds to the next iteration. Such decoding is proven lossless LLM accelcration technique, where the sampling consistent with the distribution of vanilla autoregressive decoding [49].
Prediction
2
3
5
Verificatiion parallel
Acceptance
Figure 2: MTP with self- speculative decoding, in- volving three sub-procedures.
3 L-MTP: Leap Multi-Token Prediction
Overview. Despite the potential of MTP, we go beyond it with one innovative solution to achieve broader prediction range and faster inference. Unlike conventional MTP, which focuses on consecu- tive tokens, L-MTP introduces leap-based strategy, allowing it to predict tokens at non-sequential positions within the context window. This design enables the model to efficiently capture long- range dependencies without the need for dense token predictions. During inference, L-MTP reuses partially overlapping context across prediction steps, maximizing information utilization while mini- mizing redundant calculations. Given input tokens x L-MTP aims to predict sequence of tokens

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CL MTP
3'
2
1
3
7
2'
2"
B
3
Shared O'
Warmup
3'
Figure 3: Training recipe for L-MTP with objective LL-MTP- We warm up additional heads Js and then op- timize the whole model, with multiple leap tokens as supervision.
Figure 4: Incorporation with tree-attention. We take multiple candidates concurrently to construct the tree paths (left), thus exploring the accepted one. Our back- ward decoding strategy offers consecutive sequences, which can be verified with crafted tree-attention (right).
leaping intervals, specifically at positions, Le., X(t+ 1)+ +I+ t.....+++... +.t41) where denotes the number of jumped tokens. For example, with t input tokens and k 2, the model is expected to predict the tokens at positions [t +,++1, 1, + 3, ......f t 2n 1], effectively skipping intermediate
tokens in each prediction step. We detail our L-MTP below.
3.1 L-MTP Training Recipe
We equip an LLM with multiple output heads for predicting tokens at different positions. The head multilayer perceptron (MLP) with the last layer transforming hidden states to vocabulary (see more implementation details in Appendix B.5). We utilize two stages to train the LLM with multiple heads: (1) head warm-up: (2) full model tuning.
Head warm-up. We first construct the self-distillation data by inputting the questions while col- lecting the output from the untapped LLM. These outputs follow the original distribution of LLM's predictions. We optimize new heads by assigning them different supervisions, adhering to the leap- ing pattern X(+k(n- 1)+-1 The primary goal of this stage adapt new heads to the LLM. Therefore, the original head and LLM backbone are frozen. The training objective is formulated as
M = Σ log ((-
[age (1>1)
(4)
Full model tuning. After that, we use the curated data to continue training the model. At this stage, all the components in specialized LLM, including the LLM backbone and output heads, optimized. The optimization objective defined as
(2) L.MIP = - Σ log
0', 0',0') + log pogp(x ++*) x<: ((0)))) (5)
Jss),
where 33 controls the contribution of additional heads.
3.2 L-MTP Inference Procedure
Despite L-MTP offering broader prediction range, at every pass, it can only predict an incomplete sequence. Fortunately, we can step backward to leverage the prior predictions, or forward to utilize the posterior prediction to compensate for the incompleteness (an alternative solution explained in Appendix C.1). Furthermore, by exploiting speculative decoding techniques (i.e., parallel tree decoding), L-MTP can achieve a larger accept rate, thus achieving further inference accelerate.
Looking backward. Given X-t: tokens L-MTP predicts tokens (x14k(0-1++1)e))) while leaving gaps between them (i.e., h- tokens are skipped). However, if we look backward, the desired tokens have already been predicted by prior steps. For instance, tokens (x++<(--1) ()))))))))))) are predicted given
'Tyiccally > 1 with the input containing at least one start token, like "< "<Ibeegn_ooffc -txtt |>" in Llama series.

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X-I-1- In this case, we have:
p(x+t1lxs--111 (1-1))1))))))))))) mod E (1, k(n 1) 1
(6)
The continuous token sequence is sampled by looking backwards (-) k: steps. Here, mod helps to switch the conditions. Since the priors are generated beforehand (or in parallel), we do not need to infer again, but retrieve them.
Combining with tree atfention. L-MTP seamlessly integrates with speculative decoding by sampling consecutive token sequences for verification. Drawing inspiration from parallel decod- ing [50, 51, 48, 52], we combine L-MTP with tree attention to enable efficient decoding. We con- struct hierarchical tree structure, where the i-th layer represents candidate tokens generated by the i-th prediction head. Paths in the tree explored to identify the accepted one. To facilitate parallel verification, we design a tree attention mask that restricts each hidden state to attend only to its ancestors [50, 48). Figure 4 illustrates the implementation of the tree attention with L-MTP decoding. Further details are provided in Appendix C.2.
4 Theoretical Analyses
Given the imput X LLMs are capable of predicting further future tokens, such X i 1. This motivates the development of MTP, where future tokens can be predicted from far previous tokens, rather than merely the last ones. By observing the acceptance rates of generated multiple tokens, draw two properties:
Definition 1 (Attenuation). For a language model predicting multiple tokens conditioned on Xso the marginal probability of predicting each subsequent token decreases the prediction horizon increases. Formally, p(x4-1(X<e) > p(xx+2|X<() >.... p(x(+n|X<5) (xg),, Vi E (1.2..... n., where is the maximum prediction horizon (the number of heads), assuming the probabilities well- defined and non-zero.
Remark. Attenuation reflects the increasing uncertainty the language model's predictions forecasts tokens further into the future. This behavior arises because the prediction of X,+1 relies on the fixed context Xet, and the influence of this context diminishes with increasing i. As a result, the model's confidence, as measured by the marginal probability p(x++ilx<t), decreases monotonically.
Assumption 2 (Consistency). The expected marginal probability of predicting X,44 is stable across arbitrary impuís and follows a predictable function the prediction horizon i. Formally: Exgi-D [p(x (p(x+=/x<x) = [()), vi E (1,2,....11) where [i) is function characterizing the ex- pected probability of X
Remark. Consistency ensures that the language model's predictions for future tokens x exhibit stable statistical behavior in expectation, regardless of the variability in the input sequences Xge- The function f()) encapsulates the expected confidence in predicting the i-th token ahead, which may decrease with in accordance with the Attenuation definition (i.e., f(i) > f(i ((i+1) 1)).
Acceptance length. The expected length for accepted tokens can be expressed as E[T.] n mm=1 p(L > m.. According to different prediction strategies, we have the following expectations:
E[L] = Em (IIm E[L]
(Vanilla strategy)
Emst a((n-1)+1 1)+1 (II Exer ( mm)))) (L-MTP strategy)
where vanilla strategy predicts tokens X 1 2 Xt4n sequentially using the hidden state L-MTP predicts two interleaved sequences. Specifically, L-MTP uses the hidden state at - 1 to compensate for the non-predicted tokens.
Theorem 3 (Less attenuation, more speed-up). Let y represent the attenuation coefficient, and f(i) : exp pxpl-7.(t (i-1)) be the probubility decay function modeling the predictive confidence O such that [[[]], > E.[.) holds asymptotically as + co, provided that ym2 < C, iee., 7 O(1 (1/n²). See proof in Appendix A.
at step Then there exists a constant
5

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10
y y=0.01 0.01
0.01
Y- 000.0
km2
0.05
Probebsitty
08-
0.5
2210
7-0
0.1
0.1
02
(a) expl (++ 1) mod k))
(b) IT exp[- (1
(c) Σm II. expl- (1-
Figure 5: Different curves of expected marginal probability (a), joint probability (b), and accepted length (c), with & (1, The leap strategy extends the range of prediction at position and achieves a higher length of expectation.
Remark. L-MTP introduces a longer prediction range (k(n 1) + 1) to compensate for the loss of confidence on leaping positions. Theorem 3 reveals the relation between attenuation and the number of prediction heads. Less attenuation indicates higher speed-up of L-MTP compared to the vanilla strategy. In practice, n would not be too large. Less attenuation (7) with fewer overheads of heads (n) leads to further higher speed up. We illustrate the simulated curves for better understanding of the superiority of L-MTP (see Figure 5).
Illustration of analyses. To intuitively demonstrate the effectiveness of our method, we provide the illustration of the above theoretical analyses as shown in Figure 5. We simulate the probabilities and expectations of length and observe that L-MTP (k >> 1) outperforms MTP (k 1) given different attenuation cases. Less attenuation leads to higher speedup of L-MTP.
5 Experiments
In this section, we conduct experiments to address the following research question:
How does L-MTP perform on different L.LM tasks compared to other prediction paradigms? Can it benefit the training of LLMs,, thus boosting model performance?
RQI:
RQ2: Can L-MTP bring further inference acceleration by the decoding strategy of looking back-
ward? Is L-MTP's decoding strategy extendable to further models?
RQ3: What is the prediction accuracy of each output head? Does it satisfy our theoretical analyses in Section 4?
RQ4: What the potential of I-MMP?? Does it suggest further findings on different scales of models and data?
5.1 Experimental Setup
Base LLMs. The experiments utilize the following base large language models: Qwen 2.5 (3B and 7B parameters), Llama 3.2 (3B parameters), Llama 3./ (8B parameters), and Gemma (4B and 12B parameters). These models are selected to represent diverse range of architectures and parameter scales for comprehensive evaluation. We elaborate on more details in Appendix B.2.
Baselines. For efficacy comparison, we evaluate two prediction paradigms: next token prediction (NTP) and multi-token prediction (MTP). These paradigms assess the models' ability to gener- ate accurate and contextually relevant outputs under different prediction strategies. For efficiency, we use NTP with autoregressive decoding as the basis. We compare L-MTP with MTP, which leverages self-speculative decoding, and a trivial forward decoding way (see the implementation in Appendix C. I),, to analyze the inference efficiency.
Datasets. We curate the training dataset from Math [53], GPT4 [56]. the first stage, we use the full data for self-distillation. For the second stage, we randomly select 10,000 examples with ratio of 4:4:2, corresponding to math, code, and general data, respectively. To benchmark the methods, we select Math500 [57] (4-shot) and GSM8K [58] (4-shot) for math evaluation, MBPP, MBPP+ [59, 60], HumanEval, and HumanEval+ [61, 60] for
[54, 55], and Alpaca-

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Table 1: Performance comparison with different prediction paradigms across diverse tasks and benchmarks. In each case, the best average result (Avg.) by comparing among NTP, MTP, and L-MTP is demonstrated in bold.
Math500
GSM8K
MBPP
MBPP*
HumanEval
HumanEval
MMLU
IFEval
Avg.
Base
2.20
1.06
50.00
40.48
27.44
24.39
$4.23
18.23
27 25
Elama3.2.
NTP
3.00
3.71
47.09
36.24
21.34
17.68
54.34
20.74
25.52
MTP
3.40
3.87
46.83
36.51
21.95
18.29
54.22
18.59
25.46
L-MTP
4.80
5.91
46.56
36.51
24.39
20.73
54.17
20.38
26.68
1omma.. ..88
Base
4.20
9.86
61.38
51.32
39.02
31.71
63.26
18.23
34, 34.87
NTP
5.60
11.30
61.38
51.06
42.68
35.37
63.64
20.14
36.40
MTP
6.40
10.08
60.32
49.74
41,46
35.98
63.52
19.42
35.87
L-MTP
6.40
10.92
61,38
50.53
42.68
36.59
63.70
22.18
36.80
Quen2.55555 3-8
Base
35.40
53.75
62,70
53.97
68.29
61.59
65.13
32.73
54.20
NTP
25.40
49.13
66.93
57.94
67.68
60.98
65.17
34.17
53.43
MTP
25.40
45.79
67.72
57.67
65.85
59.15
65.21
35.49
52.79
L-MTP
28.20
46.25
67,99
59,26
67.68
60.37
65.23
35.01
53.75
Qwen2 5-7B
Base
63.00
56.79
75.93
65.34
78.05
71.34
71.93
42,69
65.63
NTP
49.40
52.99
78.31
67.46
78.05
69.51
71.78
43.41
63.86
MTP
49.00
52.62
78.04
67.99
76.22
69.51
71.85
41.49
63.34
L-MTP
46.00
56.03
78.04
67.72
77.44
71.95
71.98
44.12
64.16
Gemmad--i 4-
Base
0.00
0.00
60.58
51.59
33.54
28.05
38.21
26.50
29.81
NTP
6.20
4.70
58.20
51.06
46.34
39.02
58.29
35.49
37.41
MTP
6.00
4.32
58.47
50.53
43.29
37.20
58.25
34.65
36.59
L-MIP
7.60
4.25
57.67
49.47
45.73
38,41
58.33
34.65
37.01
Gemmud- 128
Base
0.00
9.78
73.28
59.52
45,73
36.59
23.79
29.38
34.76
NTP
10.00
13.42
71.16
59.79
63.41
56.10
71.69
29.38
46.87
MTP
9.20
5.61
70.11
58.47
61.59
54.27
71.67
30.46
45.17
L-MTP
17.20
26.38
70.11
60.05
62.20
55.49
72.10
33.09
49.58
code evaluation, and MMLU [62] and IFEval [63] for general evaluation. We detail the statistics and utilization of these datasets in Appendix B.3, Appendix B.4, and Appendix B.6.
Evaluation metries. For performance comparison, utilize accuracy for both math and general tasks and pass@ for code tasks. For efficiency analysis, we employ the speedup ratio as the metric, which calculated by the relative generated tokens per second compared the original. Higher values indicate better performance.
Implementation details. To adapt L-MTP for NTP-based methods, we employ two-stage training procedure. At the head warming up stage, we freeze the LLM backbone while training the heads with learning ratio as 0.1. At the next stage, we utilize LoRA [64] with rank being 32 and alpha being 16 to tune the full model. Here only train the model for 3 epochs with the learning rate being 1010 We set l = 2 and n = by default. This training setting is also employed for MTP implementation to ensure fairness. We also provide the pseudo-code of L-MTP Appendix B. All the experiments are conducted on 2x NVIDIA H100-80G GPUs.
of 1x10-3 for 5 epochs. We utilize the cosine scheduler and set the warmup
5.2 Results and Discussions
Overall performance (RQ1). To answer RQI, we compare L-MTP with MTP and NTP across diverse datasets and involve range of base models as backbones, as shown in Table 1. Through the comparison, we can observe the improvement brought by L-MTP for different scales and series of models, especially on math tasks for the Llama and Gemma series, and code tasks for the Qwen series. Furthermore, we find models gain improvement on general tasks, exemplified by IFEval. Notably, L-MTP achieves better performance for most tasks compared to MTP. Intriguingly, we ob- serve that in some cases, even NTP also brings worse results. Although L-MTPP can compensate for the margin, the deterioration still cannot be mitigated. Carefully choosing higher-quality data would

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MTP
@r r20
12.2.0
arr
lerp
49
12
132-16
43
a 12
1a2 d.
32.53
02.3.0
38
625
025
(a) GSM8K
(b) MBPP
(c) FFEal
Figure 6: Speedup with self-speculative decoding for different series of LLMs ("G"
Llamm, and "Q"++ Qwen). The 7-axis represents the speedup ratio.
1.0-
L-MTP
MTP
0.7
40
0.7
0.8
UB
0.6
0.6
1
0.6
0.5
0.5
0.4
0.3
Llama3.x
Gemma-3
Qwen-2.5
2K
10K
50K
100K
Full
Figure 7: The prediction aceu- racy different positions esti- mated on the alpaca-eval split.
Figure 8: The prediction accu- racy for different models. My- opia worsens as scale increases.
Figure 9: The prediction accu- racy improves as training data increases (from 1K to the full).
be beneficial. However, in this paper, do focus how select data, but investigating the effect of L-MTPP compared to MTP. Such a phenomenon also motivates us to explore more in-depth analyses and discussions.
Inference acceleration (RQ2). L-MTP implements the decoding by looking backward to achieve inference acceleration without any architecture modifications complex operations. We provide the inference speedup comparison as shown in Figure 6. We also implement a trivial solution for leaping prediction by looking forward, denoted as F-MTP. We provide more implementation details in Appendix C.I. Compared to MTP, L-MTP achieves comparable yet sometimes higher speedup, especially on GSM8K. L-MTP predicts the farther position, while leaving the blank filled by the previous prediction, thus achieving faster inference.
Table 2: The speed up ratio comparison when extending L-MTP to Medusa on dif- ferent scales of models.
We also explore the potential by extending L-MTP de- coding to existing models, like Medusa [48], which is specialized for improving the acceptance rate for mul- tiple heads. We equip these models with L-MTP de- coding and showcase the results Table Directly changing the decoding strategy to the lcaping paradigm brings up to 1.3x speed up (22% relative boosting). These results demonstrate the potential of L-MTP, es- pecially for models with higher acceptance rates.
GSM8K
MBPP
MTP
1.83x
1.97x
Viccuna 7B
L-MTP
2.32x
2.01x
MTP L-MTP
2.24x
1.98x
Viccona 13B
2.43x
2.02
The expected distribution at each position (RQ3). We calculate the prediction accuracies at each position to verify our theoretical analyses in Section We plot the different accuracies for differ- ent models (box), and show the average ones at each position (line) for both MTP and L-MTP in Figure 7. These practical results manifest the property of Attenuation (ef., Definition 1) and Con- sisteney (cf., Assumption 2), and resemble our simulated illustration, particularly providing strong support for our theoretical analyses.
Comparison to MTP with = 7. Observed from Table 3, we can see that directly increasing the horizon of MTP does not improve the performance overall. But we can still observe some improvement on HumanEval. The interesting thing is that when we decrease the number of heads to 3, L-MTP (A: 3, = 3) can achieve better performance than MTP (n = 7). The theory on the prediction analysis at different positions can answer this (Section 4). Distant tokens would lead to

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Table 3: Performance comparison to MTP W.E. different prediction horizons across diverse tasks and benchmarks. MTP n= L-MTP 2m2,n= and L-MTP 3m3, can predict the next 7 tokens for
one-time decoding.
Math500
GSM8K
MBPP
MBPP+
HumanEval
HumanEval+
MMLU
IFEval
Avg.
MTP Ro
25.40
45.79
67.72
57.67
65.85
59.15
65.21
35.49
52.79
MTP 7
24.40
43.29
63.49
55.29
68.29
61.59
65.11
33.09
51.82
L-MTP 2mm
28.20
46.25
67.99
59.26
67.68
60.37
65.23
35.01
53.75
L-MTP A
28.00
51.86
60.05
52.65
66,46
62.20
65.06
32.49
52.35
Gemma3-128
Llama3.1-88
Qwen2.5-7B
MTP
MTP
L- MTP
L-MTP
L-MTP
Germma31128
Llama3.1-88
Qwen2.5-78
L-MIP
LMMTP
L-MTP
The illustration of the warm-up procedure (top) and full model fine-tuning (bottom) of adapting multiple output heads to LLMs. The curves showcase the loss changes along with the training for NTP, MTP, and L-MTP.
Figure 10:
noise, while our leap can catch future tokens, but also leap some. An accumulated noise would be smaller than MTP. A smaller number of heads (n 3) while with the leaping strategy achieve comparable performance (52.79, MTP with n = 4) or outperform MTP (51.82, n = 7).
Training loss curves. We showcase the training loss trends across different model series, i.e.. Gemma3-128 Llama3.1-88 and Qwen2.5-7B. for the two-stage training. As shown Figure 10, observe the losses steadily decreasing and convergence to stability, even if L-MTP predicts further positions with the same overhead. To endow the pre- pre-trained model with multi-head predic- tion capability, also observe turning point, indicating the myopia of models. For other smaller models, we also present the training loss trends in Figure 12 for head warm-up and Figure 13 for full model tuning (ef. Appendix D).
Potential analysis (RQ4). We emphasize the potential of L-MTP by investigating the myopia of LLMs and the effect of data amount. (I) Myopic generation. We demonstrate the prediction aceu- racy across different scales of models, as shown in Figure 8. The accuracy drops consistently when changing the small model to the larger one for all series of LLMs, indicating the inherent myopia imposed by NTP pre-training. We also provide the loss curves during training in Appendix D, which show inflection when warming up the heads. Recent work [39] suggests training model from scratch with the MTP objective. This is also promising for L-MTP to inherently benefit the model with broader range of predictions and faster inference. (2) Data scales. We illustrate the increasing prediction accuracy when adding more data in Figure at the head warming up stage. Large-scale data introduces more diversity to help additional heads adapt the LLM backbone. However, also observe that the increase is not linear. To obtain higher accuracy, equipping L-MTP with more sophisticated techniques for training or model architecture [65, 52] will also be promising.
Related Work
Multi-token prediction. Previous studies demonstrate that multi-token prediction (MTP) encour- ages pre-planning capabilities in large language models (LLMs). Qi el al. [38] pioneer n-step- ahead prediction to optimize language models, mitigating overfitting to strong local dependencies. Gloeckle et al. [39] pretrain LLMs with additional prediction heads to achieve significant perfor-

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mance improvements, particularly on code-related tasks. Industrial deployments have also adopted MTP to improve both training efficiency and pre-planning [40, 41]. MTP has sparked growing inter- est in exploring its potential, including adapting next-token prediction (NTP) models for MTP [66] and applying it to domains such as speech [67]. Furthermore, recent work investigates MTP's po- tential for inference acceleration by incorporating additional prediction heads, as exemplified by Medusa [48]. We discuss LLM inference acceleration further in the next subsection.
In addition, recent research on MTP shows significant promise, with the support of LLMs inher- ently maintaining certain pre-planning [68]. These methods typically assume prediction within an adjacent context for LLMs, predicting the next tokens simultaneously at each time step. We go beyond its prediction pattern and introduce leaps between prediction tokens, therefore extending a broader training signal.
LLM inference acceleration. There is bunch of work focusing on accelerating LLMs, especially on their inference procedure [69, 70, 71, 72]. The remarkable techniques involve quantization [73, 74), pruning [75, 76], knowledge distillation [77, 56], compact architecture design [78, 79, 80), and dynamic network [81, 82]. The production deployment also advances to improve the inference efficiency, like memory management [83, 84] and parallelism [85, 86]. In this paper, we focus on the inference acceleration benefited by LLM decoding.
Prior works accelerate inference on greedy decoding [87. 88], while recent speculative decod- ing extends it with provably losslessness [49, 89, 90]. Speculative decoding follows the prin- ciple of draft-then-verify. where a draft model (smaller) efficiently generate multiple tokens for the parallel verification via the target model (larger). The drafting procedure can employ an independent model [50, 91] or enhance the own model [92], like adding additional FFN heads [87, 48, 52]. During the verification, the vanilla sampling only process tokens in single draft sequence [49, 93], while recent methods utilize the token tree to verify multiple draft sequences in parallel [50, 51, 48, 52], further improve the token acceptance rate. In L-MTP, we apply looking backward decoding by utilizing the additional LLM heads for seef-sppeul decoding, paired with the tree-based verification.
7 Conclusion
In this paper, we propose laap multi-token prediction as an improvement over vanilla multi-token prediction in the training and inference of large language models for generative reasoning tasks. Both theoretical insights and empirical evidence are offered to justify the superiority of the proposed method, where both model performance and inference speed can be enhanced simultancously in series of scenarios. In future work, we would like to better understand how to adaptively choose and k in leap multi-token prediction losses. One possibility is determine their values based on the local uncertainty or entropy of the predicted tokens, which allows the model to leap more aggressively in low-entropy regions while maintaining finer granularity in more ambiguous contexts. Also, reinforcement fine-tuning has emerged as promising paradigm for training large language models. Incorporating our method into this training framework opens up exciting opportunities and is worth further exploration.
Acknowledgements
This research/project is supported by the National Research Foundation, Singapore under its Na- tional Large Language Models Funding Initiative (AISG Award No: AISG-NMLLP-22240002 Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore.
Xiaobo Xia is supported by MoE Key Laboratory Brain-inspired Intelligent Perception and Cog- nition, University of Science and Technology of China (Grant No. 2421002). Xiu Su is supported by National Natural Science Foundation of China (No. 62406347). Shuo Yang is supported by the NSFC Young Scientists Fund (No. 62506096)
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[95] Zhaorui Yang. Tianyu Pang, Haozhe Feng, Han Wang, Wei Chen, Minfeng Zhu, and Qian Liu. Self-distillation bridges distribution gap in language model fine-tuning. In ACL, pages 1028-1043, 2024.
[96] Chunting Zhou, Pengfei Liu, Puxin Xu, Srinivasan Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, et al. Lima: Less is more for alignment. In NeurlPS, pages 55006-55021, 2023.
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---

Appendix
Detailed Proof of Theorem
18
Implementation Details
20
B.1 Pscudo-Code for L-MTP
20
B.2 Base LLMs
B.3
Training Datasets
21
B.4
Evaluation Benchmarks
22
B.5 Head Architecture
22
B.6 Data Curation
23
Decoding Strategy
23
C.1 Forward Decoding
23
C.2 Tree Attention
23
Additional Experimental Results
23
E Broader Impact Statement
24
F Reproducibility
24
Limitations
25
17

---

A Detailed Proof of Theorem 3
For LLMs with n output heads that predict multiple tokens at once, the expectation of the accepted length can be represented as:
EL = Σ m=1
II E ==1
D
(Vanilla).
In this case, we only utilize the last hidden state, resulting in n tokens X++n+++1 Without changing the original probabilities, we propose a decoding strategy by looking backward that yields reorga- nized expectations:
k(n 4(n-1)+1
L =
Σ
(II
Ex (Dp((elsspxxxssee (i- madx)))
(L-MTP).
(9)
m==1
Proof Theorem 3.
Proof.
k(n-1)+1 m
ELLBb
Σ
II
Ex D(x mad kk)
(10)
k(n 11+1
Σ
Il f(i (i 1) mod k:)
(11)
k(n 1)+1
Σ
II
f(i (1 (1 mod k-) +
Σ
[(i + (i 1) mod k)
(12)
m=lisl
m=n+1
1=
k(n 1)+1
BIL]. L
Σ
p p(x X (1) mod
p (x+()))))
(13)
A.
m=
m=1
(n-1)+1
Σ
f(i + (i mod k:))
II f(i)
Σ m=n+1
f(i+ mod B))
A
A
(14)
Here A6 is the difference between two expectations, expressed sums involving products of prob- abilities, with function f(i) that decreases as i increases. Besides, S n, which means stride l is at most the number of heads n. That f(i) is a monotonically decreasing function, meaning f(1) 2 f() for i < j. Formally.
f(i (i mod k)) < f(), with equality only when i mod k 1.
(15)
Therefore,
A
A 50
A > 0.
(16)
For A > O, the positive A must outweigh the negative A The decay rate, controlled by y, and the number of terms, controlled by will determine this balance.
To resolve the conditions for A, 0, we assume f(i) O(1/poly(i), ie. 1(1)
1/exp/r (i 1)]. where 7 > 0 is the attenuation coefficient.
18

---

A
Σ
11
1
T7
(17)
expl>(t + (i - 1 mod k))]
exply 1)
Ann
1
A
(18)
exp (i + (i - mod k))]
m=n++
1=1
1
A
(19)
expl>(i + (i mod k))]
exply
m=
kn-1
172
(20)
expl1() + (i mod k))]
m
m
exp Y 2 (i + (i mod b)) - expl Σ
(21)
i=1
kn-
expl
i + (i 1 mod k))]
(22)
m=n+1
We resolve in the case for k Specifically,
A
expl
(i 1 mod 2))] exp[ -7 Σ i]
(23)
m-
t=1
1=1
2n
cxp
(i + (i mod 2))
(24)
m m=n+1
i=1
m(m +
m
mmm + 1)
exp
[2
exp [->
(25)
2
expl --( mmm + 1)
m
+
(26)
2
m=n+1
Σ expl -7
m(m + 11
2
exppl -
m
2
11) +
2n
Σ
expl 7
m(m + 1)
2
+ 2
(27)
Consider the upper bound of Al:
m(m + 1) (1-expl-7 [
exp
(28)
2
m
expl-> m(m + 1)
(1 exp S Vo 2 0)
(29)
2
m=l
7
m exxp 7 m(m + 1)
m
S m
(30)
2 m=1
2
2
2
2
x² expl
7/7 dx
(31)
2
J0
7 1
A(++1)
2
yexp/
Idy
(let = Vix)
(32)
2 7
Jo
2 1
(n 1)2
1-expp
1 --
expl
-
1-
(33)
2 7
2
19

---

(1 2
1
(n + 1)2
expleppppp
(34)
2
Afterward, consider the lower bound of A A:::
A 3
2n-1
Σ
expl
-7
m(m +
1)
m
(35)
2
2
m=n+1
2n-1
Σ
exp
-7
m
(36)
m=n+1
-1 x²
expl
dx
(37)
2
n+1
V--2
y²
expl
ldy
(g V
(38)
v(n+1)
2
expl 2m
expl
( ( 1)
(39)
VT
2
(11 + 1)
expl expl-12/21
expl 2²/2]
expl lapl-y' /2]dy 2
for b > > 0)
expl
22mm²
(40)
2n
Substitute the bounds:
expl-27mn 2ym² 21
(n + 1)²
>
(1 expl
expl-x-
--y
1).
2n
2
2
Introducing B yn? this becomes:
exp[-2,3
2,3
8 expl- 22
n/33/2
exp[-2.1
> exp[-2.3] > 83/2 1 > 2
n/3 2
2
vB
For the inequality to hold, it suffices that 0(1), which implies 7 (1/n2).
B Implementation Details
B.1 Pseudo-Code for L-MTP
We provide the training and inference pseudo-code for L-MTP, For training, we only need add leap control to reassign the prediction positions to modify MTP to L-MTP.
20

---

Training of L-MMTP
multi- -hadd forward computing
i range range(self..g hnelf.n,
aet.tt..ppendeeeee (self. heads [i] # multi-head forward computing <<<
(hidden_states)
Leap Multi-toke Prediction
if k 1: L-MTP MTP
for i, logits_ in enumerate (logits)
h_logits logits_[:, -(k+(i+1))] contiguous ()
h_labels labels[..., k*(i+1) :] contiguous()
loss_i self loss_fct (logits=h_logita,
labels=h_labeli
vocab_ vocab_size=self. www..o..ocaa...ii............ vocab_
loss += loss_i
# Leap Multi-toke Prediction <<<
For inference, we add a cache to store the previous hidden state for our decoding. The decoding involves both previous and current hidden states to yield k(n 1) additional tokens.
Inference of L-MTP
# multi- head forward computing >>>
for 1 in range (swlf n.ead): logits append (self. heads [i] (hidden_states)) multi-head forward computing <<<
get the previous one self model. hast_aappa__hddd_sttteeeee is None: colf.modell bidden_states(: -2]. unsquesze
=
past_hidden_stater torch stack ([self model, past_hiddenn states, hidden_states -1] unsqueeze (1)], dim-0)
logits_ self heads seaet_hidde__sseee
1mtp_logits logits flattee((start update the past hidden states self model, past_ heatthiiddn_sttteee
end_dim=1)
www.hhiddnnsttteee [-1]
B.2 Base LLMs
The experiments leverage a diverse set of base large language models (LLMs) to ensure a com- prehensive evaluation across varying architectures and parameter scales. Below, introduce the selected models: Qwen 2.5 (3B and 7B) [31] developed by Alibaba Cloud, Llama 3.2 (3B), Llama 3.1 (8B) [2] developed by Meta AI, and Gemma 3 (4B and 12B) [94] developed by Google.
B.3 Training Datasets
Math' [53]: This dataset comprises curated collection of mathematical problems and solutions, spanning topics such as algebra, calculus, geometry, and discrete mathematics. It is designed to enhance the reasoning and problem-solving capabilities of large language models, particularly in numerical and symbolic computation tasks. We utilize the training dataset with 7.5K problems.
21

---

Evol-Insttuct-Coo "odee [54, 55]: This dataset is an evolved version of instruction baase code genera- tion data, built upon iterative refinement and augmentation techniques. contains a wide range of programming tasks, solutions, and explanatory instructions across multiple languages (e.g.. Python, Java, C++). This dataset is curated following the code generation instruction process described in the WizardCoder [54]. It is based on the Code Alpaca 20k dataset [55] and evolves each instruc- tion through a randomly chosen evolution prompt, see more details in its public repository 9 As a result, this dataset is constructed with 80K examples with the merging of the seed dataset and three evolutions.
Alpaca-GPT4' [56]: The dataset is collection of English cerruction-followinn data generated by GPT-4 using Alpaca prompts, specifically designed for fine-tuning LLMs. This dataset derivative of the original Alpaca dataset and leverages the same prompts but uses GPT-4 generate the completions, resulting higher quality and more detailed responses. The original Alpaca dataset used text-davinci-000 to complete the prompts. In contrast, Alpaca-GPT4 uses GPT-4, resulting in more detailed and higher-quality responses. The dataset consists of 52K unique instruction- following examples.
B.4 Evaluation Benchmarks
MATH500 [57] is subset of the MATH dataset, comprising 500 challenging mathematical prob- lems designed to test advanced mathematical reasoning and problem-solving skills. includes problems from various domains such algebra, calculus, geometry, and number theory, primarily at high school and early undergraduate levels.
GSM8K [58] is dataset of grade-school-level math word problems. It focuses on elementary arith- metic, basic algebra, and logical reasoning, which requires models to understand natural language descriptions and perform multi-step calculations. We utilize its test split, which contains 1,319 ex- amples in total.
MBPP & MBPP [59, 60] is dataset of 974 Python programming problems designed to evaluate code generation and problem-solving abilities. Tasks range from simple functions to moderately complex algorithms, requiring correct implementation in Python. MBPP* adds more unique test- cases (30x) from the original MBPP [60].
HumanEval & HumanEval* + [61, 60] is dataset of 164 hand-crafted Python programming prob- lems, focusing on evaluating the functional correctness of code generation. Each problem includes a function signature, description, and test cases verify the solution. HumanEval adds more unique test-cases (80x) ) and fixes incorrect ground-truth solutions HumanEval [60].
MMLU [62] is comprehensive benchmark consisting of 57 tasks covering topics from STEM (science, technology, engineering, and mathematics). humanities, social sciences, and professional fields. The tasks multiple-choice questions at high school, college, and professional levels, designed to evaluate the model's broad knowledge and reasoning capabilities. Performance is mea- sured by accuracy across all tasks.
1FEval [63] is a datasct designed to assess a model's ability to follow explicit instructions in natural language. It includes variety of tasks where models must generate responses that adhere strictly to given guidelines, such as formatting, content constraints, or specific reasoning steps.
B.5 Head Architecture
We describe the head architecture Medusa [48], which is also adopted in our implementation. Specifically, given the hidden state z the last layer of LLMs, the head will first transform it via z z + SiLU(Wz + b). where W E Rdxd b E [dd11 d is the dimension of hidden state and SiLU is the Sigmoid Linear Unit (SiLU) function, denoted SiLU(x)
ax)). After that,
' http::/wwwwggaa../////////////// hateaa/eeeeeeiiiiiioiooooooeeeee 10K
"https///itthubb. "ttnss//gituub..oo/mieteet cww./iitoosstteeeoooeeeeeeeeee bttps://gthuu..co///stttttt
22

---

the transformed hidden state is mapped to the logits, with the output dimensions being the size of the vocabulary. Such a process can formulated as W head Notably, Whad initialized with the weight of the original head of the backbone LLM,, and W is initialized with zeros.
B.6 Data Curation
Self-distillation [95]. At the head warm-up stage, the main goal to align additional heads with the original head to improve acceptance rates, as also suggested in [48]. Therefore, we employ the self-distillation strategy for different backbone LLMs. In this case, we use vLLM for efficiently generating the responses for every data point. The generated dataset will be stored and then serve as the training data for warm-up training.
Downsampling [96, 70J. At the continued training stage, we downsample the dataset randomly, where we take 4,000 examples for both code and math datasets and 2,000 examples for the general dataset. Therefore, we prepare 10K examples for continuing to train the model. We keep the curated dataset fixed for fair comparison our experiments.
C Decoding Strategy
C.1 Forward Decoding
We also provide another trivial alternative by looking forward, denoted F-MTP. For instance, F-MTP predicts tokens (x++x(i-1)+2) kEjm) are predicted given xgr+1- In this case, we have:
p(x med x {0, I..... kn} }
(41)
where the token sequence sampled by looking forward (+) k - steps. Forward decoding prior- itizes early tokens, resulting in tokens (x++*) being all predicted by the original LLM head. This decoding strategy serves as our baseline for efficient analysis.
C.2
Tree Attention
Tree construction. Following the verification of token tree [50, 48), merge the candidate tokens generated from multiple L.M heads to construct the tree. We employ a greedy search method from top to bottom explore layered graph and find the node sequences (paths) with maximum cumulative expectation. The expectation value is calculated by the estimated accuracy of each head. starts from root node and iteratively expands paths by selecting the neighbor with the highest expectation, computed as the product of node accuracies along the path. Neighbors are generated by either moving the next node in the same layer or extending to the next layer, up specified maximum depth and child count calculations and return list of selected node sequences. We illustrate tree structure example in Figure 11. We can observe that the token tree provides multiple token sequences (paths) for the following verification, thus improving the token acceptance rate.
layer. We cache computed expectations to avoid redundant
Tree decoding, Upon the pre-defined token tree structure, we employ tree decoding to process the generated multiple predictions. First, we initialize the tree attention and indices given the tree paths (cf., Figure 4). Once we generate multiple tokens' logits, we select the top-k candidates, which are assembled as input for target models. By utilizing the tree attention, the target model yields the prediction of the original head for verification in parallel, finally accepting the candidates and starting the next iteration.
D Additional Experimental Results
We present the detailed training loss trends in Figure 12 for head warm-up and Figure 13 for full model tuning, with losses steadily decreasing and convergence to stability.
hhtps://dossvlllm vi
23

---

Figure 11: Token tree constructed according to the accuracy of heads. We use 3 heads for the Vicuna 7B model. The head accuracy is estimated when employing L-MTP decoding.
Gemma3-4B
Llama3.2-38
Qwen2,5-3B
MTP
MTP
MTP
L- MTP
L-MTP
L-MTP
Gemma3-128
Llama3.1-88
Qwen2.5-78
MTP
MTP
MTP
L-MTT
L-MTP
L-MTP
Figure 12: The illustration of the warm-up procedure of adapting multiple output heads to LLMs. The curves showcase the loss changes along with the head warm-up training for MTP and L-MTP.
E Broader Impact Statement
Leap multi- token prediction (L-MTP) redefines the traditional autoregressive paradigm by skipping intermediate tokens and predicting non-adjacent ones, mirroring human-like reasoning. This leap- based strategy broadens the contextual window, enhances inference efficiency, and reduces compu- tational costs, making L.LMs more suitable for complex decision-making tasks. Environmentally. L-MTP's efficient decoding lowers energy consumption and supports greener Al deployments. Its design also expands access to high-performance LLMs, reducing barriers for resource-constrained developers. Furthermore, L-MTP introduces new possibilities for non-sequential reasoning, which paves the way for more efficient and scalable language models.
F Reproducibility
We provide implementation details, including illustrative algorithm descriptions and pseudo-code. The source code is publicly released for reproducibility.

---

Gemma3-48
Llama3.2-38
Qwen2.5-38
Gemma3-128
Llama3.
Qwen2.5-k.
NTP
MTP
L-MIP
NTP
MTP
L-MTP
NTP
MTP
L-MTP
Figure 13: Full model fine-tuning with respect to different prediction paradigms. The curves show- case the loss changes along with the full model tuning for NTP, MTP, and L-MTP.
G Limitations
Modern large language models are rapidly scaling up. with recent models reaching tens or even hundreds of billions of parameters (e.g.. DeepSeck-R1-70B6671D [97] and 1--05B [2]). Our experiments are conducted on models up to 12B due to computational constraints. Despite this limitation, the results effectively validate our core ideas. In future work, we plan extend our method to larger models to further assess its scalability and effectiveness at greater capacity.
25

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Reviews:
[{"review_id": "gtR0yLupLG", "reviewer": "Reviewer_BE2L", "summary": "This paper introduces a method called Leap Multi-Token Prediction (L-MTP), which improves upon traditional multi-token prediction (MTP) methods. Through theoretical analysis, the authors demonstrate that this strategy achieves better inference acceleration. Furthermore, experiments show that this method not only enhances inference speed but also increases model capability. The paper also briefly discusses how this new token prediction method can be combined with common strategies like speculative decoding.", "questions": "See weaknesses", "limitations": "None", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths:**\n\n1. The proposed Leap Multi-Token Prediction method is highly innovative and could inspire further exploration in the area of multi-token prediction.\n    \n2. The proposed method outperforms traditional methods in both effectiveness and efficiency, with significant results.\n    \n3. The theoretical analysis is rigorous and provides valuable insights.\n    \n4. The paper's discussion on combining the method with techniques like speculative decoding is detailed and comprehensive.\n    \n\n### **Weaknesses:**\n\n1. The paper could be strengthened by a brief discussion of alternative designs for the leap mechanism, for instance, exploring leaps with non-uniform intervals instead of the current fixed stride.\n    \n2. Regarding the effectiveness improvement of L-MTP over MTP (as shown in Table 1), the paper could provide some qualitative analysis, such as a case study, to offer more intuition behind the improvements.", "was_revised": true, "final_justification": "I think this paper should be accepted to Neurips 2025. The strengths are listed in `Strengths And Weaknesses`. For the weaknesses, the response from authors has addressed most of them.", "rebuttal": "Thanks for your professional and careful review. We respond to your concerns or questions as follows.\n\n> W1: The paper could be strengthened by a brief discussion of alternative designs for the leap mechanism, for instance, exploring leaps with non-uniform intervals instead of the current fixed stride.\n\n**Response**\n\nThank you for your suggestion! We outline a more flexible leap pattern for L-MTP in Section 7, Line 297, as our future exploration. We propose adaptively selecting $n$ and $k$ based on the local uncertainty or entropy of tokens, enabling more aggressive leaps in low-entropy regions and finer granularity in high-entropy ones. However, such flexibility introduces challenges, such as organizing output tokens with variable leap ranges (how to decode). We consider this an avenue for future work. L-MTP serves as a sound prototype to inspire and support more dynamic leap patterns. Our formal analysis in Section 4 (Theoretical Analysis) provides principles to guide future research. We look forward to further explorations inspired by L-MTP.\n\n> W2: Regarding the effectiveness improvement of L-MTP over MTP (as shown in Table 1), the paper could provide some qualitative analysis, such as a case study, to offer more intuition behind the improvements.\n\n**Response**\n\nThank you for your suggestion! We provide some case studies with explanations as follows. Due to the word limitation, we highlight the differences to demonstrate the effectiveness of L-MTP. L-MTP improves upon standard MTP by predicting non-consecutive, leaped tokens instead of adjacent ones, which forces the model to learn **longer-range** dependencies and a more structured output plan, leading to better performance. Here is a case: when solving the problem \"A robe takes 2 bolts of blue fiber and half that much white fiber. How many bolts in total does it take?\", MTP predicts the next few words sequentially, [\"The\", \"amount\", \"of\", \"white\"], making it prone to error propagation, while L-MTP could simultaneously predict key non-adjacent elements like [\"total\", \"is\", \"3\", \".\"], directly linking the input's numerical logic to the final answer structure and improving robustness and accuracy, as evidenced by its superior results on math benchmarks like GSM8K in Table 1. We will provide more cases to illustrate the effectiveness of L-MTP in our revised paper.\n\n----\nWe authors sincerely thank you for your professional review attitude and comments. If you have other questions, we are happy to address them to polish this work."}, {"review_id": "CQAABngZvy", "reviewer": "Reviewer_kEie", "summary": "This paper introduces lean multi-token prediction  (L-MTP), which can further extend multi-token prediction by introducing a leap-based mechanism. It strategically skip over intermediate tokens, predicting non-sequential tokens, so that effectively accelerate inference cost. To demonstrate its effectiveness, the paper provides both theoretical analysis and empirical experiments.", "questions": "See the weakness", "limitations": "L-MTP shows limited improvement over baselines, and its low scores on challenging benchmarks raise doubts about its effectiveness in enhancing LLM reasoning capabilities.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The proposed L-MTP idea is quite novel and interesting. The method is plug-and-play, requiring no model architecture modifications and easy integration into existing LLM training pipelines.\n\n2. The paper provides theoretical analysis and extensive experiments to demonstrate its effectiveness\n\nWeaknesses:\n\n1. Limited improvement: While the proposed leap-based training objective is conceptually interesting, the empirical gains over standard baselines are relatively modest.\n\n2. Low absolute performance: On challenging benchmarks such as MATH-500 and GSM8K, the model’s absolute performance remains low, raising doubts about whether L-MTP meaningfully improves LLM capabilities in practice.", "was_revised": true, "final_justification": "My main concern is the  practical applicability  of the proposed method. That said, it cannot be demonstrated in this paper due to the limited resources. Therefore, I will maintain my original borderline accept.", "rebuttal": "Thanks for your professional and careful review. We respond to your concerns or questions as follows.\n\n\n> W1: Limited improvement: While the proposed leap-based training objective is conceptually interesting, the empirical gains over standard baselines are relatively modest.\n\n**Response**\n\nThank you for your recognition of the novelty of our work! L-MTP focuses on both the performance boosting and inference acceleration [1], which is more challenging than one goal in either performance [2] or decoding acceleration [3, 4]. However, L-MTP achieves both goals, particularly for the inference speed-up. For a comprehensive performance evaluation, we conducted extensive experiments across various scales, LLM types, and tasks, observing consistent performance improvements. We also noted limited performance in certain cases, discussed in Section 5.2, attributing these to data quality.  Selecting higher quality data would boost the performance with a branch of work that focuses on how to synthesize the data or collect new data to provide new knowledge for well-trained LLMs. However, in our work, we do not involve the data selection as our research topic. Additionally, our potential analysis in Section 5.2, Line 245, demonstrates that with more data or training resources (e.g., pre-training), L-MTP could achieve even greater performance gains. These experiments and analyses highlight the superiority and significant potential of L-MTP.\n\n[1] Gloeckle, Fabian, et al. \"Better & faster large language models via multi-token prediction.\" ICML 2024.  \n[2] Chen, Michael K., et al. \"Improving large language models with concept-aware fine-tuning.\" arXiv preprint arXiv:2506.07833 (2025).  \n[3] Cai, Tianle, et al. \"Medusa: Simple LLM inference acceleration framework with multiple decoding Heads.\" ICML 2024.  \n[4] Ankner, Zachary, et al. \"Hydra: Sequentially-dependent draft heads for medusa decoding.\" COLM 2024.  \n\n\n\n> W2: Low absolute performance: On challenging benchmarks such as MATH-500 and GSM8K, the model’s absolute performance remains low, raising doubts about whether L-MTP meaningfully improves LLM capabilities in practice.\n\n**Response**\n\nThanks for your sincere review! The absolute performance of L-MTP heavily depends on the pretrained LLMs, with stronger models yielding better results. For example, Qwen outperforms Llama and Gemma on MATH500 and GSM8K. Our experiments across various LLM scales and types confirm that larger models achieve higher absolute performance. Thus, integrating L-MTP with more advanced or larger-scale LLMs, such as DeepSeek-R1-70B/671B or Llama-3.1-405B, would further enhance performance.\n\n\n> L1: L-MTP shows limited improvement over baselines, and its low scores on challenging benchmarks raise doubts about its effectiveness in enhancing LLM reasoning capabilities.\n\n**Response**\n\nThanks! Achiving both significant performance improvement and inference acceleration is highly challenging, as discussed in W1 and its related response. Despite this, L-MTP demonstrates overall improvements, and some notable gains in reasoning-focused benchmarks like Math500 and GSM8K. Specifically, Qwen trained with L-MTP achieves a higher performance of 28.20 (vs. MTP’s 25.40) and Gemma achieves 17.20 (vs. MTP’s 9.20). A stronger base model can indeed lead to a higher absolute performance as discussed in W2. Due to the limited resources, we do not involve more powerful LLMs as our starting point for training. We also discuss this in Appendix G (Limitations). We value the practical application and broad impact of L-MTP, which motivates us to conduct an in-depth analysis for its potential (see Section 5 Potential Analysis). We investigate the myopia of current models with increased parameter size and the prediction accuracy in terms of increased data scales. It suggests that the significant potential of L-MTP with more tunable parameters (even from pre-training) or more data.\n\n----\nWe authors sincerely thank you for your professional review attitude and comments. If you have other questions, we are happy to address them to polish this work."}, {"review_id": "wsskUaIAax", "reviewer": "Reviewer_uRmg", "summary": "The paper presents a variant of multi token prediction MTP called leap MTP (L-MTP). Instead of predicting the next n tokens (with indices 1, 2, 3, 4), LMTP predicts them with a spacing of 1 (with indices 1, 3, 5, 7). That means that the last two predictions combined predict the next 7 tokens combined, instead of the next 4 as is the case with MTP.\n\nThe paper also proposes a predictive decoding algorithm that works with LMTP. The next tokens are inferred and verified if the confidence is high enough. This leads to savings at inference time.\n\nThe paper also includes theoretical results: If the tokens at a longer horizon are easier to predict, then predictive decoding brings a more significant speedup.", "questions": "The source of the improvement is unclear (applied both the the performance improvement and inference speedup):\n* The most obvious missing baseline is MTP with n=7. Is the improvement coming from the longer horizon or is it something else?\n  * If it is the longer horizon, then what is the advantage of LMPT over MTP with n=7?\n  * If it is something else, then it is an interesting scientific question of what that may be. \n\nCondition on improving the evaluation score: the paper is updated with a discussion on the source of the improvement (both performance and inference speedup) backed with experimental results.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 4, "significance": 1, "originality": 3, "strengths_and_weaknesses": "The paper presents a simple and novel idea. I am not aware of prior works discussing this idea.\n\nThe paper is also well-presented. The contributions and methods are clear and easy to understand.\n\nWhile the paper is clearly written and the results show some improvement over established baselines, the contribution appears to be incremental. The core idea is relatively simple, and the source of the observed improvement is neither thoroughly ablated nor adequately discussed, which limits the scientific insight provided.\n\nThe paper missing the ablation of the horizon (MTP with n=7), therefore it is not clear whether the improvement comes simply from having a longer horizon or something else entirely. Without this, researchers don't gain a better understanding of MTP and practitioners don't have clear evidence to support L-MTP over MTP with n=7.\n\nThe paper would be much more impactful had it figured out the source of the improvement (both in performance and inference speedup). \n\nAlso, there could be many variants of L-MTP with different pacing, variable pacing, longer/shorter horizons etc. I feel the paper had the opportunity to explore a larger idea space, but did not do so.", "was_revised": true, "final_justification": "The rebuttal addressed two key concerns:\n1. Comparison to MTP with n=7. I believe this experiment is critical in understanding the significance of the longer horizon and we saw that L-MTP works slightly better than MTP with n=7.\n2.  L-MTP has substantially lower compute cost than MTP with n=7. The authors gave a detailed breakdown of the compute costs.\n\nMy last concern remains unaddressed. It is not clear to me why L-MTP improves slightly over MTP with n=7. They have the same horizon, I don't see why predicting fewer tokens would result in better predictions.\n\nEven with my last concern unaddressed, I believe it is fair to say that L-MTP achieves the same prediction horizon and as good or slightly better prediction performance at a lower compute cost.\n\nWhile I think that the paper should have been more detailed on its comparison to MTP with n=7 (either do not claim an improvement over it, or give a clear intuition why there is an improvement), the paper could be a useful tool for practitioners to increase the prediction horizon at a low computational cost. Therefore, I do not want to hold the paper back with a low score. I increased my score from 2 to 4.", "rebuttal": "Thanks for your professional and careful review. We respond to your concerns or questions as follows.\n\n\n> W1: While the paper is clearly written and the results show some improvement over established baselines, the contribution appears to be incremental. The core idea is relatively simple, and the source of the observed improvement is neither thoroughly ablated nor adequately discussed, which limits the scientific insight provided.\n\n**Response**\n\nThank you for raising this concern, and we’re happy to clarify our contribution! MTP, introduced in recent works [1,2], predicts the next $n$ adjacent tokens simultaneously, inspiring applications like speech language models and inference acceleration. The insight, not every token is equally important, is validated in LLMs [3] and aligned with human thinking. This inspires us, yet disappointingly, no research focuses on new prediction patterns, especially the non-adjacent token prediction, a leap paradigm against the recent adjacent prediction of MTP. L-MTP introduces this leap paradigm with look backward decoding, achieving broader and faster predictions than MTP using the same resources (training data and model architecture). We analyze this comprehensively through prediction principles (Section 4) and empirical verification (Section 5). Our theoretical analysis links L-MTP to probabilistic attenuation, showing that lower attenuation yields greater speedups. The empirical analysis demonstrates consistent improvements and provides in-depth insights (e.g., Section 5, Potential Analysis), highlighting L-MTP’s strong promise through analyses of myopic effects and data scales.\n\n[1] Gloeckle, Fabian, et al. \"Better & faster large language models via multi-token prediction.\" ICML 2024.  \n[2] Liu, Aixin, et al. \"Deepseek-v3 technical report.\" arXiv preprint arXiv:2412.19437 (2024).  \n[3] Lin, Zhenghao, et al. \"Rho-1: Not all tokens are what you need.\" NeurIPS 2024.  \n\n> W2: The paper missing the ablation of the horizon (MTP with n=7), therefore it is not clear whether the improvement comes simply from having a longer horizon or something else entirely. Without this, researchers don't gain a better understanding of MTP and practitioners don't have clear evidence to support L-MTP over MTP with n=7.\n\n**Response**\n\nThank you for your interest in MTP with $n=7$, a concern also raised by Reviewer SKtJ. We did not evaluate MTP with $n=7$, as our study ensures a fair comparison by using the same resources (both MTP and L-MTP have 4 heads). \nSetting $n=7$ for MTP would nearly double the new parameters compared to L-MTP, making it an unfair comparison rather than a proper ablation study. \nHowever, we are open to conducting this experiment to provide further insights. Due to time and resource constraints, we cannot test this across all LLM scales and types. Below are the results:\n\n||Math500|GSM8K|MBPP|MBPP+|HumanEval|HumanEval+|MMLU|IFEval| Avg.|\n|-|-|-|-|-|-|-|-|-|-|\n|MTP ($n=4$)|25.40|45.79|67.72|57.67|65.85|59.15|65.21|35.49|52.79|\n|MTP ($n=7$)|24.40|43.29|63.49|55.29|68.29|61.59|65.11|33.09|54.49|\n|L-MTP ($k=2,n=4$)|28.20|46.25|67.99|59.26|67.68|60.37|65.23|35.01|53.75|\n|L-MTP ($k=3,n=3$)|28.00|51.86|60.05|52.65|66.46|62.20|65.06|32.49|**55.18**|\n\nIncreasing MTP's heads ($n=7$) improves performance for its longer horizon (54.49 vs. 52.79). However, L-MTP achieves comparable results with **nearly half the new parameters** (4 vs. 7 heads). Additionally, the new leap pattern ($k=3,n=3$) yields higher performance (55.18 vs. 54.49), particularly on GSM8K and HumanEval+. We will incorporate this analysis into our revised paper.\n\n\n\n> W3: The paper would be much more impactful had it figured out the source of the improvement (both in performance and inference speedup). \n\n**Response**\n\nThanks! We agree with you that the source of performance improvement and inference speedup should be clarified. That is the reason why we provide a thorough theoretical analysis and extensive empirical results.  L-MTP achieves a broader prediction horizon with the same resources as MTP by skipping intermediate tokens. Beyond intuitive motivation and sophisticated implementation, we provide an in-depth analysis.\n\n**Inference Aspect**: We formally link token prediction to attenuation, supporting L-MTP’s inference speedup. While a longer horizon increases uncertainty, L-MTP’s look-backward decoding utilizes prior predictions, thus yielding higher expected prediction lengths than MTP. We also introduce a decoding variant, F-MTP, for comparison, which uses look-forward decoding to compensate for leaped tokens but requires an additional inference step, increasing inference time (see Figure 6). The combination of leaping prediction and look-backward decoding drives L-MTP’s inference efficiency.\n\n**Performance Aspect**: Inspired by the insight that not every token matters [3] and human thinking, L-MTP aligns with recent work on reasoning step compression and abstraction [4, 5]. The longer horizon is key to performance gains, as seen in meaningful units like code blocks versus single tokens (e.g., `{`). Experiments with MTP at $n=7$ further validate this. L-MTP’s leap design enhances performance by using two tokens (when $k=2$) to predict $m$ tokens, creating a flexible mapping that correlates both input and output tokens (2-to-m tokens), unlike MTP’s single-token-to-m-token approach. Increasing $k$ while keeping the number of output tokens can further boost performance, as observed in the results of L-MTP at $k=3,n=3$.\n\n[4] Chen, Zhipeng, et al. \"Not Everything is All You Need: Toward Low-Redundant Optimization for Large Language Model Alignment.\" EMNLP 2024.  \n[5] Xia, Heming, et al. \"Tokenskip: Controllable chain-of-thought compression in llms.\" arXiv preprint arXiv:2502.12067 (2025).\n\n\n> W4: Also, there could be many variants of L-MTP with different pacing, variable pacing, longer/shorter horizons etc. I feel the paper had the opportunity to explore a larger idea space, but did not do so. \n\n**Response**\n\nWe explore L-MTP with different horizons to identify an effective leaping and horizon configuration for evaluation. Our theoretical analysis indicates that longer horizons introduce noise due to increased uncertainty in predicting distant tokens, while shorter horizons (e.g., $n=2$) may not fully leverage multi-token prediction. We select $k=2, n=4$ as a practical balance, aligning with prior MTP methods for a fair and effective comparison. We appreciate your suggestions and conduct additional experiments with $k=3, n=3$, with results discussed earlier. Exploration of more flexible leaping patterns is planned as future work, building on L-MTP as shown in Section 7. \n\n\n> Q1: The source of the improvement is unclear (applied both the performance improvement and inference speedup): The most obvious missing baseline is MTP with n=7. Is the improvement coming from the longer horizon or is it something else? If it is the longer horizon, then what is the advantage of LMPT over MTP with n=7? If it is something else, then it is an interesting scientific question of what that may be.\n\n**Response**\n\nThank you for your question! We address the source of L-MTP’s improvement in W3 and the corresponding response, supported by additional empirical evidence in W2. Our theoretical analysis and empirical results demonstrate L-MTP’s superiority in both performance and inference. The additional potential analysis further offers insights on MTP and the significant promise of L-MTP. Results from L-MTP ($n=2, k=4$ and $n=3, k=3$) and MTP ($n=4$ and $n=7$) show that performance gains can benefit from a longer horizon.\n\n----\nWe sincerely appreciate your review and hope our response, bolstered by additional empirical results, aids in re-evaluating our work."}, {"review_id": "LjMngSnHY4", "reviewer": "Reviewer_SKtJ", "summary": "This paper introduces leap multi-token prediction (L-MTP) as an improvement over vanilla multi-token prediction (MTP). Unlike MTP, which predicts the next N consecutive tokens (e.g., positions 1,2,3,4), L-MTP employs a leaping mechanism that skips intermediate tokens and directly predicts non-adjacent future tokens (e.g., positions 1,3,5,7). \n\nDuring training, L-MTP yields a broader training signal, as the model learns to capture longer-range dependencies. During inference, L-MTP can look backward and leverages past prediction to generate longer candidate sequences, which improves the acceleration rate of speculative decoding.\n\nExperiments are performed under a post-training setting. Experimental results across diverse benchmarks demonstrates the effectiveness of L-MTP in both boosting model performance and accelerating inference.", "questions": "The work in [1] would be a valuable addition to the references, as it provides complementary insights on multi-token prediction for accelerating LLM training.\n\n[1] Shao et al. Beyond Next Token Prediction: Patch-Level Training for Large Language Models. ICLR 2025.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The paper is well-written and clearly motivated. The proposed solution is innovative and clever, particularly the looking backward inference strategy.\n2. The experimental results are pretty promising.\n\nWeaknesses\n1. The evaluation is limited to post-training scenarios. The potential impact of L-MTP on pre-training LLMs remains unexplored, leaving an important aspect of its applicability unverified.\n2. The comparison between L-MTP(k=2,n=4) and MTP(n=7) is missing, where both methods align in maximum prediction position. It would be valuable to examine whether L-MTP maintains its acceleration advantage over MTP(n=7) under the same candidate length.\n3. Experiments are only conducted on the (k=2,n=4) configuration. What is the performance of other configurations, for example, (k=3, n=3)?", "was_revised": true, "final_justification": "The response addresses my concern, so I'll keep my positive rating.", "rebuttal": "Thanks for your professional and careful review. We respond to your concerns or questions as follows.\n\n> W1: The evaluation is limited to post-training scenarios. The potential impact of L-MTP on pre-training LLMs remains unexplored, leaving an important aspect of its applicability unverified.\n\n**Response**\n\nThanks! We acknowledge that pre-training would bring more impressive results, according to our potential analysis in Section 5. The effectiveness of pre-training for MTP is well-verified [1]. However, due to resource constraints, we could not pre-train LLMs with L-MTP. We believe future pre-training efforts can leverage L-MTP’s potential, which motivated our inclusion of the potential analysis.\n\n\n> W2: The comparison between L-MTP(k=2,n=4) and MTP(n=7) is missing, where both methods align in maximum prediction position. It would be valuable to examine whether L-MTP maintains its acceleration advantage over MTP(n=7) under the same candidate length.\n\n**Response**\n\nThanks! We conduct the experiments when setting $n=7$ for MTP. A longer horizon indeed benefits the performance, achieving an average performance of 54.49 compared to 52.79 for MTP ($n=4$).\n\n||Math500|GSM8K|MBPP|MBPP+|HumanEval|HumanEval+|MMLU|IFEval| Avg.|\n|-|-|-|-|-|-|-|-|-|-|\n|MTP ($n=4$)|25.40|45.79|67.72|57.67|65.85|59.15|65.21|35.49|52.79|\n|MTP ($n=7$)|24.40|43.29|63.49|55.29|68.29|61.59|65.11|33.09|54.49|\n|L-MTP ($k=2,n=4$)|28.20|46.25|67.99|59.26|67.68|60.37|65.23|35.01|53.75|\n|L-MTP ($k=3,n=3$)|28.00|51.86|60.05|52.65|66.46|62.20|65.06|32.49|**55.18**|\n\nHowever, MTP ($n=7$) nearly doubles the heads (new parameters) compared to L-MTP ($k=2,n=4$ and $k=3,n=3$). Despite this, L-MTP delivers comparable or superior performance (e.g., 55.18 for $k=3,n=3$) with greater efficiency, particularly on GSM8K and HumanEval+. L-MTP is much more efficient in achieving a comparable yet sometimes better performance. The inference acceleration of L-MTP, enabled by the leap strategy and look-backward decoding, allows it to outperform MTP with the same resources (4 heads). The theoretical analysis in Section 4 supports this, establishing MTP ($n=7$) as the upper bound for L-MTP ($k=2,n=4$) speedup. We will include this analysis in the revised paper.\n\n> W3: Experiments are only conducted on the (k=2,n=4) configuration. What is the performance of other configurations, for example, (k=3, n=3)?\n\n**Response**\n\nThanks! Your suggestion is reasonable to further demonstrate the application of L-MTP. We conducted this experiment as shown in W2 and the corresponding response. Overall, L-MTP ($k=3, n=3$) performs better than others, especially the improvements on GSM8K and HumanEval. Exploring more leap patterns would be promising. We also discuss a potential leap pattern via entropy estimation in Section 7 to showcase a broader application of L-MTP. We will include these results in our revised paper.\n\n\n> Q1: The work in [1] would be a valuable addition to the references, as it provides complementary insights on multi-token prediction for accelerating LLM training.\n\n**Response**\n\nThanks for your share! This is a very interesting work, which predicts patches of tokens for LLMs by aggregating adjacent tokens with higher information density. This aligns closely with our discussion in Section 7 on extending L-MTP with flexible leaps, where we propose skipping low-entropy regions to focus on high-entropy ones. Combining [1] with L-MTP could create significant synergy. We will incorporate a discussion of this paper and explore further possibilities in our revised manuscript.\n\n[1] Shao et al. Beyond next token prediction: Patch-level training for large language models. ICLR 2025.\n\n----\nWe authors sincerely thank you for your professional review attitude and comments. If you have other questions, we are happy to address them to polish this work."}]

Author rebuttal:

Meta-review: This paper proposes a new multi-token prediction approach to accelerate inference speed by allowing leaps between tokens. 

Strengths: the idea is neat; the results are significant (significant speed up with better or comparable quality on a diverse dataset); and some theorem is provided.

Weaknesses: the idea might be incremental to multi-token prediction.

Reason to accept: It is a solid paper with a nice idea and solid execution. The reviewers have converged to accept.

Rebuttal: both the reviewers and authors actively participated in the rebuttal. The reviewers asked for additional experiments, explanations on why post-training only, and the authors successfully addressed those concerns.
Decision: Accept (poster)