{"id":"e46061e3-fa27-4e06-8d05-35a6274b186f","arxiv_id":"2504.19274","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Pruning weights and teleporting activations before proof generation cuts ZK-SNARK prover memory by up to 67% and proof time by up to 54% on vision models at about 1% accuracy cost.","lead":"TeleSparse makes zero-knowledge proofs of neural network inference cheaper by pruning network weights and rescaling activation values before proof generation. In tests on MobileNet, ResNet-20, and a vision transformer it cuts prover memory by roughly 45 to 67 percent and proof time by about 20 to 54 percent, with roughly one percent accuracy loss.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Teleportation objective is unbounded: scaling a layer's tau by c drives the range term to zero, so reported teleportation gains (Table 4) may be artifacts of unconstrained tau rather than principled optimization.","rationale":"The reader's weakest assumption matches my analysis. Eq. (15) is degenerate: the range term is homogeneous of degree -1 in tau within a layer, so the objective's infimum is 0 and the minimum is not attained. Since Algorithm 2 only lower-bounds tau, the optimizer can inflate tau without bound; the reported reductions in activation range (Figure 6) and memory/time (Table 4) may be produced by runaway tau rather than by a meaningful compressed range. The paper does not report tau values, the hyperparameter lambda in Eq. (20), or early-stopping criteria, so the teleportation results are not reproducible from the text. A normalization or penalty would make the objective well-posed, and the proposed experiment would settle whether the gains persist. I also considered the privacy argument's reliance on weights in fixed columns and the inconsistencies in the headline numbers, but the unbounded objective is the most direct threat to the central efficiency claim, which is the paper's main contribution. Therefore the CONDITIONAL verdict is appropriate: the method is promising and the resource measurements are plausible in direction, but the teleportation component needs a principled formulation and reported hyperparameters before the G2 claim can be accepted.","tokens_in":29369,"tokens_out":14299,"duration_ms":139539,"concrete_test":"Run the teleportation optimization (Algorithm 2) for ResNet-20 on CIFAR-100 with a normalization constraint, e.g., fix the geometric mean of each layer's tau to 1 (or add a penalty on log tau), and remeasure Table 4's Teleportation row. If memory/time reductions (38.9%/23.8%) shrink substantially or the activation range no longer narrows, the reported G2 gains depend on unbounded tau. Additionally, print the resulting tau values; if max tau_j or tau ratios exceed the 2^12 quantization scale, the fixed-point circuit is not faithfully represented.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The G2 claim (lookup-table reduction) rests on solving Eq. (15): min_{tau>0} sum_i (max_j z_j/tau_j - min_j z_j/tau_j). For any fixed z_j, choosing all tau_j = c in one layer makes the i-th term (max z - min z)/c, which tends to 0 as c -> infinity; the infimum is 0 and is not attained. Algorithm 2 only enforces tau_j >= epsilon, with no upper bound or normalization, so the optimizer can inflate tau arbitrarily to trivially minimize the range. The paper never reports tau values, the reconstruction lambda in Eq. (20), or the stopping criterion for the CGE loop. The reported range reductions (Figure 6: mean 27.39 -> 16.98, about 38%) and resource gains (Table 4: ResNet-20 38.9% memory, 23.8% time) are therefore not demonstrated to be the result of a well-defined optimization. Moreover, with fixed-point quantization scale 2^12 (Section 6.3), extreme tau (or extreme ratios tau_{i+1}/tau_i in Eq. (9)) can overflow the field or underflow scaled pre-activations, potentially invalidating the circuit accuracy figures. This directly undermines the central claim that teleportation shrinks lookup tables and thereby reduces prover memory and time.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes TeleSparse, a post-processing pipeline for deep neural networks intended to make ZK-SNARK inference verification practical. It combines unstructured sparsification (RD_PRUNE, CAP) to reduce circuit constraints with a neural-teleportation-inspired scaling of network parameters aimed at shrinking activation ranges and hence lookup tables. Using Halo2 via the EZKL toolkit, the authors report memory and prover-time reductions on MobileNetV1/CIFAR-10, ResNet-20/CIFAR-100, and Tiny-ViT/ImageNet, with accuracy losses around 1%, and they present a privacy analysis that explicitly assumes leakage of the layer-wise sparsity ratio.","tokens_in":1977,"tokens_out":2571,"duration_ms":105815,"significance":"If the reported results hold, TeleSparse would be a useful and largely orthogonal post-processing layer for the ZK-ML stack: it is model-agnostic, complementary to arithmetization-specific optimizations, and supported by a public code release. The experimental coverage across convolutional, mobile, and transformer architectures is a strength, as is the candid discussion of sparsity-ratio leakage. However, the teleportation objective is degenerate as written and the simulator argument in the privacy proof has a gap, so the significance currently hinges on unverified assumptions rather than on the mechanisms actually demonstrated.","major_comments":[{"comment":"The objective in Eq. (15) is unbounded in a way that makes the reported teleportation gains (Table 4, Figure 6) not attributable to a principled optimization. For a fixed layer i, setting tau_j = c for all j makes the term (max_j z_j/tau_j - min_j z_j/tau_j) equal to (max_j z_j - min_j z_j)/c, which tends to 0 as c tends to infinity; the infimum is 0 and is not attained. Algorithm 2 only enforces tau_j >= epsilon and imposes no upper bound or normalization. For scale-invariant activations such as ReLU, the teleported network function is identical for every tau, so the reconstruction penalty in Eq. (20) does not constrain tau and the optimizer can inflate the scaling factors arbitrarily. The paper never reports the learned tau values, the learning rate eta, the perturbation size mu, the maximum iterations, or the stopping criterion, so the 38.9% memory reduction attributed to teleportation in Table 4 cannot be reproduced or distinguished from a trivial scaling artifact. This directly undermines the central G2 claim. Please add a normalization constraint (e.g., geometric mean of tau_j fixed to 1 per layer), report the resulting tau statistics, and re-run the ablation with accuracy figures for teleportation alone.","section":"Section 5, Eqs. (14)-(15); Algorithm 2"},{"comment":"The headline numbers are internally inconsistent. The abstract states reductions of 67% in prover memory and 46% in proof generation time; Section 1 states 67% in proof generation time and 46% in prover memory; the conclusion states 67% memory and 54% time. Table 1 reports 66.8%/45.6% for ResNet-20 and 59.2%/54.0% for MobileNetV1, so the '67%/46%' and '54%' figures refer to different models. Since these are the paper's central quantitative claims, please state explicitly which model and dataset each headline figure corresponds to and correct the swapped values in Section 1 and the conclusion.","section":"Abstract, Section 1, Section 8"},{"comment":"The extension to non-scale-invariant activations such as GELU is asserted but not validated. Eq. (20) introduces a reconstruction penalty with hyperparameter lambda, but the paper does not report lambda, eta, mu, max iterations, or any teleportation-only accuracy result. Table 3 reports accuracy only for the dense and combined sparse+teleported models, so the approximately 1% accuracy trade-off cannot be attributed between sparsification and teleportation. Given that teleportation alone produces large resource reductions in Table 4, a missing accuracy column for that configuration makes it impossible to assess whether the resource savings come at an unstated accuracy cost. Please provide hyperparameter values and an accuracy ablation for teleportation alone, including for the GELU-based ViT.","section":"Section 5.2 and Section 6.4"},{"comment":"The proof of Theorem 7.1 has a simulation gap. The simulator is said to 'generate model weights V_t_sparse that produce y given X' using only the sparsity ratio and access to the ideal functionality. In a standard NIZK, the zero-knowledge simulator can produce a proof only for statements in the language; it cannot produce a valid proof for a false statement (that would break soundness). If the simulator picks its own V, there is no guarantee that f(X; V) equals the public output y provided by the ideal functionality, so the simulated proof would be for a statement that is not necessarily true. The proof should instead leverage the hiding property of the polynomial commitment to replace the committed weights and use the NIZK simulator on a true statement, or explicitly model a stronger simulation soundness property. As written, the privacy guarantee is not established.","section":"Section 7.2 and Appendix H"},{"comment":"The Tiny-ViT numbers in Tables 2 and 4 are inconsistent as presented. Table 2 reports EZKL memory 650 GB and proving time 1087 s, while Table 4 lists 'No Post-Processing' for Tiny-ViT as 1002.2 GB and 541 s, with a note that the metrics correspond only to MLP parts. The caption of Table 4 should state this scope, and the baseline and reduction percentages should be recomputed consistently; as presented, a reader cannot reconcile a 20.05% time reduction in Table 2 with a 52.7% time reduction in Table 4 for what appear to be the same model.","section":"Tables 2 and 4"}],"minor_comments":[{"comment":"The abstract contains a grammar error: 'TeleSparse, a ZK-friendly post-processing mechanisms' should be 'a ... mechanism'.","section":"Abstract"},{"comment":"The sentence 'TeleSparse achieves about 67% reduction in proof generation time and a 46% reduction in prover memory usage' reverses the abstract's numbers; this should be corrected.","section":"Section 1"},{"comment":"The notation table defines g^(i)_j as pre-activation and z^(i)_j as activation output, but Eq. (13) uses z^(i)_j as the input to the activation function; please unify the notation.","section":"Notation table and Section 5"},{"comment":"The pruning objective in Algorithm 1 is written as an L2 reconstruction over layers, but Eq. (8) defines the CAP importance score; the relation between these two formulations should be clarified.","section":"Algorithm 1 and Eq. (8)"},{"comment":"The figure caption refers to 'Mean Activation Loss' and 'Standard Deviation of Activation Loss'; these terms are not defined and appear to mean the mean and standard deviation of the activation range. Please use consistent terminology.","section":"Figure 6"},{"comment":"The paper should specify the exact EZKL version and configuration (e.g., Halo2 parameters, KZG or IPA commitment settings), as these materially affect the reported resource figures.","section":"Section 6.1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a revised version (arXiv v2) and the remaining issues are fixable but require additional experiments (tau normalization, hyperparameter reporting, accuracy ablation) and a corrected simulation proof. The unbounded teleportation objective is a serious flaw that should have been caught in earlier review; the privacy proof gap is also load-bearing for the 'privacy-preserving' claim. If the authors can address these, the paper could be suitable for publication, but in its current state the central efficiency and privacy claims are not fully supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuinely new combination—post-training sparsification plus neural teleportation to reduce Halo2 proving costs—and the empirical direction is right for zkML. But the paper is not ready as written. The teleportation objective is underspecified to the point of being trivially minimizable, the privacy model appears to put private weights in public fixed columns, and the headline numbers disagree across abstract, intro, conclusion, and Table 1.\n\nWhat is new and good: nobody has applied pruning specifically to cut circuit constraints for ZK inference, or used teleportation to shrink activation lookup ranges. The sparsification theorem (Theorem 4.1) is simple but fine. The evaluation spans MobileNet, ResNet, and ViT on CIFAR and ImageNet, with 50% sparsity and roughly 1% accuracy loss; the ablation in Table 4 is a useful decomposition. If the measurements are reproducible, this is a meaningful step.\n\nThe soft spots, in order of severity. First, Eq. (15) is not a well-posed optimization as written: for fixed preactivations z, taking all tau_j to a common large c drives each layer's range term to zero. Algorithm 2 only enforces a lower bound. The paper never reports tau values, the reconstruction lambda in Eq. (20), or a stopping rule. More fundamentally, for scale-invariant activations teleportation leaves the network function unchanged, and it is not obvious that the argument to the activation inside the circuit can be shrunk at all; the paper needs to define exactly which quantity is entering the lookup table and prove the range reduction is real rather than an artifact of unnormalized tau. Second, the privacy argument: weights placed in fixed columns are public in Halo2; saying the columns mix weights with selectors does not make them private. Either move weights to advice columns or spell out a nonstandard model where fixed columns are secret. Third, numbers: abstract says 67% memory and 46% time; intro says the reverse; conclusion says 54% time; Table 1 gives 66.8/45.6 for ResNet and 59.2/54.0 for MobileNet. Fourth, the \"code is available at this link\" has no link and no hyperparameter settings for teleportation.\n\nI would send this to review, but with a strong expectation of major revision. The combination is worth a referee's time; the current formulation of the central claim is not.","headline":"A useful zkML post-processing combination that is not yet trustworthy: the teleportation math is underspecified to the point of being trivially minimizable, the privacy model puts weights in public fixed columns, and the headline numbers disagree across sections.","tokens_in":30217,"tokens_out":9914,"would_cite":false,"duration_ms":109919,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"TeleSparse claims that pruning weights and teleporting activations makes zero-knowledge verification of deep model inference practical, cutting prover memory by about 67 percent and proof time by about 46 percent with roughly 1 percent…","keywords":["zero-knowledge proof","verifiable inference","neural network sparsification","neural teleportation","Halo2","lookup table optimization","privacy-preserving machine learning","deep learning verification"],"falsifier":"Take a GELU-based transformer, optimize the teleportation scalars with the reconstruction term removed (lambda = 0), and compare the teleported model's outputs with the original on a held-out set. If the activation range collapses while accuracy drops well beyond the reported one percent, or if with the recommended lambda no scaling keeps both the range small and the output distance small, then the approximate-scale-invariance assumption is doing the work and the reported savings do not transfer. A cheaper check is to measure the per-layer activation spreads before and after teleportation and confirm that the resource reduction in the ablation study is actually driven by lookup-table size rather than by quantization or pruning effects.","tokens_in":2091,"feed_emoji":"🧠","tokens_out":2581,"duration_ms":88010,"temperature":0.7,"pith_summary":"The paper tries to establish that the main obstacles to ZK-SNARK verification of modern neural networks, namely too many circuit constraints and oversized lookup tables for non-linearities, can be attacked by post-processing the model itself rather than only optimizing the proof system. It claims that pruning roughly half the weights and applying a neural-teleportation rescaling that squeezes activation values into a narrow range makes Halo2 proof generation tractable. For ResNet-20 on CIFAR-100, the paper reports prover memory dropping about 67 percent and proving time about 46 percent, with roughly 1 percent accuracy loss, and similar gains across MobileNet and Tiny-ViT. If true, this would make privacy-preserving, verifiable inference viable for existing CNNs and transformers without retraining or revealing model weights.","feed_headline":"Sparsity plus teleportation cuts ZK proof memory by up to 67 percent","feed_subtitle":"Post-processing pre-trained models shrinks Halo2 circuits and lookup tables, cutting proving time 46 percent with about 1 percent accuracy…","key_machinery":"The workhorse is the Halo2 PLONKish circuit, in which a matrix-vector multiplication is represented by a fixed column holding weights, advice columns holding inputs and running sums, and copy constraints chaining accumulation across rows; deleting rows whose fixed value is zero removes constraints without touching soundness. On top of that sits neural teleportation, with change-of-basis scalars $\\tau^{(i)}_j$ transforming each weight $w^{(i)}_{j,k}$ into $\\sqrt{\\tau^{(i+1)}_k/\\tau^{(i)}_j}\\,w^{(i)}_{j,k}$ and each activation $f(x)$ into $\\tau f(x/\\tau)$. The optimization objective minimized by zero-order coordinate gradient estimation is the per-layer spread of scaled pre-activations, augmented by the reconstruction term $\\lambda \\lVert f(\\boldsymbol{\\theta},1) - f(\\boldsymbol{\\theta},\\tau)\\rVert^2$ for non-scale-invariant activations; this is what shrinks the lookup tables, while the sparse circuit handles the constraint count.","core_discovery":"At its core, the paper argues that model size is not the only factor that makes SNARK verification expensive: the distribution of activation values matters as much as the number of parameters. Two post-processing moves target these costs. First, sparsification (via RD_PRUNE or CAP) zeros out roughly half the weights, and because weights live in fixed columns of the Halo2 circuit, rows corresponding to zero entries can be deleted without changing what the circuit proves (Theorem 4.1). Second, neural teleportation rescales each neuron's input and weight by positive scalars $\\tau^{(i)}_j$, chosen to minimize the per-layer spread $\\max_j (z^{(i)}_j/\\tau^{(i)}_j) - \\min_j (z^{(i)}_j/\\tau^{(i)}_j)$; for scale-invariant activations this preserves the network function exactly, and for non-scale-invariant activations such as GELU a reconstruction penalty keeps the teleported function close to the original. Together these mechanisms reduce prover memory by about 67 percent and proving time by about 46 percent on ResNet-20/CIFAR-100, with accuracy dropping roughly one percentage point, and the paper reports analogous gains on MobileNetV1 and Tiny-ViT.","pith_inferences":["The same range-minimization objective could be applied during training as a ZK-friendly regularizer rather than only as post-processing; this would likely yield even smaller lookup tables than teleporting a fixed model, though the paper does not test it.","Teleportation's benefit is concentrated in lookup-heavy layers, so a layer-wise cost model that allocates sparsity and teleportation effort according to constraint cost versus lookup cost could outperform the uniform 50 percent sparsity used in the experiments.","The teleportation objective resembles rotation-based outlier suppression used in quantization; combining change-of-basis rescaling with such rotations or with per-layer fixed-point scales might reduce lookup range further, at the cost of extra circuit gates.","A cleaner privacy statement would require a quantified mechanism for hiding the sparsity ratio; the paper's dummy-constraint idea points toward a differential-privacy-style noise trade-off but leaves the actual mechanism unspecified."],"forward_implications":["If the claims hold, proving a Tiny-ViT on ImageNet no longer requires over 10 TB of prover memory; TeleSparse reports about 357 GB across 24 split proofs, roughly 45 percent below the baseline, making verifiable inference feasible on reachable hardware.","Because both steps are post-processing on a pre-trained model, existing deployed networks can be converted to ZK-friendly form without retraining or architectural changes, and the conversion overhead is reported as under 2 percent of proof memory for teleportation.","The two mechanisms are complementary: sparsification mainly attacks constraint count, teleportation mainly attacks lookup-table cost, so the best gains come from applying both together, with teleportation contributing little on models dominated by linear constraints such as MobileNet.","The approach composes with existing ZK-friendly arithmetization: it inherits Halo2's soundness and zero-knowledge properties and leaves open the option of parallel or recursive proof composition across split circuits.","The sparsity ratio leaks through the verification key size; the paper's proposed mitigation is dummy constraints, which would trade proof overhead for hiding the ratio, an explicit design knob for privacy."],"supporting_citations":[{"why":"Defines neural teleportation and the change-of-basis scalars in Eqs. (9)-(10), the mechanism for shrinking activation ranges.","marker":"[2]"},{"why":"PLONK arithmetization that Halo2 extends, supplying the custom gates and permutation arguments used for circuit construction.","marker":"[26]"},{"why":"Prior Halo2-based ZKML system using lookup tables for non-linear activations; it is the baseline TeleSparse extends and compares against.","marker":"[36]"},{"why":"The Halo2 proving system specification, including PLONKish circuit layout, lookup arguments, and the security properties the scheme inherits.","marker":"[82]"},{"why":"EZKL toolkit used to implement the circuits and measure baseline memory, proving time, and verification time.","marker":"[87]"},{"why":"RD_PRUNE, one of the two post-training pruning methods that produce the sparse weights used for constraint reduction.","marker":"[77]"},{"why":"CAP, the correlation-aware Hessian-based pruning method used to sparsify transformer and CNN models while preserving accuracy.","marker":"[46]"},{"why":"DeepZero coordinate gradient estimation, the zero-order optimizer used to minimize the teleportation objective in Eqs. (16)-(18).","marker":"[12]"},{"why":"Recursive proof composition without trusted setup, which underlies Halo2 and the paper's discussion of split and nested proofs for large models.","marker":"[10]"}],"fun_headline_variants":["TeleSparse: ZK proof memory down 67%, proving time 46% faster","TeleSparse: Zero-knowledge DNN verification with 67% less memory","Sparsity + teleportation: ZK proof cost cut by 67% memory","TeleSparse: Practical ZK for DNNs, 46% faster proofs, 67% less memory"],"cache_read_input_tokens":32256,"weakest_assumption_plain":"The load-bearing premise is that rescaling neuron inputs via teleportation leaves the network's function essentially unchanged even for activations such as GELU that are not perfectly scale-invariant, so that the lookup-table savings do not hide an accuracy cost; the reconstruction penalty is what is supposed to make this true.","fun_headline_variants_meta":{"raw":{"variants":["TeleSparse: ZK proof memory down 67%, proving time 46% faster","TeleSparse: Zero-knowledge DNN verification with 67% less memory","Sparsity + teleportation: ZK proof cost cut by 67% memory","TeleSparse: Practical ZK for DNNs, 46% faster proofs, 67% less memory"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000931,"raw_usage":{"total_tokens":4080,"prompt_tokens":1134,"completion_tokens":2946,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":750,"completion_tokens_details":{"reasoning_tokens":2847}},"tokens_in":750,"tokens_out":2946,"duration_ms":19921,"temperature":1.0,"reasoning_tokens":2847,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:57:20.158448+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a GELU-based transformer, optimize the teleportation scalars with the reconstruction term removed (lambda = 0), and compare the teleported model's outputs with the original on a held-out set. If the activation range collapses while accuracy drops well beyond the reported one percent, or if with the recommended lambda no scaling keeps both the range small and the output distance small, then the approximate-scale-invariance assumption is doing the work and the reported savings do not transfer. A cheaper check is to measure the per-layer activation spreads before and after teleportation and confirm that the resource reduction in the ablation study is actually driven by lookup-table size rather than by quantization or pruning effects.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"PLONK arithmetization that Halo2 extends, supplying the custom gates and permutation arguments used for circuit construction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Halo2 proving system specification, including PLONKish circuit layout, lookup arguments, and the security properties the scheme inherits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"EZKL toolkit used to implement the circuits and measure baseline memory, proving time, and verification time."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"RD_PRUNE, one of the two post-training pruning methods that produce the sparse weights used for constraint reduction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"CAP, the correlation-aware Hessian-based pruning method used to sparsify transformer and CNN models while preserving accuracy."}],"review_version":1}