zip2zip++: Towards Inference-Time Token Compression with Minimal Quality Loss

Saibo Geng; Andrea Gentilini; Xinxian Ma; Nathan Ranchin; Yunzhen Yao; Robert West

cs.CLOct 9, 2026

zip2zip++: Towards Inference-Time Token Compression with Minimal Quality Loss

Authors: Saibo Geng, Andrea Gentilini, Xinxian Ma, Nathan Ranchin, Yunzhen Yao, Robert West

Organizations: EPFL · Technical University of Munich · Zuse School ELIZA · ETH Zürich

Abstract

Dynamic vocabularies built on-the-fly via Lempel-Ziv-Welch (LZW) compression let a language model represent the same text in fewer tokens, but prior work shows that this efficiency comes at a cost to reasoning and perplexity. We show that this quality gap is not a fundamental price of compression but can be substantially closed through targeted improvements to the compression layer and LZW codec, without modifying the underlying pretrained language model. Our analysis reveals four key issues: (1) LZW's compression algorithm creates an implicit conflict between the input embedding and the output embedding, a tension that a single shared embedding cannot resolve; (2) naively applying RoPE to LZW-compressed sequences ignores that merged tokens can span multiple tokens; (3) merging certain tokens (notably digits) disproportionately hurts downstream accuracy; and (4) dynamic vocabularies introduce an inherent segmentation ambiguity that confounds standard evaluation. We address these through decoupled input/output dynamic embedding layer, size-aware RoPE positioning, and a modified LZW codec supporting selective merges and multi-view segmentations. Across four models, our recipe improves perplexity on every corpus we evaluated as well as mathematical reasoning accuracy, closing roughly half the quality gap between zip2zip and the uncompressed baseline at a similar compression ratio on general text. This represents a significant step toward lossless adaptive-vocabulary compression for language models.

Figures & tables

Figure 1: Why LZW induces prefix-aligned output codes. (a) The LZW dictionary is prefix-closed: an entry is registered only after its own prefix, so the entries available at a given position form a chain under the prefix order (

\{AB,ABC,ABCD\}

), all sharing the same first constituent. (b) The mirror image—a suffix-closed dictionary

\{CD,BCD,ABCD\}

—never arises under LZW. (c) Consequence for the language model: at a single decoding position the output hyper-encoder must score every member of such a chain against the same hidden state, which pushes their unembedding vectors toward one another and imposes a prefix-aligned geometry on

f_{\phi}^{\text{out}}

Figure 2: Substitution probe on LZW hypertokens (zip2zip++, Phi-3.5-mini). Bars report the mean cosine similarity between a hypertoken embedding and the same embedding after replacing its first ( Prefix Substitution ) or last ( Suffix Substitution ) constituent. The ratio

r_{K}=\cos_{\text{last}}/\cos_{\text{first}}

(right) quantifies positional asymmetry. The output hyper-encoder is strongly prefix-dominated at every span length, whereas the input hyper-encoder is balanced. The corresponding BPE control, which shows no comparable asymmetry, is deferred to Figure 7 .

Panel of Figure 3 — Figure 3: Identity initialization of the hyper-encoder. (a) With the residual, the encoder only predicts a correction $\Delta X$ on top of $e_{x_{1}}$ and is zero-initialized ( $f_{\phi_{0}}=0$ ), so a hypertoken embedding starts out exactly at $e_{x_{1}}$ . (b) Training dynamics: identity initialization removes the early loss shock and reaches both a better final loss and a better accuracy.

Panel of Figure 4 — Figure 4: (a) Position assignment for a compressed sequence ( Section 3.3 ). The base tokens $ABABCBAC$ occupy positions $0$ – $7$ ; LZW merges them into $A$ , $B$ , $AB$ , $C$ , $BA$ , $C$ . Default numbers the compressed tokens consecutively; start , mid and end indexing take the first, mean and last base position of each span and leave the other base tokens in place. The learned rule interpolates between end indexing and the default index with a gate $g$ on the low-frequency rotary pairs ( $g=0$ is end indexing, $g=1$ the default). (b) Two hyper-encoder variants ( Section 3.4 ). Flat encodes all constituents tokens in a single pass and is tied to the training-time merge size; hierarchical folds them pairwise with a shared composition function. (c) Perfect versus imperfect LZW compression of the same code snippet ( Section 4 ). Coloured boxes mark different hypertokens.

Figure 5: Segmentation tree for multi-view scoring. Segmentation tree for the text to be or not to be or to be or not . The canonical chain (grey and blue) carries the greedy LZW segmentation; all views of a position decode to the same base-token string.

Model	Method	ARC-c	ARC-e	HS	OBQA	PIQA	WG	Wiki	Pile	mC4	dC4
Phi-3.5-4B	Uncompressed	0.59	0.84	0.74	0.48	0.82	0.75	1.58	1.67	1.77	1.82
	zip2zip	0.54	0.81	0.71	0.46	0.80	0.75	1.70	1.82	1.86	1.92
	zip2zip++	0.57	0.83	0.72	0.47	0.80	0.74	1.66	1.78	1.83	1.89
Phi-3-14B	Uncompressed	0.65	0.88	0.81	0.51	0.83	0.79	1.43	1.61	1.71	1.76
	zip2zip	0.61	0.85	0.78	0.51	0.81	0.77	1.58	1.76	1.80	1.85
	zip2zip++	0.62	0.86	0.79	0.50	0.82	0.78	1.53	1.72	1.77	1.82

Table 1: Main results. Two-shot accuracy on six benchmarks and byte-level perplexity (

\downarrow

) on four corpora with a 1024-token context; details in Section C.1 . Uncompressed is the same base model finetuned on uncompressed sequences under the same conditions as in Appendix C . Bold marks the better of the two compressed models in each column. Results for Llama-3.2-1B/3B-Instruct are in Table 7 .

		Wiki				Pile				mC4				dC4
Model	Training	PPL	PPL ⋆	BPB	BPB ⋆	PPL	PPL ⋆	BPB	BPB ⋆	PPL	PPL ⋆	BPB	BPB ⋆	PPL	PPL ⋆	BPB	BPB ⋆
Phi-3.5-4B	Uncompressed	11.5	11.5	0.66	0.66	31.5	31.5	0.74	0.74	30.4	30.4	0.82	0.82	35.2	35.2	0.87	0.87
	zip2zip	16.8	14.8	0.76	0.73	57.9	49.5	0.87	0.83	41.0	37.3	0.89	0.87	47.5	43.0	0.94	0.91
	zip2zip++	14.9	13.6	0.73	0.70	49.3	43.4	0.83	0.81	37.8	35.0	0.87	0.85	44.0	40.7	0.92	0.90
Phi-3-14B	Uncompressed	6.8	6.8	0.52	0.52	25.0	25.0	0.69	0.69	24.9	24.9	0.77	0.77	28.6	28.6	0.81	0.81
	zip2zip	11.6	9.9	0.66	0.62	45.4	38.7	0.82	0.78	33.6	30.5	0.84	0.82	38.5	34.9	0.89	0.86

Table 2: Perplexity evaluation on four corpora using a 1024-token context window.

\star

denotes the exact multi-view variants of Section 4.1 , which sum the probability of every valid segmentation of the target. The uncompressed reference has a unique tokenization, so its multi-view scores coincide with its strict ones. PPL is per whitespace-delimited word, BPB per byte.

		GSM8K	MATH-500	HumanEval	IFEval	RULER
Scale	Model	acc	acc	pass@1	prompt acc	4K	8K	16K	32K
Phi-3.5-4B	Uncompressed	0.75	0.36	0.58	0.38	86.4	81.5	78.1	73.7
	zip2zip	0.36	0.15	0.26	0.32	46.6	28.1	21.0	15.2
	zip2zip++	0.68	0.24	0.32	0.32	70.7	60.6	53.2	52.8
Phi-3-14B	Uncompressed	0.70	0.39	0.57	0.49	81.6	47.9	40.6	32.2
	zip2zip	0.51	0.22	0.36	0.43	52.5	23.2	14.0	11.6

Table 3: Post-SFT evaluation on generation tasks and long context. All three recipes share the same data stream and update budget and differ only in the training representation and its window filter ( Section D.7 ); per-benchmark details are in Section C.1 and strict-format variants in Section C.2 . Bold marks the better of the two compressed models in each column; Uncompressed is the reference.

Configuration	ARC-c	ARC-e	HS	OBQA	PIQA	WG	GSM8K	Wiki	Pile	mC4	dC4
zip2zip	0.54	0.81	0.71	0.46	0.80	0.75	0.36	1.70	1.82	1.86	1.92
+ Digit protection	0.54	0.81	0.70	0.47	0.79	0.71	0.61	1.71	1.83	1.87	1.93
+ Untied hyper-encoders	0.56	0.82	0.72	0.47	0.79	0.74	0.62	1.69	1.81	1.85	1.91
+ Size-aware RoPE	0.55	0.82	0.71	0.46	0.80	0.74	0.65	1.69	1.81	1.85	1.91
+ Identity-init residual	0.57	0.83	0.72	0.47	0.80	0.74	0.68	1.66	1.78	1.83	1.89
+ Continued Pretraining	0.55	0.82	0.72	0.46	0.80	0.75	0.64	1.63	1.74	1.82	1.88

Table 4: Ablation study on Phi-3.5-mini. Rows are cumulative, in the order in which the recipe was developed; the last row of the ladder is the zip2zip++ model of Table 1 . Two-shot accuracy and byte-level perplexity

\downarrow

, as in Table 1 . The continued-pretraining row is a single run after 200B additional tokens of compressed pretraining, not compute-matched to the others. Per-component gains and paired significance tests are in Section D.3 . Bold marks the best value along the ladder; the rows below the rule are references.

Figure 6: Hypertoken length generalization examples. Left:

M_{3}

evaluated with its training-time maximum merge size (

3{\rightarrow}3

, baseline). Center: the same

M_{3}

model evaluated with the unseen merge size 4 (

3{\rightarrow}4

, length generalization). Right:

M_{4}

, trained and evaluated with maximum merge size 4 (

4{\rightarrow}4

, native reference). Blue : base tokens. Yellow : hypertokens (composed of 2 base tokens). Orange : hypertokens (composed of 3 base tokens). Red : hypertokens (composed of 4 base tokens).

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: BPE base-table control for the substitution probe (zip2zip++, Phi-3.5-mini). The identical probe applied directly to the pretrained

\mathbf{W}_{\text{in}}

and

\mathbf{W}_{\text{out}}

, with no hyper-encoder in the path. Panels and metrics match Figure 2 . Both tables stay within

r_{K}\in[0.71,1.33]

at every

K

, i.e. no asymmetry comparable to the

4.8

–

6.6

of the output hyper-encoder.

Figure 8: Substitution probe on Llama-3.2-3B hypertokens. The untied output hyper-encoder is strongly prefix-aligned, whereas the untied input hyper-encoder exhibits substantially weaker positional asymmetry. When the two hyper-encoders are tied, their input and output ratios coincide by construction and consistently fall between the corresponding untied output and input ratios. The base-token embeddings remain close to or below

r_{K}=1

, showing no comparable prefix-aligned asymmetry.

Figure 9: Sequence probe: pairwise similarity of contiguous sub-spans (zip2zip++, Phi-3.5-mini). Cosine similarity between the embeddings of all contiguous sub-spans of length $\geq 2$ of “It is a dog” . Left: the output hyper-encoder shows clear block structure—spans sharing a prefix cluster at $\cos\geq 0.88$ while cross-block pairs fall to $0.21$ – $0.44$ . Right: the input hyper-encoder shows no such blocks but a smooth gradient in the number of shared constituents, consistent with the balanced geometry of Section 3.1 .

Base models	Phi-3.5-mini-instruct (3.8B), Phi-3-medium-4k-instruct (14B),
	Llama-3.2-1B-Instruct, Llama-3.2-3B-Instruct
Adapter	LoRA rank 32, $\alpha=32$ , all attention and MLP projections;
	decoder otherwise frozen
Optimizer	AdamW, $\beta=(0.9,0.999)$ , weight decay 0.01
Learning rate	cosine $3\times 10^{-4}\rightarrow 10^{-5}$ , 800 warm-up steps
Steps	8,000, at $32{,}768$ decoder positions per step

Appendix

Table 5: Finetuning configuration, shared across all runs and the control.

Recipe	GSM8K flexible	GSM8K strict
Protected digits, untied encoders	.6232	.066
$+$ end-indexed positions	.6497	.210
$+$ identity init.	.6778	.215
Uncompressed reference	.7468	.372

Appendix

Table 6: GSM8K under the two extraction rules along the ablation ladder of Table 4 . The flexible column uses the combined rule defined above. Strict matching demands the #### template verbatim; it moves by 14 points between the first two rungs, whose combined-rule scores differ by 2.7, which is why we report the combined rule throughout.

Model	Method	ARC-c	ARC-e	HS	OBQA	PIQA	WG	Wiki	Pile	mC4	dC4
Phi-3.5-4B	Original	0.56	0.79	0.71	0.48	0.78	0.73	1.58	1.68	1.79	1.84
	Uncompressed	0.59	0.84	0.74	0.48	0.82	0.75	1.58	1.67	1.77	1.82
	zip2zip	0.54	0.81	0.71	0.46	0.80	0.75	1.70	1.82	1.86	1.92
	zip2zip++	0.57	0.83	0.72	0.47	0.80	0.74	1.66	1.78	1.83	1.89
Phi-3-14B	Original	0.64	0.86	0.82	0.57	0.83	0.79	1.43	1.62	1.72	1.77
	Uncompressed	0.65	0.88	0.81	0.51	0.83	0.79	1.43	1.61	1.71	1.76

Appendix

Table 7: Main results, all four base models. Columns and conventions as in Table 1 . Original is the released instruct checkpoint with no finetuning; Uncompressed is the same model finetuned on uncompressed sequences. Bold marks the better of the two compressed models in each column.

	GSM8K accuracy $\uparrow$				$C_{\text{gen}}\uparrow$
	Original	Uncompressed	zip2zip	zip2zip++	zip2zip	zip2zip++
Phi-3.5-mini	.78	.75	.36	.68	1.53	1.25
Phi-3-medium	.84	.70	.51	.69	1.52	1.27
Llama-3.2-1B-Inst	.42	.34	.20	.24	1.37	1.26
Llama-3.2-3B-Inst	.76	.64	.41	.53	1.37	1.29

Appendix

Table 8: GSM8K accuracy (two-shot, combined extraction rule of Section C.2 ) and generation compression

C_{\text{gen}}

(base tokens per emitted token over the generated answers) for all four models. Original uses flexible extraction; the two rules give identical scores on the released Llama models. Bold marks the better of the two compressed models.

	GSM8K $\uparrow$	Compression $C\uparrow$
Protection strategy	flexible	WikiText	MC input	Math decode
No protection	.356	$1.209$	$1.079$	$1.53$
same weights, digits protected at eval	.458	$1.169$	$1.077$	$1.30$
same weights, uncompressed eval	.483	$1.000$	$1.000$	$1.00$
Digits protected (train $+$ eval)	.610	$1.169$	$1.077$	$1.28$
same weights, uncompressed eval	.679	$1.000$	$1.000$	$1.00$

Appendix

Table 9: Token protection with FT-LZW. Rows sharing a checkpoint differ only in the evaluation representation, so the block structure instantiates Equation 5 : protecting digits at evaluation alone recovers 10.2 of the 12.7-point representation penalty, and protecting them during training as well repairs both terms, a 25.4-point gain over the unprotected baseline. All compressed rows in this paper use the FT-LZW codec and differ only in its protected-token set. The cost is localized to math-heavy generation; general-text and multiple-choice compression are barely affected. Protecting operators and L a T e X control tokens in addition yields

+0.5

points, confirming that protection should target empirically fragile atoms rather than be applied broadly.

Corpus	Control	Strict	Exact multi-view	First-token bound
WikiText	1.5777	1.6573	1.6290	1.5882
Pile	1.6678	1.7819	1.7488	1.6972
mC4	1.7660	1.8311	1.8084	1.7696
dC4	1.8221	1.8913	1.8668	1.8240

Appendix

Table 10: Byte-perplexity of zip2zip++ (Phi-3.5-mini) against the update-matched control, on WikiText and the fixed 1,000-document Pile/mC4/dC4 subsets of Section C.3 .

Figure 10: Hierarchical merge-size generalization. (a) Compression as the evaluation-time maximum merge size increases; WikiText

{\times}4

and

{\times}8

provide progressively stronger transfer exposure. (b) Strict and exact multi-view byte perplexity for transferred

M_{3}:3{\rightarrow}4

and native

M_{4}:4{\rightarrow}4

. (c)

M_{3}

, trained with

K=3

, evaluated at

K_{\mathrm{eval}}=3,\ldots,8

on WikiText

{\times}8

, with native

M_{4}

K_{\mathrm{eval}}=4

for reference.

Corpus	coverage	$3\!\rightarrow\!3$	$3\!\rightarrow\!4$	$4\!\rightarrow\!4$	Strict	Exact MV	First-token
	Length-4	Strict byte-PPL			Penalty of $3\!\rightarrow\!4$
Repeat-4	6.54%	1.1890	1.2050	1.1922	1.07%	.94%	.25%
Repeat-8	29.90%	1.1057	1.1535	1.1122	3.71%	3.54%	.33%

Appendix

Table 11: Merge-size transfer.

a\!\rightarrow\!b

denotes training with maximum merge size

a

and evaluating with size

b

. Penalties are for

3\!\rightarrow\!4

relative to the native

4\!\rightarrow\!4

model. Single runs.

Training path	GSM8K	Wiki byte-PPL
zip2zip++, direct SFT, 8k steps	.6778	1.6574
20B raw $+$ SFT, 8k	.6088	1.6377
20B raw $+$ SFT, 16k	.6255	1.6390
20B raw $+$ SFT, 48k	.6391	1.6554
200B raw $+$ SFT, 8k	.6414	1.6331

Appendix

Table 12: A raw-text pretraining stage before the standard SFT mixture. Single runs, without a matched long-run uncompressed control. The 200B row is the “Continued Pretraining” row of Table 4 .

Intervention	Parent	Training / LM proxy	$\Delta$ GSM	Takeaway
Reformat math SFT as chat	zip2zip	Wiki PPL $1.695\!\rightarrow\!1.719$	$+2.3$	Narrow style gain, broad MC/PPL trade-off
Freeze decoder LoRA for 200 steps	+ untied	Final loss flat	$-6.6$	Co-adaptation is preferable here
Hyper-encoder 2 $\!\rightarrow\!$ 4 layers	+ untied	Loss $1.51\!\rightarrow\!1.45$ ; PPL flat	$-2.6$	Capacity fits training, does not transfer
Exact online codebook mask	final	Loss $1.434\!\rightarrow\!1.376$	$-2.4$	Better proxies, worse downstream
25% uncompressed microsteps	final	PPL flat	$-3.6$	No measurable transfer
Two-axis RoPE (fixed 50/50 split)	final	Wiki PPL flat	$-2.4$	Mixed coordinates do not help

Appendix

Table 13: One-variable branches that did not improve the recipe.

\Delta

GSM is in percentage points relative to each branch’s parent (the zip2zip baseline, the “+ untied” rung of Table 4 , or the final recipe). “Flat” means no practically meaningful change. All are single runs; see Section D.7 for seed spread.

Figure 11: FT-LZW decoding, step by step. The same stream “to be or not to be or to be or not” under canonical (left) and non-canonical (right) compression. Columns show the input codes, the decoder state, the codebook entry created at that step, and the emitted base tokens. Canonical input keeps the decoder in Normal at every step, one code creating one entry. Non-canonical input triggers the guard: Skip (no entry, the candidate already exists), Resume (the deferred entry is created on the next code), and Early Exit (a novel combination is reached partway through the expansion). Both cases emit the same base-token sequence.

Figure 12: Tree attention for multi-view scoring. The corresponding attention mask over the packed sequence. A shaded cell means the row (query) may read the column (key). The canonical backbone is causal; each branch sees only the shared prefix and its own ancestors, so sibling views and views of different targets cannot contaminate one another. All views are scored in one forward pass.

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Embedded Intelligence Lab (EMILAB)

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Mar 18, 2026

ZipServ: Fast and Memory-Efficient LLM Inference with Hardware-Aware Lossless Compression

Lossless model compression holds tremendous promise for alleviating the memory and bandwidth bottlenecks in bit-exact Large Language Model (LLM) serving. However, existing approaches often result in substantial inference slowdowns due to fundamental design mismatches with GPU architectures: at the kernel level, variable-length bitstreams produced by traditional entropy codecs break SIMT parallelism; at the system level, decoupled pipelines lead to redundant memory traffic. We present ZipServ, a lossless compression framework co-designed for efficient LLM inference. ZipServ introduces Tensor-Core-Aware Triple Bitmap Encoding (TCA-TBE), a novel fixed-length format that enables constant-time, parallel decoding, together with a fused decompression-GEMM (ZipGEMM) kernel that decompresses weights on-the-fly directly into Tensor Core registers. This "load-compressed, compute-decompressed" design eliminates intermediate buffers and maximizes compute intensity. Experiments show that ZipServ reduces the model size by up to 30%, achieves up to 2.21x kernel-level speedup over NVIDIA's cuBLAS, and expedites end-to-end inference by an average of 1.22x over vLLM. ZipServ is the first lossless compression system that provides both storage savings and substantial acceleration for LLM inference on GPUs.

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The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Harbin Institute of Technology, Shenzhen, Shenzhen, China · The Hong Kong University of Science and Technology, Hong Kong, Hong Kong SAR

Model Compression LLM Compression Memory-Efficient Inference LLM Inference Acceleration

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Abstract

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