{"id":"ea82ba80-7f3f-42b4-bfdb-da269359fba9","arxiv_id":"2501.13230","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Treating state-space layers as tensor networks with CNN-style connectivity and optimized contraction orders yields hybrid SSM networks that outperform homogeneous SSMs on raw audio tasks and enable competitive streaming ASR without attention.","lead":"This paper introduces Centaurus, a family of state-space models whose blocks mimic classical convolutional designs (depthwise, full, grouped, bottleneck) and are trained via optimized tensor contractions. The hybrid networks beat their uniform counterparts on keyword spotting, denoising, and speech recognition, and give a fully state-space ASR system that is competitive with streaming attention-based models.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The abstract's 'first fully state-space ASR' claim is contradicted by Table 2: competitive WERs come only from variants with explicit Conv1d (causal conv-block, Mamba macro-block), while the pure Centaurus SSM base is not competitive.","rationale":"The reader's formal weakest_assumption was fairness of efficiency comparisons (Appendix D estimates, under-tuned baselines). My stress-test identifies a different but equally load-bearing gap: the abstract's ASR 'first fully state-space' claim is internally inconsistent with Table 2. The reader's rationale did note that 'the ASR headline claim is overstated relative to the paper's own data,' so there is partial agreement, but the reader did not place this as the primary weakest assumption. The concern does not invalidate the tensor-contraction contribution or the KWS/denoising experiments; it requires a softened or precisely qualified claim and a clear separation of pure-SSM from hybrid results. Since the reader's verdict was already CONDITIONAL to address exactly these kinds of overstatements, my stress-test does not move the verdict.","tokens_in":23789,"tokens_out":5714,"duration_ms":56633,"concrete_test":"From the released code, annotate each Table 2 row with whether the module stack contains any Conv1d/Conv2d layer (including the causal depthwise Conv1d inside the Mamba macro-block) or any attention/linear-attention layer. Then compute the best WER among rows with no such layers (expected: Base or 'with FFN'). If that best WER is more than 10% relative worse than the streaming Conformer test-clean WER of 4.6, the abstract's 'competitive' and 'first' claims are not supported by the paper's own experiments.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline claim (Abstract) is that Centaurus is 'the first network with competitive performance that can be made fully state-space based, without using any nonlinear recurrence (LSTMs), explicit convolutions (CNNs), or (surrogate) attention mechanism.' Table 2 does not support this. The base Centaurus (full SSM) row reports WER 6.0/13.1 on test/dev, while the streaming Conformer baselines are 4.6/9.9 and 4.5/10.0; the base is not competitive. The two rows that approach or beat the Conformer numbers, 'with Mamba macro-block' (4.4/10.2) and 'with causal conv-block' (4.8/10.6), both include explicit convolutions: the causal conv-block is a Conv1d module, and Appendix D states that the Mamba block contains 'a lightweight causal depthwise Conv1D layer.' Hence the competitive results violate the 'without explicit convolutions' condition. The only variant that avoids both conv and attention is 'with FFN' (5.4/11.5), which is roughly 17% relative worse than streaming Conformer on test-clean and still worse than ContextNet/Conformer; whether this is 'competitive' is a stretch, and it is not the configuration highlighted in the claim. Additionally, the 'first' claim is undercut by Mamba itself being a state-space network and by the paper's own references to concurrent SSM-based speech systems (Section 5.2). The central claim is therefore internally inconsistent with the paper's data; either 'competitive' must be defined quantitatively and shown for a variant with no Conv1d, or the claim must be restricted to the hybrid (SSM+conv) setting or to 'competitive among pure linear SSMs.'","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Centaurus, a class of state-space models in which SSM operations are expressed as tensor contractions in the frequency domain and the contraction order is optimized per block. It generalizes the connective structure of SSM blocks from the usual depthwise-separable form to full, grouped, and bottleneck configurations inspired by classical CNN designs. The authors report experiments on keyword spotting (SC35/SC10), speech enhancement (VB-DMD), and LibriSpeech ASR, claiming that a heterogeneous Centaurus network outperforms homogeneous SSM baselines and that, for ASR, it is the first network with competitive performance that is fully state-space based without explicit convolutions or attention.","tokens_in":24139,"tokens_out":4012,"duration_ms":38137,"significance":"The tensor-contraction formulation of SSM blocks and the formal derivation of feasible contraction orders (Lemma 1 and Appendix B) are clean, self-contained, and potentially useful for practitioners seeking to speed up SSM training. The hybrid block design is a reasonable exploration of architectural diversity beyond the standard depthwise-separable SSM. However, the paper's headline empirical claim for ASR is not supported by its own Table 2, and the efficiency comparisons against baseline SSMs rely on author-estimated FLOPs and possibly undertuned baselines. If the contraction-order analysis is correct and the block designs are adopted, the work could have practical value, but the current presentation overstates the empirical results.","major_comments":[{"comment":"The abstract's claim that Centaurus is \"the first network with competitive performance that can be made fully state-space based, without using any nonlinear recurrence (LSTMs), explicit convolutions (CNNs), or (surrogate) attention mechanism\" is contradicted by the data in Table 2. The base (full SSM) Centaurus achieves 6.0/13.1 WER on test/dev, while the streaming Conformer baseline is 4.6/9.9 and ContextNet is 4.5/10.0. The two variants that approach or beat these baselines, \"with causal conv-block\" (4.8/10.6) and \"with Mamba macro-block\" (4.4/10.2), both include a causal depthwise Conv1D layer, as described in Appendix E.3 and Appendix D, so they violate the \"without explicit convolutions\" condition. The only variant without an explicit convolution, \"with FFN\" (5.4/11.5), is roughly 17% relative worse than streaming Conformer on test-clean and still worse than the other streaming baselines. The claim therefore requires either a competitive configuration that is truly free of convolution and attention, or a quantitative definition of \"competitive\" that makes the FFN variant acceptable.","section":"Abstract and Section 5.3, Table 2"},{"comment":"The efficiency comparison against baseline SSMs is not on equal footing. The FLOPs and parameter counts for S4, S4D, S5, S6, and Mamba are estimated using the authors' own rules described in Appendix D, and the entries in Table 5 are marked with asterisks, while the Centaurus numbers are computed for the actual architecture. In Section 5.2, the homogeneous DWS and bottleneck variants \"suffered from severe training plateaus\" and produced no usable audio, and the paper reports unstable training for Mamba-based variants in the ASR experiments. If the baselines are undertuned or the FLOP estimates are inconsistent with standard implementations, the \"orders of magnitude fewer FLOPs\" claim (Section 5.1) and the PESQ/FLOP advantage in Table 1 would not hold. Please provide measured training/inference times or standard-library FLOP counts for the baselines, or state clearly the assumptions and justify them.","section":"Appendix D and Section 5.2 (Tables 1 and 5)"}],"minor_comments":[{"comment":"In the second branch of opt_fft_conv (lines 38-39), the variable `x` is used before it is defined; it should be `u`.","section":"Listing 1 in Appendix C"},{"comment":"The inequality `1/B + 1/N > 1/H + 1/H'` is stated without an equation number; please number it and explicitly define B as the batch size.","section":"Section 4.3"},{"comment":"Several offline rows (Full Conv, Transformer, Wav2Vec2) do not report parameter counts or FLOPs; please fill these entries or state why they are omitted.","section":"Table 2"},{"comment":"The tensor network diagrams are difficult to read at the printed size; consider increasing the font size and edge labeling.","section":"Figure 1"},{"comment":"The word \"Surprisingly\" is subjective; consider rephrasing to a neutral statement about the observed training plateaus.","section":"Section 5.2"}],"recommendation":"major_revision","confidential_remarks":"The technical core—the contraction-order analysis and the new SSM block designs—is sound and could be a useful contribution if the empirical framing is corrected. The ASR claim in the abstract and Section 5.3 is the main obstacle; it is internally inconsistent with the reported results. The efficiency comparisons also need better justification. I would encourage the editor to request a revised version that either provides a competitive convolution-free ASR configuration or substantially softens the claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the core algorithmic idea is real and useful: expressing SSM operations as tensor contractions, designing full/grouped/bottleneck SSM blocks, and systematically choosing contraction order with FFT placement is a fresh, clearly explained contribution. Second, the ASR headline oversells the results; the stress-test note is correct.\n\nThe derivation of feasible contraction orders (Lemma 1 and Appendix B) is clean and self-contained, and the FLOP-based analysis is parameter-free rather than fitted. On keyword spotting, the hybrid Centaurus network scales better than homogeneous variants and matches S4/S5 with far fewer FLOPs. On denoising, the hybrid gets competitive PESQ (3.12) with 0.51M parameters and 0.29G FLOPs/s, and adding a causal conv pushes it to 3.25. Code is provided.\n\nThe soft spot is the abstract's claim that Centaurus is \"the first network with competitive performance that can be made fully state-space based, without using any explicit convolutions.\" Table 2 does not support that. The base full-SSM model gets 6.0/13.1 WER versus streaming Conformer's 4.6/9.9; it is not competitive. The two rows that approach or beat Conformer—\"with causal conv-block\" (4.8/10.6) and \"with Mamba macro-block\" (4.4/10.2)—both include explicit Conv1d layers, as the paper's own Appendix D states. The only variant without conv or attention, \"with FFN\" (5.4/11.5), is roughly 17% relatively worse than streaming Conformer. So \"competitive\" is doing a lot of work, and the \"first\" claim is also undercut by the existence of Mamba as a state-space network.\n\nThe efficiency comparisons also lean on estimated FLOPs for baselines (S4, S4D, S5, S6, Mamba) using the author's own rules in Appendix D, with several homogeneous variants suffering training plateaus; those baselines may be under-tuned, and no error bars are reported for the main WER/PESQ numbers. These are fixable. The algorithmic contribution stands; the claims need softening or a quantitative definition of \"competitive\" applied to a genuinely conv-free variant.\n\nThis paper deserves a serious referee and conditional acceptance. I'd bring it to a reading group to discuss the tensor-contraction technique and the overclaim, and I'd cite the contraction-order work in my own research.","headline":"Solid tensor-contraction framework for SSMs, but the 'first fully state-space ASR' claim is contradicted by the paper's own Table 2.","tokens_in":24707,"tokens_out":1845,"would_cite":true,"duration_ms":17991,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"SSM layers are tensor contractions; choosing each block's contraction order unlocks CNN-style connector blocks and a hybrid network that beats uniform SSM stacks on keyword spotting, denoising, and streaming ASR.","keywords":["state-space models","tensor networks","einsum contraction order","FFT convolution","heterogeneous network design","keyword spotting","speech enhancement","automatic speech recognition"],"falsifier":"Run the Table 5 and Table 1 comparisons at the same configurations using standard released implementations of the S4, S4D, S5, and Mamba baselines and a general-purpose FLOP profiler instead of the paper's estimation rules: if a canonical depthwise-separable network matches the hybrid's accuracy on Speech Commands at comparable measured cost, the efficiency claim fails. A complementary check: train the homogeneous depthwise denoising variant with the hybrid's exact width schedule, optimizer, and data pipeline — if it escapes the reported plateau and approaches PESQ 3.12, the claim that heterogeneity is what makes the hybrid train would be falsified.","tokens_in":23512,"feed_emoji":"🎙️","tokens_out":21858,"duration_ms":198308,"temperature":0.7,"pith_summary":"Centaurus is the claim that state-space model (SSM) layers can be designed and trained the way convolutional networks are: each layer is a tensor contraction whose connective pattern — depthwise, grouped, full, or bottleneck — is a free architectural choice, and whose contraction order is chosen per layer for efficiency. In the frequency domain an SSM layer's long convolution becomes an einsum expression, so training cost is whatever the cheapest valid contraction path costs; the paper proves which paths stay feasible for the bottleneck block and derives the exact dimension condition for choosing between the two efficient ones. The payoff is heterogeneity: dense full SSM blocks in shallow layers, sparse bottleneck blocks where channels are large, following classical CNN scaling rules. The paper reports that this hybrid beats every homogeneous SSM variant on Speech Commands keyword spotting, achieves competitive PESQ scores on speech denoising at a fraction of the size of heavier real-time systems, and reaches competitive word error rates on LibriSpeech streaming ASR with a fully state-space stack that uses no nonlinear recurrence, explicit convolution, or attention. If the paper is right, SSM network design gains the per-layer freedom that made CNNs flexible, at a fraction of the usual inference cost.","feed_headline":"State-space blocks redesigned as ConvNets cut speech FLOPs ~100x","feed_subtitle":"A hybrid of dense and bottleneck state-space blocks beats uniform SSM stacks on keyword spotting, denoising, and streaming ASR.","key_machinery":"The carrying object is the frequency-domain einsum expression of an SSM block, treated as a tensor network in which the DFT operator is itself a contractable operand; this makes FFT placement part of the contraction-path optimization, justified by the linearity identity $F(E\\cdot K)=E\\cdot F(K)$. Lemma 1 does the heavy lifting: for the bottleneck block $\\hat{y}_{bif}=\\hat{u}_{bif}B_{ni}\\hat{k}_{nf}C_{jn}$, all intermediate tensors stay at most three-dimensional if and only if the input is contracted only with its neighbours, which leaves exactly two feasible contraction patterns whose relative cost is settled by the inequality $\\frac{1}{B}+\\frac{1}{N} > \\frac{1}{H}+\\frac{1}{H'}$, with an additional shape check deciding whether to Fourier-transform the projected input or the built kernel. The block family — depthwise, depthwise-separable, grouped, full, and (pointwise) bottleneck — is read directly off the tensor-network index pattern, mirroring classical CNN blocks, and the hybrid architecture orders them by the classical rule of dense connectivity in shallow layers and sparser connectivity deeper.","core_discovery":"The central claim is that an SSM layer, written in the frequency domain, is a tensor network — an einsum expression such as $\\hat{y}_{bif} = \\hat{u}_{bif}B_{ni}\\hat{K}_{nmf}E_{nm}C_{jn}$, where $\\hat{u}$ is the input, $\\hat{K}_{nmf}$ are basis kernels generated by the state matrix $A$, $E_{nm}$ weights the oscillation modes, and $B_{ni}$ and $C_{jn}$ project channels — so its computational cost is determined by the order in which the tensors are contracted. Standard depthwise-separable SSM blocks (one state evolution per input channel, as in the S4 and Mamba families) are a single point of this design space, and group, full, and bottleneck connectivities are natural alternatives read off the index pattern. The technical core is that because the Fourier transform is linear, $F(E\\cdot K)=E\\cdot F(K)$, the FFT itself can be moved around like an operand; Lemma 1 then restricts the bottleneck block to exactly two feasible contraction patterns — project-convolve-project, or build the full kernel and convolve once — when no intermediate tensor may exceed three dimensions, with the cheaper pattern selected by the inequality $\\frac{1}{B}+\\frac{1}{N} > \\frac{1}{H}+\\frac{1}{H'}$. Using these blocks, the paper builds the hybrid Centaurus network and reports that it outperforms its homogeneous counterparts on keyword spotting, speech denoising, and end-to-end streaming ASR, claiming it as the first competitive ASR network that is fully state-space based, with no nonlinear recurrence, no explicit convolution, and no (surrogate) attention.","pith_inferences":["If the contraction machinery is as general as the paper argues, the same block family and path-selection rule should transfer to 2D SSMs, strided or dilated variants, and vision tasks — an extension the paper names but does not test, which would turn the block family into a general-purpose sequence and image toolkit.","The failure of homogeneous depthwise and bottleneck blocks to train on raw-waveform denoising suggests per-channel independent state evolution is a poor inductive bias for that task and that heterogeneity acts as structured capacity allocation; this is testable by training the depthwise variant with the hybrid's channel schedule and optimization recipe.","Combining Centaurus blocks with data-gating (input-dependent $A$, $B$, $C$, as in selective-scan models) is the paper's stated open direction; if the contraction machinery can absorb the extra sequence dimension that data-dependence introduces, the training-speed and expressivity gains would compound and could plausibly extend the approach to language modeling."],"forward_implications":["The depthwise-separable template is not intrinsic to SSMs: group, full, and bottleneck connectivities are direct generalizations, so classical CNN design rules (dense early, sparse deep) transfer to state-space architectures.","Training any SSM block type, including existing S4D/S5-style ones, can be accelerated by systematically choosing contraction order and FFT placement; the bottleneck block's training time is shown to scale smoothly with batch, state count, and sequence length under the optimized path.","On Speech Commands the hybrid reaches 98.53% accuracy on the 10-class set with roughly a hundred times fewer inference FLOPs than the reported S4/S4D/S5 baselines, and its scaling curves beat every homogeneous variant on the 35-class set.","On VB-DMD speech enhancement the hybrid scores PESQ 3.12 with 0.51M parameters and 0.29 GFLOPs per second, rising to 3.25 when a small causal Conv1d is prepended to each block — above every listed real-time baseline — while the homogeneous depthwise and bottleneck variants plateau and fail to train.","On LibriSpeech streaming ASR the fully state-space base reaches 6.0/13.1 test WER, improving to 4.4/10.2 with a Mamba-style gated macro-block, staying competitive with streaming ASR systems built with convolutions or attention while using no attention and no explicit convolution."],"supporting_citations":[{"why":"Defines the structured state-space layer whose depthwise-separable configuration is the baseline that Centaurus generalizes.","marker":"Gu et al., 2021"},{"why":"Supplies the diagonal-state parameterization, zero-order-hold discretization, and the S4D initialization used by every Centaurus block.","marker":"Gu et al., 2022"},{"why":"Introduces the MIMO SSM with B and C projection matrices that becomes the pointwise-bottleneck (S5-like) block template.","marker":"Smith et al., 2022"},{"why":"Provides the data-gated S6 baseline and the gated macro-block used in the ASR variant, along with the data-gating direction left open.","marker":"Gu & Dao, 2023"},{"why":"Supplies the tensor-network contraction-order viewpoint (memory and compute as a graph problem) that motivates the training-time optimization.","marker":"Gray & Kourtis, 2021"},{"why":"Provides the systematic cost evaluation of einsum contraction paths that the paper augments with FFT-operator placement.","marker":"Daniel et al., 2018"},{"why":"Supplies the depthwise-separable convolutional template and the lightweight-network design philosophy reused in Appendix D.","marker":"Howard et al., 2017"},{"why":"Supplies the bottleneck-block and residual-connection templates used in the Centaurus block design.","marker":"He et al., 2016"},{"why":"Supplies the scaling rule of increasing connective sparsity with depth that shapes the hybrid architecture.","marker":"Tan & Le, 2021"}],"fun_headline_variants":["SSMs as tensor nets: hybrid blocks beat uniform stacks on speech","First fully state-space ASR: no CNN, LSTM, or attention","Optimal tensor contractions turn SSMs into ConvNet-like blocks","Hybrid SSM blocks beat homogeneous ones on speech tasks","Centaurus: state-space blocks optimized as tensor contractions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the efficiency comparisons are fair: the baseline SSMs are counted with the paper's own estimation rules rather than measured, and some homogeneous variants were effectively tuned out of contention by training plateaus, so inflated baseline costs would shrink the reported margins.","fun_headline_variants_meta":{"raw":{"variants":["SSMs as tensor nets: hybrid blocks beat uniform stacks on speech","First fully state-space ASR: no CNN, LSTM, or attention","Optimal tensor contractions turn SSMs into ConvNet-like blocks","Hybrid SSM blocks beat homogeneous ones on speech tasks","Centaurus: state-space blocks optimized as tensor contractions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000957,"raw_usage":{"total_tokens":4168,"prompt_tokens":1125,"completion_tokens":3043,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":741,"completion_tokens_details":{"reasoning_tokens":2956}},"tokens_in":741,"tokens_out":3043,"duration_ms":24426,"temperature":1.0,"reasoning_tokens":2956,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:20:11.120582+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the Table 5 and Table 1 comparisons at the same configurations using standard released implementations of the S4, S4D, S5, and Mamba baselines and a general-purpose FLOP profiler instead of the paper's estimation rules: if a canonical depthwise-separable network matches the hybrid's accuracy on Speech Commands at comparable measured cost, the efficiency claim fails. A complementary check: train the homogeneous depthwise denoising variant with the hybrid's exact width schedule, optimizer, and data pipeline — if it escapes the reported plateau and approaches PESQ 3.12, the claim that heterogeneity is what makes the hybrid train would be falsified.","supporting_citations":[{"cited_title":"language head","cited_arxiv_id":null,"evidence_quote":"Provides the data-gated S6 baseline and the gated macro-block used in the ASR variant, along with the data-gating direction left open."}],"review_version":1}