On Task Scope and Information Retention in Source Coding

Alireza Furutanpey; Kerstin Bunte

cs.ITSep 29, 2026

On Task Scope and Information Retention in Source Coding

Authors: Alireza Furutanpey, Kerstin Bunte

Organizations: NeverBlink, Warszawa, Poland · Rijksuniversiteit Groningen, Groningen, Netherlands

Abstract

We argue that dividing codec design into Coding for Machines (CfM) and Coding for Humans (CfH) is a misleading distinction for deciding what information a codec may discard. Receiver identity does not determine admissible information loss. The required rate depends on task scope, including the predictions to support, their losses and tolerated risks, the encoder observation, and the permitted decoding procedures. Notably, a machine task may have a higher minimum rate than a restricted human decision. Rate savings on selected machine tasks apply only to the stated requirements, not to an intrinsic ordering by receiver type. We extend source and feature coding to finite task families, derive when restricting the encoder observation preserves the minimum rate, and show that equality between source and split-feature coding rates can no longer hold as the task scope expands.

Figures & tables

Figure 1: ImageNet ResNet-50 inversions for Indigo Bunting (top) and Blue Grosbeak (bottom). Boxes mark the wing regions enlarged below. The chestnut patch becomes less visible at later blocks. Species-pair accuracy uses 200-way CUB readers restricted to these species, with 30 test photographs each. Filled points show two fits per observation and open points their means (Appendix B.7 ).

Figure 2: Exact asymptotic rates for two noisy task families. (a) Label noise and original-task error are

0.05

. Minimum additional-task error from

Y

0.20

. At or above this floor, the rates coincide. (b) At noise probabilities

(0.05,0.45)

, both observations have Bayes prediction

Z

and minimum error

0.25

, with different rates at intermediate tolerances. (c) Reversing these probabilities for a complementary task makes the rates equal at

D_{1}=D_{2}=D

, with Bayes tuple

(Z,Z)

. Circles mark

D=0.30

. Single-task curves specialize Martinian et al. (2008) ’s formula. The pair rate is equation 15 .

Figure 3: Finite codes at

0.81251

bits per symbol, below the

0.81876

minimum for satisfying both requirements from

Y

. (a,b) Codes whose encoders observe class and confidence satisfy both requirements. (c) Their errors concentrate in negative-confidence states, where they incur less additional-task loss.

Figure 4: ImageNet accuracy drops from uncompressed references. Rows list fitting losses and complete validation rates. Open and filled markers show validation and selected test means. Small dots show individual fits, and bars show conditional 95% paired-image intervals. Dashed lines mark the allowances.

Figure 5: Test results for validation-selected CIFAR codes and nearby lower-rate feature-preserving candidates. (a,b) Accuracy drops from uncompressed references, with dashed allowance lines. (c) Fine readouts applied to each unchanged logit-preserving message. In (a,b), diamonds show means over paired codec fits, hollow circles show individual runs, and bars show conditional 95% paired-image intervals.

Figure 6: Normalized Taskonomy test risks for twelve codecs. Filled symbols show risks with matched task decoders. Arrows connect risks to those obtained from the same RGB-preserving message by reconstructing RGB and applying frozen reference predictors (hollow symbols). The latent edge decoder is unchanged. Dashed lines mark tolerated risks, and bars show conditional 95% image-bootstrap intervals.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Finite-code sensitivity. Filled circles show three fits per condition and hollow diamonds the unrestricted asymptotic rates. (a) Single-task rate above its asymptotic minimum at lengths 12 and 16. (b) Length-16 rates as the second-task limit varies, with the first fixed at

0.30

. (c) Three-state families at length 16. Horizontal offsets separate fits. We compute rates from index, header and padding bits.

Figure 8: CIFAR validation candidates by teacher. Dashed lines mark the coarse and fine allowances. Open circles show codec fits, diamonds paired means, and stars the six selections. Single-fit controls have no paired mean. Fine accuracies average two refitted tensor readouts.

			Fine, early tensor		Fine, logits
Split	Teacher	Coarse	Mean	Range	Mean	Range
Validation	A	85.68	63.370	[63.36, 63.38]	45.970	[45.84, 46.10]
	B	85.86	62.810	[62.40, 63.22]	46.410	[46.38, 46.44]
	C	86.16	62.430	[62.30, 62.56]	45.390	[45.38, 45.40]
Test	A	85.38	62.615	[62.43, 62.80]	44.485	[44.28, 44.69]
	B	85.27	62.480	[62.46, 62.50]	45.060	[44.65, 45.47]

Appendix

Table 1: Uncompressed CIFAR-100 reference accuracies (%). Fine-readout means and ranges summarize two fits. We use the early-tensor mean as the fine-accuracy reference.

Family	Multiplier	Rate	Depth	Semantics	Edges	Object	Depth
		(bpp)	$L_{D}$	$L_{S}$	$L_{E}$	mIoU	RMSE (m)
D	0.3	0.07096	0.07669	0.84068	0.02827	0.0444	1.251
	3	0.01752	0.07551	0.92659	0.03642	0.0284	1.223
	30	0.00718	0.08833	1.03715	0.04183	0.0082	1.350
DS	0.3	0.12416	0.07607	0.66453	0.02421	0.1303	1.228
	3	0.03346	0.07688	0.66444	0.03263	0.1345	1.257

Appendix

Table 2: Complete Taskonomy test pool with task decoders selected on validation. We compute rates from complete message lengths and exclude background from object mIoU. Depth RMSE is in metres.

Metric	$D,30$	$DS,3$	$DE,3$
Rate (bpp)	0.00725 [0.00718, 0.00736]	0.03199 [0.03077, 0.03346]	0.02808 [0.02429, 0.03142]
Depth $L_{D}$	0.08963 [0.08833, 0.09099]	0.07598 [0.07543, 0.07688]	0.07706 [0.07675, 0.07740]
Semantics $L_{S}$	1.05059 [1.03715, 1.05881]	0.64969 [0.63882, 0.66444]	0.88166 [0.87632, 0.88692]
Edges $L_{E}$	0.04171 [0.04155, 0.04183]	0.03232 [0.03180, 0.03263]	0.01054 [0.00758, 0.01439]
Object mIoU	0.00864 [0.00819, 0.00917]	0.13315 [0.12376, 0.14116]	0.03844 [0.03589, 0.04273]
Depth RMSE (m)	1.355 [1.350, 1.364]	1.255 [1.251, 1.257]	1.271 [1.260, 1.282]

Appendix

Table 3: Taskonomy test means [ranges] over three fits with available-decoder selection. All fits satisfy the moderate depth requirement. The last row counts fits satisfying moderate

DS

DE

, and

DSE

requirements.

	Required	Single	Validation			Mixture test
$\alpha$	tasks	code	Single rate	Mixture rate	Reduction	Rate	Unsatisfied requirement
0.10	$DS$	$DS,3$	0.03376	0.03123	7.50%	0.03095	None
	$DE$	$DE,1$	0.06241	0.03791	39.26%	0.03837	Edge
	$DSE$	$DSE,1$	0.09171	0.04897	46.60%	0.04991	Edge
0.25	$DS$	$DS,3$	0.03376	0.02459	27.18%	0.02436	None
	$DE$	$DE,3$	0.03123	0.02692	13.81%	0.02706	Edge

Appendix

Table 4: Validation-selected codes and image-independent mixtures. We count all transmitted bits. We select

D,30

for depth only at every tolerance. Its test risk exceeds only the stringent tolerance.

Figure 9: Semantic and edge predictions from five decoded validation images. RGB references and class colors are identical across methods. Gray target pixels are excluded from loss. Edge intensity scale is $[0,1]$ .

Observation	Block 13	Block 14	Block 15	Block 16
Native feature, fit 1	96.7	95.0	93.3	93.3
Native feature, fit 2	96.7	96.7	93.3	93.3
Reconstructed RGB, fit 1	91.7	86.7	88.3	83.3
Reconstructed RGB, fit 2	88.3	85.0	86.7	81.7

Appendix

Table 5: Species-pair accuracy (%) for each of the two fitted readers.

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A declared task can sometimes certify a reduced source before a downstream encoder, codebook, rate, distortion target, or optimizer is chosen. This paper studies when one such reduction preserves the complete downstream problem family, a property termed Task-Sufficient Contraction. The reduced source is fixed by the task before the later operating point is selected. An exact contraction allows the later problem to be solved on that source with the same result as if the full source had been retained. For a machine with a fixed set of possible actions and a fixed loss, the paper identifies a consumer-specific source by merging states only when every available action has the same regret in both. For finite action sets, replacing the richer source by this reduced source preserves the complete one-step rate-regret curve, even though the reduction is fixed before the distortion target is chosen. A second result gives an exact characterization for quadratic loss on affine feasible-action sets: the canonical reduced source is the projection onto the directions in which feasible actions can differ. Under a fixed energy budget, this becomes centered load, while retaining only the optimal water-filled action is too coarse. Earlier Information Bottleneck, semantic rate-distortion, and goal-oriented quantization results are then used to distinguish exact, architecture-conditioned, approximate, failed, and corrected contractions. The framework suggests a way for heterogeneous machines to exchange what a receiving task needs without first aligning their full internal representations.

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