{"id":"20154bab-6a6b-4ec8-81c6-4abe15e423f9","arxiv_id":"2501.02715","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper repackages the authors' prior VDC-2^n low-discrepancy encoding work for stochastic and hyperdimensional computing as a unified framework, without new experiments or derivations.","lead":"This paper proposes using a type of evenly spread number sequence, Van der Corput (VDC-2^n), to generate the random-looking bitstrings used in stochastic and hyperdimensional computing. It reports improved accuracy and lower energy cost for small AI and arithmetic circuits, but most of the designs and numbers come from the authors' earlier papers.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"HDC improvement may stem from dropping position hypervectors, not from VDC-2^n sequences; no ablation or orthogonality evidence supports the central claim.","rationale":"The reader identified the same weak assumption. The paper's most consequential claim is that its encoding method is generally beneficial; the HDC results are its empirical core. The proposed HDC design (➏) changes two variables simultaneously relative to baseline: the random source (LFSR→VDC) and the encoding structure (position×level → single-source level only). Without an ablation, any accuracy change could be due to either. The orthogonality of hypervectors is a fundamental requirement for HDC; if the VDC-generated hypervectors are not sufficiently orthogonal, the method's success on MNIST may be a lucky artifact. A direct ablation measuring accuracy with and without position hypervectors while holding the sequence source fixed would isolate the cause. If the VDC source alone does not improve over LFSR when the architecture is otherwise identical, the central claim of 'encoding improvement' is not supported. Thus the concern directly tests the paper's core assertion, and the REJECT verdict is appropriate.","tokens_in":10316,"tokens_out":5970,"duration_ms":59349,"concrete_test":"Re-run the MNIST experiment for the proposed design ➏ with the VDC-generated level hypervectors but retaining the baseline position hypervectors and the binding operation (i.e., current level HVs replaced by VDC, but the architecture otherwise matches the baseline ➎). Compare the accuracy to both the baseline and the proposed no-position-HV design across D=1K, 2K, 8K, and report the mean and standard deviation over 20 random seeds for the baseline. If the VDC+position design does not improve over the LFSR baseline, the reported gain is due to dropping position hypervectors, not to the LD sequence quality.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Central to the claimed HDC gains (Table III) is the assertion that a single VDC-2^n source can generate orthogonal hypervectors from a single deterministic run, eliminating the need for position hypervectors (Section III, Fig. 2(b)➏). The paper provides no derivation or measurement of the correlation properties of the generated hypervectors; it only cites prior self-authored work [30]–[35]. The reported accuracies are single point estimates without error bars, while the baseline LFSR method is stochastic and its performance varies with seed. If the VDC-generated hypervectors are not genuinely orthogonal, the encoding is noisy and the improvement over baseline may not generalize. Moreover, the design ➏ differs from baseline in two respects: the LD sequence source and the removal of the position-binding step. No ablation separates these two changes, so the observed accuracy improvement cannot be attributed to the VDC-2^n encoding as claimed. This is the load-bearing weakness: the paper's central causal claim is not established by the presented evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes using powers-of-2 bases of Van der Corput (VDC-2^n) low-discrepancy sequences as deterministic random sources for both stochastic computing (SC) bitstream generation and hyperdimensional computing (HDC) hypervector generation. It reports that this approach improves accuracy and reduces hardware cost compared with LFSR-based pseudo-random baselines, presenting results for an SC sin(x) design, MNIST HDC classification, several other image-classification datasets, and a DermaMNIST end-to-end unary HDC design. The manuscript is written largely as a consolidation of the authors' prior publications, with Figures and Tables summarizing those results and citing the earlier papers for design details.","tokens_in":10490,"tokens_out":5795,"duration_ms":55629,"significance":"If the central claim were established, the work would be valuable: a hardwired counter-based deterministic RNG that generates high-quality SC bitstreams and HDC hypervectors could reduce area, power, and run-to-run variance in resource-constrained systems, and the combination of unary processing with HDC is a promising direction. The paper's strengths are its clear identification of a hardware-friendly VDC-based RNG and its concrete numerical comparison with LFSR-based baselines in Tables I-IV. However, the manuscript in its current form does not provide the experimental methodology, ablations, or statistical support needed to attribute the observed gains to VDC-2^n encoding, and one headline efficiency number is contradicted by the paper's own table. The significance is therefore conditional on substantial additional evidence being supplied.","major_comments":[{"comment":"The text in Section IV states that the proposed design 'improves the accuracy and reduces energy consumption by up to 77% and 92%, respectively,' but Table II shows proposed sin(x) energy of 365.9 pJ versus baseline 936.8 pJ, which is a 61% reduction, and power of 812.2 μW versus 2178.2 μW, which is a 63% reduction; the 92% figure is not supported by the table. The 98% power reduction claimed for the DermaMNIST end-to-end unary design in Fig. 3 is also presented without any measurement details or supporting table. These unsupported numbers undermine the efficiency claims that are central to the paper.","section":"Section IV, Tables I/II and Fig. 3"},{"comment":"The proposed HDC design ➏ differs from the baseline ➎ in two respects: the source of randomness is changed from LFSR to Sobol+VDC-2^n, and position hypervectors and their binding operations are removed. Because no ablation separates these two changes, the improved MNIST accuracy in Table III cannot be attributed specifically to VDC-2^n encoding; it may stem from eliminating the position-binding step or from a different classification protocol. Moreover, Table III labels the proposed method 'Sobol+VDC-2^n', not VDC-2^n alone, so the contribution of VDC-2^n is not isolated.","section":"Section III, Fig. 2(b) ➏ and Table III"},{"comment":"The manuscript provides no experimental methodology: there is no statement of the number of runs, no error bars or standard deviations for the proposed methods, no dataset split or training epochs/retraining procedure, and no synthesis technology or tool flow for the hardware results. Many reported differences are small (e.g., Breast MNIST 68.59 versus 68.47 and CIFAR-10 41.97 versus 41.71 at D=8K in Table IV), so without variance measures the claim of 'significantly improves' is not supported. This missing methodology is load-bearing because the baselines are stochastic LFSR-based designs whose performance varies with the random seed.","section":"Section IV, Tables III and IV and Fig. 3"},{"comment":"The assertion that deterministic VDC-2^n sequences generate sufficiently orthogonal hypervectors so that position hypervectors can be dropped is supported only by citations to the authors' prior works [30]–[35]. No derivation, correlation measurement, or ablation appears in this manuscript. Because the success of HDC encoding hinges on hypervector orthogonality, the paper needs to provide direct evidence (e.g., cosine-similarity distributions, or classification accuracy with and without position hypervectors) rather than relying on self-citations.","section":"Section III, Fig. 2(b) ➏"}],"minor_comments":[{"comment":"The notation is inconsistent: the text refers to 'VDC-2^n' while Table I reports 'VDC4' and 'VDC128,256,512'; a brief mapping between base notation and sequence names would improve clarity.","section":"Sections II and III, Table I"},{"comment":"Figure 2 is very dense, with markers ➊–➑ distributed between two panels; the reader must search across the figure to connect each marker to the corresponding text. Splitting the SC and HDC panels into separate figures or adding a marker-to-design table would substantially improve readability.","section":"Fig. 2"},{"comment":"Several key references are the authors' own unpublished or under-review works, patents, or workshop papers (e.g., [11], [26], [29], [31], [34]); no code or data availability statement is provided, which limits reproducibility.","section":"References and reproducibility"},{"comment":"The 'SOTA HDCs accuracy' comparisons in Table III are reported at different dimensions (D=2K versus D=10K) and with different retraining conditions (w/ versus w/o retraining); the table should state these conditions explicitly so that the comparison is not misleading.","section":"Table III"},{"comment":"The phrase 'improves the accuracy and reduces energy consumption by up to 77% and 92%, respectively' is ambiguous; the accuracy improvement should be reported as an MSE reduction (from 2.256e-4 to 0.523e-4) rather than a percentage, which may be confused with classification accuracy.","section":"Section IV"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reads as a consolidation of the authors' prior publications, and the central design properties are credited to self-citations [13], [24]–[35] rather than derived or demonstrated here. This raises a novelty and circularity concern that the editor may wish to weigh: if the journal accepts consolidation papers, the authors should state explicitly what is new in this submission; otherwise, the overlap with prior work is substantial. The unsupported energy claim and the missing ablation are fixable in revision, but they require genuine additional experiments, not just rewriting."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a compact summary of the authors' own prior papers on VDC-2^n low-discrepancy sequence encoding for stochastic and hyperdimensional computing. The four bullet contributions in the conclusion are already reported in [24], [25], [30], [33], [35], and [43]. There is no new derivation, no new experiment, and no new hardware result in this manuscript. If all you need is a doorway into that body of work, it does that job; as a research contribution it doesn't.\n\nWhat the paper does well: the VDC-2^n generator is a genuinely cute hardware trick—a hardwired counter produces a deterministic low-discrepancy sequence with nearly uniform coverage, and the sin(x) results show ~4x lower MSE than the LFSR baseline (0.523e-4 vs 2.256e-4). The background section gives a clear, accurate intuition for why low-discrepancy sequences reduce correlation problems in cascaded SC circuits. The unary level-HV generator idea in Fig. 2(b)➑ is also worth knowing about.\n\nWhere it falls down. First, the paper's central causal claim in HDC—that VDC-2^n sequences themselves improve accuracy—is not established. The proposed design ➏ differs from baseline in two ways: it swaps the RNG source and it drops position hypervectors entirely. The table shows the combined effect only. No ablation separates the two, and the paper merely cites the authors' own prior work for the claim that the generated HVs are orthogonal. That is a load-bearing missing piece. Second, almost all numbers are single point estimates with no error bars or methodology. The LFSR baseline is stochastic and seed-sensitive; reporting one run is not enough to measure a 6-point accuracy jump. Third, the 'up to 92% energy reduction' in Section IV isn't supported by Table II, which shows about 61% for the sin(x) case. Fourth, the abstract and conclusion overstate novelty: this is not a new encoding strategy, it's a re-packaging of previously published results.\n\nWho is this for? A reader who wants a short survey of the authors' VDC-2^n work, with references to the originals, will find it useful. A referee for a research venue should not be asked to evaluate it as new work; it would need extensive revisions to become an honest survey, or the authors would need to add the missing ablation and variance analysis to make it a research paper. Recommendation: desk reject as a research submission, or require resubmission as a tutorial. The underlying prior work is worth citing on its own.","headline":"A compact summary of the authors' own VDC-2^n encoding work, presented as new contributions; the HDC accuracy gain is confounded with dropping position hypervectors.","tokens_in":11028,"tokens_out":3381,"would_cite":false,"duration_ms":33229,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Hardwired Van der Corput low-discrepancy sequences replace pseudo-random sources in stochastic and hyperdimensional computing, delivering higher accuracy and lower power.","keywords":["stochastic computing","hyperdimensional computing","Van der Corput sequences","low-discrepancy sequences","data encoding","pseudo-randomness","quasi-randomness","unary computing"],"falsifier":"Run the position-free HDC encoder on an image dataset with strong spatial semantics, such as CIFAR-10, and compare against the same encoder with position hypervectors included; if removing position hypervectors drops test accuracy by more than the small margin reported in the paper's MNIST results, the claim that deterministic encoding eliminates the need for position hypervectors is falsified.","tokens_in":10089,"feed_emoji":"🔢","tokens_out":6922,"duration_ms":59471,"temperature":0.7,"pith_summary":"Stochastic computing and hyperdimensional computing both represent data as long streams of bits, and both usually rely on pseudo-random number generators (typically LFSRs) to produce those streams. This paper claims that a deterministic class of low-discrepancy sequences—Van der Corput sequences with powers-of-two bases (VDC-2^n)—produces better streams: more uniform value coverage and weaker correlation between streams, with a hardware cost of just a hardwired binary counter. The paper reports concrete gains across both paradigms: a sine function in stochastic computing drops mean squared error from 2.256e-4 to 0.523e-4, a hyperdimensional MNIST classifier rises from 81.29% to 87.12% average accuracy at dimension 2K, and an end-to-end unary hypervector generator cuts power by 98%. These results matter because randomness is the main source of error and hardware overhead in both SC and HDC, so replacing it with a simple deterministic generator could make these AI paradigms practical on edge devices.","feed_headline":"Van der Corput counters beat LFSR randomness in AI chips","feed_subtitle":"A hardwired counter replaces pseudo-random generators, cutting error and power in stochastic and hyperdimensional computing.","key_machinery":"The central object is the Van der Corput sequence with base a power of two, written VDC-2^n. The nth term is obtained by writing the integer index in binary (or more generally in base 2^n), reversing its digits, and interpreting the reversed digits as a fraction in [0,1). Because the base is a power of two, the sequence is produced with no arithmetic at all: an ordinary n-bit up-counter (T flip-flops) outputs the sequence when the flip-flop outputs are taken in reverse weight order, and different rewiring schemes yield distinct sequences simultaneously. The low-discrepancy property—points spread evenly rather than clustering—is what does the work: it gives each bitstream a uniform distribution of values and keeps different streams weakly correlated, which is exactly what SC multiplication and HDC orthogonality require. For the HDC encoder, the sequence is quantized and binarized to form hypervectors directly, and a single D-sized sequence is reused with different starting offsets to produce all m hypervectors, removing the need for m independent random generators.","core_discovery":"The central claim is that VDC-2^n sequences—generated by reversing the base-2^n digits of consecutive integers, which in hardware amounts to rewiring the output bits of an n-bit binary counter—can serve as the randomness source for encoding both stochastic bitstreams and hypervectors. In stochastic computing, using VDC-2^n instead of LFSR-generated pseudo-random bits for the sin(x) design lowers the mean squared error from 2.256e-4 to 0.523e-4 while cutting area and energy (Tables I and II). In hyperdimensional computing, generating hypervectors from deterministic low-discrepancy sequences yields 87.12% accuracy on MNIST at D=2K versus an 81.29% average for the LFSR baseline, and because the sequences are naturally well-distributed, the encoding no longer needs orthogonal position hypervectors or the multiplication step that binds them (Fig. 2(b)). The paper also introduces an end-to-end unary design in which level hypervectors are generated deterministically from unary bitstreams rather than randomized, eliminating the traditional random level hypervectors and reducing generator power by 98% while improving learning dynamics on DermaMNIST.","pith_inferences":["A natural next test is whether VDC-2^n also beats other low-discrepancy sources like Sobol or Halton under the same HDC settings, since those are also deterministic but require more hardware; if it does, the specific structural simplicity of VDC-2^n, not just any low-discrepancy property, is the key virtue.","Because the generator is deterministic and seed-free, SC and HDC results become exactly repeatable across runs and chips, which could ease verification and make numerical results in these paradigms more trustworthy than the averaged-over-seeds numbers common in the literature.","The approach may extend to other probabilistic computing schemes such as Bayesian neural networks or in-memory computing, where replacing random sources with hardwired low-discrepancy sequences could offer similar gains—though the paper does not test those settings."],"forward_implications":["If the deterministic encoding holds up beyond the reported benchmarks, stochastic circuits for functions like sin(x), division, and other nonlinear blocks can be built with lower error and smaller area, making SC competitive for approximate AI and signal processing on chips where LFSRs were the bottleneck.","Hyperdimensional encoders can drop position hypervectors and the binding multiplication entirely, simplifying the memory hierarchy and reducing latency for image classification and other structured-data tasks.","The single-source dynamic unary generator enables online or continuous learning of new classes, since hypervectors can be generated on the fly at negligible power.","A unified VDC-2^n generator block could serve both SC and HDC modules in a single chip, replacing separate RNGs and cutting design and verification cost."],"supporting_citations":[{"why":"Prior paper introducing Van der Corput sequences as the source for stochastic computing bitstreams; the paper builds directly on this.","marker":"[13]"},{"why":"Defines the P2LSG powers-of-2 low-discrepancy sequence generator, the hardware implementation the proposed approach relies on.","marker":"[24]"},{"why":"Supplies the TriSC design for trigonometric functions that the paper adapts for its sin(x) stochastic implementation.","marker":"[25]"},{"why":"Shows deterministic hypervector encoding without multiplication, the basis for removing position hypervectors in the HDC encoder.","marker":"[30]"},{"why":"Introduces UnaryHD, the unary processing approach applied to HDC that the paper extends into the end-to-end unary design.","marker":"[33]"},{"why":"Describes the end-to-end unary bit-stream processing architecture whose single-source HV generator yields the reported 98% power reduction.","marker":"[35]"},{"why":"Provides the LFSR-based stochastic computing design for sin(x) that serves as the accuracy and hardware baseline.","marker":"[1]"},{"why":"Shows parallel Sobol sequences as a deterministic alternative in SC, setting the context that low-discrepancy sequences improve over pseudo-random sources.","marker":"[16]"}],"fun_headline_variants":["Deterministic counters beat random bits in stochastic and hyperdimensional AI","Van der Corput counters slash error and power in AI encoding","Counter-based randomness improves stochastic and hyperdimensional accuracy","Hardwired counters replace LFSR for efficient AI encoding"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that hardwired VDC-2^n sequences, which are deterministic and periodic, produce bitstreams and hypervectors that are sufficiently uncorrelated and uniform for all input values in a single run, and that position hypervectors can be dropped from HDC encoding without hurting accuracy.","fun_headline_variants_meta":{"raw":{"variants":["Deterministic counters beat random bits in stochastic and hyperdimensional AI","Van der Corput counters slash error and power in AI encoding","Counter-based randomness improves stochastic and hyperdimensional accuracy","Hardwired counters replace LFSR for efficient AI encoding"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000606,"raw_usage":{"total_tokens":2821,"prompt_tokens":939,"completion_tokens":1882,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":555,"completion_tokens_details":{"reasoning_tokens":1825}},"tokens_in":555,"tokens_out":1882,"duration_ms":12546,"temperature":1.0,"reasoning_tokens":1825,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:07:08.306154+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the position-free HDC encoder on an image dataset with strong spatial semantics, such as CIFAR-10, and compare against the same encoder with position hypervectors included; if removing position hypervectors drops test accuracy by more than the small margin reported in the paper's MNIST results, the claim that deterministic encoding eliminates the need for position hypervectors is falsified.","supporting_citations":[{"cited_title":"Accurate and energy-efficient stochastic computing with Van Der Corput sequences,","cited_arxiv_id":null,"evidence_quote":"Prior paper introducing Van der Corput sequences as the source for stochastic computing bitstreams; the paper builds directly on this."},{"cited_title":"P2LSG: Powers-of-2 low-discrepancy sequence generator for stochastic comput- ing,","cited_arxiv_id":null,"evidence_quote":"Defines the P2LSG powers-of-2 low-discrepancy sequence generator, the hardware implementation the proposed approach relies on."},{"cited_title":"Late breaking results: TriSC: Low-cost design of trigonometric functions with quasi stochastic computing,","cited_arxiv_id":null,"evidence_quote":"Supplies the TriSC design for trigonometric functions that the paper adapts for its sin(x) stochastic implementation."},{"cited_title":"No-multiplication deter- ministic hyperdimensional encoding for resource-constrained devices,","cited_arxiv_id":null,"evidence_quote":"Shows deterministic hypervector encoding without multiplication, the basis for removing position hypervectors in the HDC encoder."},{"cited_title":"uHD: Unary processing for lightweight and dynamic hyperdimensional computing,","cited_arxiv_id":null,"evidence_quote":"Introduces UnaryHD, the unary processing approach applied to HDC that the paper extends into the end-to-end unary design."},{"cited_title":"All you need is unary: End-to-end unary bit-stream processing in hyperdimen- sional computing,","cited_arxiv_id":null,"evidence_quote":"Describes the end-to-end unary bit-stream processing architecture whose single-source HV generator yields the reported 98% power reduction."},{"cited_title":"Computing arithmetic functions using stochastic logic by series expansion,","cited_arxiv_id":null,"evidence_quote":"Provides the LFSR-based stochastic computing design for sin(x) that serves as the accuracy and hardware baseline."},{"cited_title":"Toward energy-efficient stochastic circuits using parallel sobol sequences,","cited_arxiv_id":null,"evidence_quote":"Shows parallel Sobol sequences as a deterministic alternative in SC, setting the context that low-discrepancy sequences improve over pseudo-random sources."}],"review_version":1}